lecture note for the course - ms.src.ku · differences between these three financial statements?...

759425 Financial Modelling 2/2550 1 Chatuporn Tangkathach

Lecture Note for the course

Prepared by Chatuporn Tangkathach

No matter what your role in a corporation, an understanding of why and how financial decisions are made is essential. The focus of this book is how to make optimal corporate financial decisions.

Jonathan Berk, Peter DeMarzo (Corporate Finance)

Table of Contents

Financial Statements Models page 3 Financial Basis for Valuation: Time Value of Money page 20 Financial Modelling for Project Analysis Net Present Value and Other Investment Rules page 26 Cash Flow and Capital Budgeting page 42 Risk Analysis in Capital Budgeting page 55 Portfolio Models page 58 The Cost of Capital page 72 Firm Valuation: Free Cash Flows Model page 81 Financial Analysis of Leasing page 85 Working Capital Management page 88 International Financial Management page 96


10 Principles that Form the Foundations of Financial Management Principle I: THE RISK-RETURN TRADE-OFF

We won’t take on additional risk unless we expect to be compensated with additional return Principle II: THE TIME VALUE OF MONEY A dollar received today is worth more than a dollar received in the future. Principle III: CASH IS KING

Cash – not profits – is king.

Principle IV: INCREMENTAL CASH FLOWS

Incremental cash flows – It’s only what changes that count. Principle V: THE CURSE OF COMPETITIVE MARKETS

Why it is hard to find exceptionally profitable projects. Principle VI: EFFICIENT CAPITAL MARKETS

The markets are quick and the prices are right. Principle VII: THE AGENCY PROBLEM

Managers won’t work for the owners unless it’s in their best interest. Principle VIII: TAXES BIAS BUSINESS DECISIONS Principle IX: ALL RISK IS NOT EQUAL

Some risk can be diversified away, and some cannot. Principle X: ETHICAL BEHAVIOUR IS DOING THE RIGHT THING

… and Ethical dilemmas are everywhere in finance.


Financial Statement Models

Answer the following questions: 1. What are three most recognised financial statements? What are main

differences between these three financial statements?

2. Name some important accounting principles.

3. What are sources and uses of funds?

4. What is contra account?

5. How many methods are there for deprecating the fixed assets?

6. How many methods are available to take into account the inventory?

7. What is Financial Shenanigan?

8. What are the roles of accountant and auditor?

9. Briefly describe the accounting cycle.

10. What is financial management?


11. How finance is related to other areas of a company?

12. What is the relationship between finance and accounting?

13. Give some examples of financial ethical issues.

14. Why financial accounting is required prior to first finance course?

15. Which skills are intensely required for finance people, how about accountants?

INCOME STATEMENT US Composite Corporation: For Years Ending 31st December (US$ in millions) 2006 2005 Total operating revenues 2,262 2,110 Cost of goods sold 1,655 1,610 Gross profit 607 500 Selling, general and administrative expenses 327 270 Earnings before interest, taxes, depreciation, and amortisation (EBITDA) 280 230 Depreciation expenses 90 85 Amortisation 0 0 Operating profit 190 145 Other income / expense 29 82 Earnings before interest, and taxes (EBIT) 219 227 Interest expense 49 48 Earnings before taxes (EBT) 170 179 Current 71 75 Deferred 13 14 Total taxes 84 89 Net income before preferred dividends 86 90 Preferred stock dividends 4 4 Net income to common equity 82 86 Common stock dividends 39 41 Per share data: Earnings per share (EPS-common) Dividends per share (DPS-common) Price per share 15.25 14.50 Common shares outstanding


BALANCE SHEET US Composite Corporation: at 31st December (US$ in millions) ASSETS 2006 2005 Cash and equivalents 140 107 Accounts receivable 294 270 Inventories 269 280 Other current assets 58 50 Total current assets 761 707 Net property, plant and equipment 873 814 Intangible assets 245 221

Total fixed assets 1,118 1,035 Total assets 1,879 1,742

LIABILITIES AND EQUITY 2006 2005 Accounts payable 213 197 Notes payable 50 53 Accrued expenses 223 205 Total current liabilities 486 455 Deferred taxes 117 104 Long-term debts* 471 458 Total long-term liabilities 588 562 Total liabilities 1,074 1,017 Preferred stock 39 39 Common stock (US$1 par value) 55 32 Capital surplus 347 327 Retained earnings 390 347 Less: Treasury stock 26 20 Total equity 805 725 Total liabilities and equity** 1,879 1,742 *Long-term debt rose by US$13 million: the difference between US$86 million new debt and US$73 million in retirement of old debt. **US Composite reports US$43 million in new equity. The company issued 23 million shares at a price of US$1.87 per share.


Product life cycle versus Cash flows life cycle What are the relationship of income flows and cash flows from operations, investing, and financing at various stages of product life cycle?

Cycle of cash flow patterns

Revenue

Introduction Growth Maturity Decline Net Income + Introduction Growth Maturity Decline – Cash Flows + Introduction Growth Maturity Decline –


FINANCIAL STATEMENT ANALYSIS • Analyse financial status of the company by rearranging information in financial

statements into more meaningful format • Standardised financial statements (Common-size financial statements)

- Common-Size Balance Sheets - Compute all accounts as a percent of total assets

- Common-Size Income Statements - Compute all line items as a percent of sales

- Standardised statements make it easier to compare financial information, particularly as the company grows

- They are also useful for comparing companies of different sizes, particularly within the same industry

Standardised financial statements (Common-size income statement) 2006 2005 Total operating revenues 100.00 Cost of goods sold 76.30 Gross profit 23.70 Selling, general and administrative expenses 12.80 Earnings before interest, taxes, depreciation, and amortisation (EBITDA) 10.90 Depreciation expenses 4.03 Amortisation 0.00 Operating profit 6.87 Other income / expense 3.89 Earnings before interest, and taxes (EBIT) 10.76 Interest expense 2.27 Earnings before taxes (EBT) 8.48 Current 3.55 Deferred 0.66 Total taxes 4.22 Net income before preferred dividends 4.27 Preferred stock dividends 0.19 Net income to common equity 4.08 Common stock dividends 1.94

Trend analysis • Directional analysis of particular items • Ratios also allow for better comparison through time or between companies • As we look at each ratio, ask yourself what the ratio is trying to measure and why is

that information important • Ratios are used both internally and externally


Standardised financial statements (Common-size balance sheet) ASSETS 2006 2005 Cash and equivalents 6.14 Accounts receivable 15.50 Inventories 16.07 Other current assets 2.87 Total current assets 40.59 Net property, plant and equipment 46.73 Intangible assets 12.69

Total fixed assets 59.41 Total assets 100.00

LIABILITIES AND EQUITY 2006 2005 Accounts payable 11.31 Notes payable 3.04 Accrued expenses 11.77 Total current liabilities 26.12 Deferred taxes 5.97 Long-term debts* 26.29 Total long-term liabilities 32.26 Total liabilities 58.38 Preferred stock 2.24 Common stock (US$1 par value) 1.84 Capital surplus 18.77 Retained earnings 19.92 Less: Treasury stock 1.15 Total equity 41.62 Total liabilities and equity** 100.00

Financial Statement Analysis

Trend Target (benchmark) ratios Competitors’ ratios (comparative advantage) Industrial ratios


• 6 set of ratios Liquidity or short-term solvency Efficiency and turnover Leverage or long-term solvency Profitability Market Cash flow

I. LIQUIDITY OR SHORT-TERM SOLVENCY RATIOS Measurement of the company’s ability to pay off its short-term commitments out of liquid current assets that are expected to be converted to cash in a period roughly corresponding to the maturity of the short-term claims Current ratio = Quick ratio = Cash ratio = • Indication of the ability of a company to repay short-term obligations using its

current assets; also indicate whether maturity mismatch occurs • Risk-return trade-off concept Cautions • Current ratio defects from inventory • Using cash ratio shows pessimistic view of analyst

II. ASSET UTILISATION OR ASSET EFFICIENCY AND TURNOVER RATIOS

Measurement of the company’s ability to utilise its assets, efficiency from asset utilisation, or ability to manage the invested assets; some ratios indicate the efficiency in working capital management

Account receivable turnover = • Also known as average collection period and days sales outstanding


Account receivable days =

• Indication of the effectiveness of credit policy of the company Cautions • Credit treatment of each customer may be different • Competitors’ credit policies • Seasonally sales • Uncollected accounts receivable Inventory turnover = Inventory days = • Indication of the effectiveness of inventory management (and operational

management) and marketing department of the company • Indication of obsolete inventory when low inventory turnover exists Cautions • Trade-off between shortage costs and carrying costs • Ordering time cause high level of inventories • Company with branches usually carry high inventories Account payable turnover = Account payable days = • Indication of the company’s credit in terms of supplier aspect Cautions • Dependency of monopoly supplier • Suppliers differ among companies or across the years • Seasonal products Total asset turnover =


Fixed asset turnover = • Indication of how effective the company utilises its total assets or fixed assets Caution • Company’s choices of production • Total asset turnover aggregated assets, no specific effect can be pinpointed • Factors affect are strategy of the company in various areas and appropriateness of

capital expenditures • Out-of-fashioned and high depreciated fixed assets can improve this ratio • Decreasing trend of fixed asset turnover ratios may cause by the business

expansion • Outsourcing of manufacturing may improve this ratio

III. LEVERAGE OR LONG-TERM SOLVENCY OR DEBT MANAGEMENT RATIOS

Measurement of the company’s historical financing options and future debt obligations. The indication of future or additional borrowing capacity and the company’s ability to repay both principal and interest payments (Total) Debt ratio = Long-term debt ratio = Debt-to-equity ratio = Equity multiplier = • Indication of company’s future borrowing capacity and level of bankruptcy risk • Financial leverage benefits shareholders since this allows earnings to be magnified • Risk-return concept Caution • How the analyst perceives the riskiness of the company’s borrowing; interest

payment and repayment schedule can provide additional benefit to analysis


Times interest earned =

Times interest earned ratio equals earnings before interest and taxes divided by total interest payments; or

Times interest earned ratio equals the summation of net income, total interest expense, tax, and minority interest in earnings divided by total interest expense • How long the company can stay in business without any business transactions Caution • Other fixed charges are ignored; TIE ratios are actually overestimated • Cash flow availability is ignored

Fixed charge coverage = Earnings before interest and taxes + Lease payments Interest payments + lease payments + [preferred stock dividend + Sinking fund payment]

(1-Tax rate) • Company has (fixed charge coverage) times of operating profits to cover fixed

charge payments • Operating profits can decline at a maximum rate of fixed charge coverage ratio

minus 1 then divided by fixed charge coverage • Excessive utilisation of fixed charge financing indicates

financial risk • How long the company can stay in business without any

business transactions Caution • Fixed obligations among companies vary • Cash flow availability is ignored

IV. PROFITABILITY RATIOS Gross Profit Margin = Operating profit margin = Net profit margin =


• Indication of the ability of the company to generate (each type of) profit and

control (each type of) cost Caution • Extraordinary or non-recurring items deduction or addition Basic earning power = • Indication of the ability of the company to generate earnings available for all fund

providers Caution • Priority and portion of each fund provider Return on assets = Return on equity = Return on common equity = • Indication of the ability of the company to generate profit given level of

contribution from the each source of fund Caution • Some equity-holders may be more concern with the cash

dividend payout, or capital gain on price appreciation; hence not taking into account of much return the firm can generate given their contributions

• Dividend to preferred stockholder • Extraordinary or non-recurring items deduction or addition


Disaggregation of ROE

1) Three-step

Return on equity =

2) Four-step

Tax - EBITExpenseInterest -Tax - EBIT x

SalesNet Tax - EBIT x

Assets TotalSalesNet x

Equities TotalAssets Total ROE =

ROE = Equity Multiplier x Total Assets Turnover x Profit Margin x Debt Burden 3) Five-step (1)

Equities TotalAssets Total x


SalesNet EBIT x

EBITEBT x

EBTIncomeNet ROE =

ROE = Effects of Taxes x Effects of Financing x Effects of Operations

x Total Assets Turnover x Equity Multiplier 4) Five-step (2)

⎟⎠⎞

⎜⎝⎛

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛=

Taxes Before IncomeNet Taxes Income - 100% x

Equities TotalAssets Total x

Assets TotalExpInterest -


SalesNet EBIT ROE

ROE = [(Operating Profit Margin x Total Asset Turnover) – Interest Expense Rate] x Financial Leverage Multiplier x Tax Retention Rate


Disaggregation of ROCE

1) Three-step (1) ROCE = ROA x Common Earnings

Leverage x Capital Structure

Leverage Net income +

Interest expense(1 – Taxes)

+ Minority interest in earnings

Net income to common

Average total assets

Average total assets

Net income + Interest expense

(net of taxes) + Minority interest in

earnings

Average common

shareholders’ equity

2) Three-step (2)

EquityCommon AverageAssets Total Average x

Assets Total AverageSalesNet x

SalesNet Dividends Preferred - IncomeNet ROCE =

ROCE = Adjusted profit margin x Total Asset Turnover x Common Equity Multiplier

V. VALUATION RATIOS Earnings per share = • Indication of the amount earnings of the company generated to each common stock

holder Caution • Earnings to common stock holders not realised return to common stock holders Dividend per share = Caution • Dividend is not only source of return to stockholders


Dividend payout ratio = Retention ratio = • Indication of the portion the company retained and paid out as dividends Caution • Conflict of dividend and capital gain oriented investors • Future investment opportunities of the company

Price-earnings ratio = • Indication of the investors’ prospect of the company • The reciprocal of P/E ratio is called the earning yield Caution • Earnings can be less meaningful for either dividend or

capital appreciation only oriented investors • High P/E ratio may subject to speculative or

manipulative activities Market-to-book value ratio = Book value per share = • Indication of the management ability given the original contribution to the company Caution • High market-to-book value ratio may subject to speculative or manipulative

activities Dividend yield = Caution • Dividend yield may be less meaningful for capital appreciation oriented investors • Dividend yield may subject to speculative or manipulative activities


VI. CASH FLOW RATIOS

activities bearing-interestCurren debt term-long Totalactivities operatingby provided flowCash ratiodebt Total / flowCash

debt term-long of Book valueactivities operatingby provided flowCash ratiodebt term-Long / flowCash

expenseInterest expenseInterest activities operatingby provided flowcash Net ratio coverage flowCash

+=

=

+=

OTHER RATIOS • Actually ratios can be computed from (at least) any combination of a large set of

numbers available but not limited to those in financial statements. There are chances that more specific ratios may be meaningful in certain circumstances or certain industries.

• Cash flows related ratios may give meaningful ratios compared to aforementioned ratios such as operating cash flow to current liabilities rather than current ratio. However, certain group of investors may encounter difficulty interpreting cash flows related ratios.

OVERALL CAUTIONS IN RATIO

ANALYSIS • Timing issue is important from analysis point of view • Dealing with accounting numbers may create illusion due to

window dressing • Negative figures may yield meaningless or unable to

interpret ratios • Direction of changes in numerator and denominator • Industry average ratio may be questionable, comparable ratio to that of industry

average may not indicate the satisfied level of company performance • Where ratio can be computed using alternative items, comparison of ratios

computed by different numbers are not meaningful • Appropriated level of any ratios vary industry to industry • Off-balance sheet financing and obligations are not taken into account in ratio

analysis • Capitalisation of interest affects leverage ratios • Conglomerate companies cannot be precisely analysed; segmented data may be more

meaningful


• Consolidated financial statements are difficult to analyse the cause and effect; notwithstanding, minority interest concerns

• Financial institutions required different methods of financial statement analysis • Particular areas of financial statement analysis benefit specific issues such as

financial distress likelihood, acquisition, and forecasting • Valuation ratios may be affected from speculative and manipulative activities • Effect of inflation may substantial in certain environment • Exotic securities required complex analysis Questions 1. Is it true that the total asset turnover ratio can never exceed the fixed asset

turnover ratio? 2. Not-True Inc. has inventory of 100,000 baht. The firm’s current ratio is 3.0, while

its quick ratio is 2.5. What are Not-true’s current assets? 3. Cannot Company has enjoyed a rapid increase in sales in recent years,

following a decision to sell on credit. However, the firm has noticed a recent increase in its collection period. Last year, total sales were 1 million baht, and 250,000 of these sales were on credit. During the year, the accounts receivable account averaged 41,664 baht. It is expected that sales will increase in the forthcoming year by 50 percent, and, while credit sales should continue to be the same proportion of total sales, it is expected that the days sales outstanding will also increase by 50 percent. If the resulting increase in accounts receivable must be financed by external fund, how much external funding will Cannot Company need?

4. Hardly Supplies Inc. has a current ratio of 3.0, a quick ratio of 2.4, and an inventory

turnover ratio of 6. Hardly’s total assets are 1 million baht and its debt ratio is 20 percent. The firm has no long-term debt. What is Hardly’s sales figure if the total cost of goods sold is 75% of sales?

5. A firm estimates that its interest charges for this year will be 700,000 baht and

that its net income will be 3 million baht. Assuming its average tax rate is 30 percent, what is the company’s estimated times interest earned ratio?

6. Calculate EBIT from the following data:

Assets: 100,000 baht Net Profit Margin: 6.00 percent Tax rate: 40% Debt ratio: 40 percent Interest rate: 8.00 percent Total asset turnover = 3.00


7. Better Inc. and Ordinary Corp. each have assets

of 10 million baht and a return on common equity equal to 15%. Better has twice as much debt and twice as many sales relative to Ordinary Corp. Better’s net income equals 750,000 baht, and its total asset turnover is equal to 3.00. What is Ordinary’s net profit margin?

8. The Morelose Corporation’s common stock currently is selling at 100 baht per share,

which represents a P/E ratio of 10. If the firm has 100 shares of common stock outstanding, a return on equity of 20 percent, and a debt ratio of 60 percent, what is its return on assets?

9. It is Sunday and you just opened your briefcase to work with Nowhere Company’s

31st December, Year 6, balance sheet. To your dismay you discover the computer printouts your assistant stuffed into your briefcase contain only the following sketchy information: 1. Beginning and ending balances are identical for both accounts receivable and

inventory 2. Net income is 1,300,000 baht 3. Times interest earned is 5 (income taxes are zero.) Company has 5 percent-

interest bonds outstanding and issued at 1,000 face value 4. Net profit margin is 10 percent. Gross profit margin is 30 percent. Inventory

turnover is 5. 5. Days’ sales in receivables is 72 days. Assume 360-day in a year. 6. Sales to end-of-year net working capital is 4. Current ratio is 1.5. 7. Acid-test ratio is 1.0 (excluding prepaid expenses.) 8. Plant and equipment (net) is 6 million baht. It is one-third depreciated. 9. Dividends paid on 8 percent non-participating preferred stock are 40,000 baht.

There is no change in common shares outstanding during Year 6. Preferred shares where issued two years ago at face value 100 baht each.

10. Earnings per common share are 3.75 baht 11. Common stock has a 5 par value and was issued at par. 12. Retained earnings at 1st January, Year 6, are 350,000 a. Given the information available, prepare this company’s balance sheet as of 31st

December, Year 6 (including the following account classifications: cash, accounts receivable, inventory, prepaid expenses, plant and equipment (net), current liabilities, bonds payable, and stockholders’ equity.)

b. Determine the amount of dividends paid on common stock in Year 6.


Time Value of Money 1. Present Value and Future Value of Single sum 2. Present Value and Future Value of Ordinary (regular) annuity 3. Present Value and Future Value of Annuity due Compound one period more for both PV and FV of ordinary annuity 4. Present Value of Perpetuity 5. Present Value of Growing perpetuity 6. Uneven cash flows

Discount or compound all cash flows as if they are single sum then sum all of them.

FVFVnn = PV(1+i)= PV(1+i)nn

⎭⎬⎫

⎩⎨⎧

−+

=i1

i)i1(CFV

n

n⎭⎬⎫

⎩⎨⎧

+−= n0 )i1(i

1i1CPV

iC

i1CPV0 =⎥⎦

⎤⎢⎣⎡=


Questions 1. For the 1,000 baht which Bruce Wayne deposits with the financial institution,

find the total amount that he has after 1 year under each of the following cases:

• 12% interest compounded annually • 12% interest compounded semi-annually • 12% interest compounded quarterly • 12% interest compounded monthly Also, disaggregate the principal and interest amounts

2. You are the winner of the blackbox quiz show of 100,000 baht after taxes. You

invest your winnings in a five year deposit at Kasikorn Bank. The deposit pays 4 percent per year compounded annually. This KBank also lets you reinvest the interest at the same rate for the duration of five years. How much will you have at the end of five years if your money remains invested at 3 percent for five years with no withdrawals of interest?

3. Carrie deposited 240,000 dollars in a savings account that pays 5 percent interest, compounded quarterly, planning to use it to ease her life during her retirement. Eighteen months later, she met with Petrovsky whom she would like to spend the rest of her life with. So, rather than continue to plan for her retirement alone, she starts to build her family and closes out her account. However, Petrovsky needed Carrie to move to Paris with him. How much money will Carrie receive in euro, given 1.40 euros/dollar?

4. After Phantom had kidnapped Christine, he sent Raoul a message saying that if Raoul wanted Christine back, he just gave Phantom 500,000 French francs (a monetary unit used during that period) in return. However, Raoul had cash only 20% of the amount Phantom asked. Thus, he borrowed the rest from his business, the Opera House. He is required to repay a lump sum of 608,350 francs three years from borrowing. What was the nominal interest rate that the Opera House charged Raoul?

5. Barbie were sold at auction in 2000 by Christie’s International PLC for US$16,500 each. At the time, it was estimated that this represented a 18 percent annual rate of return. For this to be true, what was the car have sold for new in 1961?

6. Homer is selling his house. Charles Montgomery Burns has offered Homer $115,000. He will pay you immediately. Apu Nahasapeemapetilon has offered you $150,000, but he cannot pay you until three years from today. The interest rate is 10 percent. Which offer should Homer choose?


7. To the closest year, how long will it take £200 to double if it is deposited and earns the following rates?

• 7 percent • 10 percent • 18 percent • 100 percent

8. Seven dwarfs own a diamond mine. They promised Snow

White to pay her $3,000 for her carriage when she gets married with Prince Charming one year from now. However, the jealous queen offered her $3,500 for the carriage now. The prevailing interest rate is 12 percent. If the future value of the benefit from owning the carriage for one additional year is $1,000, should Snow White accept the offer from seven dwarfs? She is not planning to buy another carriage and will not need it after staying with Prince Charming.

9. Piglet intends to collect money for retirement. If Piglet deposits £100 at the end of each of the next 50 years into an account paying 7 percent interest, annually compounded, how much money will Piglet have in the account in 50 years?

10. Dre wants to have 100,000 pound in his savings account five years from now; he is prepared to make equal deposits into the account at the end of each year. If the account pays 12 percent interest, annually compounded, what amount must he deposit each year?

11. From prior example, what amount must Dre deposit each year, if the account pays 12 percent interest, quarterly compounded?

12. Romeo met Juliet in the party when he was 15. He promised to buy her a special gift 9 years from the first day they met. At the time he met her, his annual income was £720.00, and was expected to be constant for 15 years. In order to have enough money for the £776.83 gift (the expected price 15 years from the time they met,) he saved 5 percent of his annual income, with the first saving made 1 year after they met and the last years he met her. What was the annual compound interest rate he should earn so that his goal was accomplished?

13. Beginning three months from now, Peter wants to be able to withdraw 10,000 dollars each quarter from his bank account to cover his personal expenses over the next four years. If the account pays 16 percent interest, compounded quarterly, how much Peter need to have in his bank account today to meet his expense needs over the next four years?

14. J.O.’s subscription to the “Journal of British Accounting”, monthly academic release, is about to run out and she has the choice to renewing it by sending in the £250 a year regular rate or of


getting a lifetime subscription to the magazine by paying £3,000. Her opportunity cost is 7 percent. How many years would she have to live to make the lifetime subscription the better buy? Payments for the regular subscription are made at the beginning of each year.

15. Sungthong plans to marry Rojana in the near future. He saves 40% of his annual income in a time-deposit account, which earns 12 percent interest, compounded annually. The first and last deposits are made today and 1 year before marriage, respectively. His annual income is constant at 100,000 baht. If the dowry to be paid on the wedding day is 786,183 baht, when will Sungthong marry Rojana?

16. Mam deposits 5,000,000 baht for the education of her child. Her child supposed to withdraw an equal amount of money from the account once a year for the next 12 years. The first withdrawal will be made today. After the last withdrawal is made, the account balance is zero. If the account earns an interest rate of 12 percent per annum, semi-annually compounded, how large is each withdrawal?

17. Kwun is considering the purchase of 40 square yards of land. Ream, his girlfriend, indicates that if the land is used for cattle grazing, this will produce cash flow of 25,000 baht per year indefinitely. If Kwun requires a return of 13 percent on this investment, what is the most that Kwun should be willing to pay for the land?

18. Monsters, Inc.’ preferred stock has a 100-baht par value. It pays quarterly dividend of 6 percent per annum. If the required rate of return on this preferred stock is 12 percent, how much should be the price for this stock?

19. Aladdin would like to set aside an amount of cash in the specific account that aims to provide an even stream of donation to various foundations. If the account pays 5 percent interest, annually compounded, and Aladdin would like to donate 500 baht per year forever, starting the first donation today, what is the appropriate amount he needs to deposit today? Also, prove that this amount satisfied his donation desire.

20. Harry invests in common stock of the Gringotts Bank that expected to pay 15.00 Galleons per share dividend for next year. The Bank pledges to increase its dividend by 3.50 percent per year, indefinitely. If Harry requires a 12.50 percent return on this investment, how much is the most Harry can pay for this stock?

21. The present value (t = 0) of the following cash flow stream is £4,696.74 when discounted at 10 percent annually. What is the value of the missing (t = 2) cash flow?

Year 0 Year 1 Year 2 Year 3 Year 4 0 £1,500 £ ? £3,000 £3,000


22. Prepare an amortisation schedule for a three-year loan of £30,000. The interest rate is 8 percent per year, and the loan calls for equal annual payments. How much interest is paid in the third year? How much total interest is paid over the life of the loan?

23. Your friend is celebrating her 35th birthday today and wants to start saving for her anticipated retirement at age 65. She wants to be able to withdraw US$80,000 from her savings account on each birthday for 15 years following her retirement; the first withdrawal will be on her 66th birthday. Your friend intends to invest her money in the local credit union, which offers 9% interest per year. She wants to make equal annual payments on each birthday into the account established at the credit union for her retirement fund.

a. If she starts making these deposits on her 36th birthday and continues to make deposits until she is 65 (the last deposit will be on her 65th birthday), what amount must she deposit annually to be able to make the desired withdrawals at retirement?

b. Suppose your friend has just inherited a large sum of money. Rather than making equal annual payments, she has decided to make 1 lump-sum payment on her 35th birthday to cover her retirement needs. What amount does she have to deposit?

c. Suppose your friend’s employer will contribute US$1,500 to the account every year as part of the company’s profit-sharing plan. In addition, your friend expects a US$30,000 distribution from a family trust fund on her 55th birthday, which she will also put into the retirement account. What amount must she deposit annually now to be able to make the desired withdrawals at retirement?

24. A cheque-cashing store is in the business of making personal loans to walk-up customers. The store makes only one-week loans at 10% interest per week.

a. What APR must the store report to its customers? What is the EAR that the customers are actually paying?

b. Now suppose the store makes 1-week loans at 11% discount interest per week What’s the APR now? The EAR?

c. The cheque-cashing store also makes 1-month add-on interest loans at 9% discount interest per week. Thus, if you borrow US$100 for one month (four weeks,) the interest will be (US$100 x 1.094) – 100 = US$41.16. Because this is discount interest, your net loan proceeds today will be US$58.84. You must then repay the store US$100 at the end of the month. To help you out, though, the store lets you pay off this US$100 in instalments of US$25 per week. What is the APR of this loan? What is the EAR?

25. Antonio is discussing the loan with Shylock to borrow £12,000 for one year. The interest rate is 12 percent. Both agree that the interest on the loan will be 0.12 x £12,000 = £1,440. So, Shylock deducts this interest amount from the loan up


front, called the “discount interest,” and gives Antonio £10,560. What’s wrong here?

26. You are serving on a jury. A plaintiff is suing the city for injuries sustained after a freak street sweeper accident. In that trial, doctors testified that it will be 5 years before the plaintiff is able to return to work. The jury has already decided in favour of the plaintiff. You are the foreperson of the jury and propose that the jury give the plaintiff an award to cover the following: 1) The present value of two years’ back pay. The plaintiff’s annual salary for the last 2 years would have been US$40,000 and US$43,000, respectively. 2) The present value of five years’ future salary. You assume the salary will be US$45,000 per year. 3) US$100,000 for pain and suffering. 4) US$20,000 for the court costs. Assume that the salary payments are equal amounts paid at the end of each month. If the interest rate you choose is a 9% EAR, what is the size of the settlement? If you were the plaintiff, would you like to see a higher or lower interest rate?

27. Bilbo Baggins wants to save money to meet three objectives. First, he would like to be able to retire 30 years from now with retirement income of US$25,000 per month for 20 years, with the first payment received 30 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 10 years at an estimated cost of US$350,000. Third, after he passes on at the end of the 20 years of withdrawals, he would like to leave an inheritance of US$750,000 to his nephew Frodo. He can afford to save US$2,100 per month for the next 10 years. If he can earn an 11% EAR before he retires and an 8% EAR after he retires, how much he have to save each month in years 11 through 30?

28. An All-Pro defensive lineman is in contract negotiations. The team has offered the following salary structure:

Year 0 1 2 3 4 5 6 Salary $8.0 $4.0 $4.8 $5.7 $6.4 $7.0 $7.5 (unit: millions)

All salaries are to be paid in a lump sum. The player has asked you as his agent to renegotiate the terms. He wants a US$9 million signing bonus payable today and a contract value increase of US$750,000. He also wants an equal salary paid every 3 months, with the first paycheque 3 months from now. If the interest rate is 4.5% compounded daily, what is the amount of his quarterly chequer? Assume 365 days in a year.

29. Chicken Little, a senior-year student, has just been offered a job at 80,000 baht a year. He anticipates his salary increasing by 9 percent a year until his retirement in 40 years. Given an interest rate of 20 percent, what is the present value of his lifetime salary?


Net Present Value and Other Investment Rules

Capital

• Operating assets used in production

Capital Investment • Investments in long-lived assets such as plant, equipment, and advertising

Budget A plan that details projected cash flows during some future period

• Capital budgeting: Long-term budget • Cash budget: Short-term budget

Capital budgeting

The process of identifying which long-lived investment projects a firm should undertake. • The process of analysing potential projects or fixed asset investments • The process of analysing projects and deciding which ones to include in the capital

budget • Long-term decisions; involve large expenditures. • Very important to firm’s future.

Capital Budget • An outline of planned investments in operating assets

Importance of Capital Budgeting

• Define strategic direction: move into new products, markets • Large amount of spending (investing) called “Capital Expenditures” and large amount

of money is not available automatically • Erroneous forecast of asset requirements can have serious consequences • Importance of timing; assets must be ready in timely fashion


Steps in Capital Budgeting

• Estimate cash flows (inflows & outflows). • Assess risk of cash flows. • Determine r = WACC for project. • Evaluate cash flows.

Independent and mutually exclusive projects

Projects are: • independent, if the cash flows of one are unaffected by the acceptance of the

other. • mutually exclusive, if the cash flows of one can be adversely impacted by the

acceptance of the other. Project Classifications

• Replacement o maintenance of business o cost reduction

• Expansion o existing products or markets o into new products or markets

Investment Criteria

• Methods to rank projects and to decide whether or not they should be accepted for inclusion in the capital budget

Necessary Conditions of Criterion

• Utilise all cash flows • Inhibit concepts of time value of money • Indicate shareholders’ value • Adjust return for the level of risk • Possess value additivity principle Capital Budgeting Decision Rules

• Payback period • Discounted payback period • Accounting rate of return • Net present value • Internal rate of return • Modified internal rate of return • Profitability index


Payback period (PBP)

• The amount of time it takes for a given project’s cumulative net cash flows to recoup the initial investment.

PBP = Year before full recovery + Unrecovered cost at start of year Cash flow during year Payback Period Decision Rule

Accept Reject

Cash flows (in millions) for Project F (Fast) and S (Slow) Project CF0 CF1 CF2 CF3 CF4

F – €1,000 €500 €400 €300 €100 S – €1,000 €100 €300 €400 €600

Discounted Payback Period (DPBP)

• The amount of time takes for a project’s discounted cash flows to recover the initial investment.

DPBP = Year before full recovery + Unrecovered present value of cost at start of year Present value of cash flow during year Discounted Payback Period Decision Rule

Accept Reject


F – €1,000 €500 €400 €300 €100 S – €1,000 €100 €300 €400 €600

Given the discount rate of 10 percent


Net Present Value (NPV)

• The sum of the present value of all of a given project’s cash flows, both inflows and outflows, discounted at a rate consistent with the project’s risk. Also, a method for valuing capital investments.

Net Present Value Decision Rule

Accept Reject


F – €1,000 €500 €400 €300 €100 S – €1,000 €100 €300 €400 €600

Given the discount rate of 10 percent Important Assumption in the Net Present Value Calculation

• Interim cash flows are reinvested at the discount rate

( ) ( ) ( )

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Internal Rate of Return (IRR)

• The compound annual rate of return on a project, given its up-front costs and subsequent cash flows.

• Discount rate that equates the present value of a project’s expected cash inflows to the present value of the project’s costs

• Same concept as yield-to-maturity

PV (Inflows) = PV (Investment costs) Internal Rate of Return Decision Rule

Accept Reject

Example: Internal Rate of Return Cash flows (in millions) for Project F (Fast) and S (Slow) Project CF0 CF1 CF2 CF3 CF4

F – €1,000 €500 €400 €300 €100 S – €1,000 €100 €300 €400 €600

Given the discount rate of 10 percent One Important Assumption in the Internal Rate of Return (IRR) Calculation

• Interim cash flows are reinvested at the IRR rate

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• Mathematically, the NPV and IRR methods will always lead to the same

accept/reject decisions for independent projects. • The NPV and IRR can give conflicting rankings for mutually exclusive projects. NPV Profiles: Comparison of the NPV and IRR Methods

• A plot of a project’s NPV (on the y axis) against various discount rates (on the x axis.) It is used to illustrate the relationship between the NPV and the IRR for the typical project.

Example: NPV Profiles: Scale Difference Cash flows (in millions) for Wireless Network Project in Western Europe and Toehold Project in Eastern Europe

Project CF0 CF1 CF2 CF3 CF4 CF5

Wireless Network – €450 €63 €144 €234 €288 €315 Toehold – €90 €32 €40 €45 €54 €58

Given the discount rate of 16 percent To Find the Crossover Rate 1. Find cash flow differences between the projects. 2. From these cash flows differences, find IRR, which is crossover rate 3. If profiles don’t cross, one project dominates the other. Two Reasons NPV Profiles Cross

1. Size (scale) difference: Smaller project frees up funds at t = 0 for investment. The higher the opportunity cost, the more valuable these funds, so high r favors small projects.

2. Timing difference: Project with faster payback provides more CF in early years for reinvestment. If r is high, early CF especially good, NPVF > NPVS.

Example: NPV Profiles: Timing Difference Cash flows (in millions) for Project F (Fast) and S (Slow) Project CF0 CF1 CF2 CF3 CF4

F – €1,000 €500 €400 €300 €100 S – €1,000 €100 €300 €400 €600



Example: Problem with the Internal Rate of Return (1) Find IRR of the following cash flows (in millions):

CF0 CF1 CF2

Project Cash Flows – €1,600 €10,000 – €10,000 Example: Problem with the Internal Rate of Return (2) Find IRR of the following cash flows (in millions):

CF0 CF1 CF2

Project Cash Flows – €1,000 €3,000 – €2,000

• The multiple IRRs can arise when the IRR criterion is used with a project that has non-normal cash flows.

• Use of the IRR method on projects having non-normal cash flows could produce other problems such as no IRR or an IRR that leads to an incorrect accept/reject decision.

• The NPV criterion should be applied rather than IRR criterion. Normal Cash Flow Project:

• Cost (negative CF) followed by a series of positive cash inflows. One change of signs.

Non-normal Cash Flow Project:

• Two or more changes of signs. Most common: Cost (negative CF), then string of positive CFs, then cost to close project. Nuclear power plant, strip mine.

Inflow (+) or Outflow (-) in Year

0 1 2 3 4 5 N NN

- + + + + + N

- + + + + - NN

- - - + + + N

+ + + - - - N

- + + - + - NN


Example: Problem with the Internal Rate of Return (3) Make a decision at 10% using NPV and IRR. What is the decision?

CF0 CF1

Project L – €1,000 €1,500 Project B €1,000 – €1,500

Modified Internal Rate of Return (MIRR)

• The modification of the IRR to a better indicator of relative profitability Modified Internal Rate of Return Decision Rule

Accept Reject


F – €1,000 €500 €400 €300 €100 S – €1,000 €100 €300 €400 €600

Given the discount rate of 10 percent Why use MIRR versus IRR?

• MIRR correctly assumes reinvestment at opportunity cost = WACC. MIRR also avoids the problem of multiple IRRs.

• Managers like rate of return comparisons, and MIRR is better for this than IRR.

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Profitability Index (PI)

• The present value of a project’s cash inflows divided by its initial cash outflows • Ratio of present value of cash inflows to present value of initial investments Profitability Index Decision Rule

Accept Reject


F – €1,000 €500 €400 €300 €100 S – €1,000 €100 €300 €400 €600


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outflows)cash (all PVinflows)cash (all PV Index ity Profitabil


Comparison among Alternative Criteria Payback Period

Advantages Disadvantages

Discounted Payback Period


Net Present Value


Internal Rate of Return



Modified Internal Rate of Return


Profitability Index


Assumptions on Investment Criteria

• Future cash flows are certain • Reinvestment rate assumption must be considered • Projects with different lives should not be compared • Capital to be invested is assumed to be unlimited

The Post-Audit

• Compare actual results with those predicted by the project’s sponsors • Explain why any differences occurred

Purposes of Post-Audit

• Improve forecasts • Improve operations • Identify termination opportunities


Special Issues in Capital Budgeting

• Capital Rationing • Compare Project with Unequal Lives • Economic Life vs. Physical Life

Capital Rationing

• Capital rationing occurs when a company chooses not to fund all positive NPV projects.

• The company typically sets an upper limit on the total amount of capital expenditures that it will make in the upcoming year.

Reason: Companies want to avoid the direct costs (i.e., flotation costs) and the indirect costs of issuing new capital. Solution: Increase the cost of capital by enough to reflect all of these costs, and then accept all projects that still have a positive NPV with the higher cost of capital. Reason: Companies don’t have enough managerial, marketing, or engineering staff to implement all positive NPV projects. Solution: Use linear programming to maximize NPV subject to not exceeding the constraints on staffing. Reason: Companies believe that the project’s managers forecast unreasonably high cash flow estimates, so companies “filter” out the worst projects by limiting the total amount of projects that can be accepted. Solution: Implement a post-audit process and tie the managers’ compensation to the subsequent performance of the project. Example Make a decision at 10% with 10,000 capital limitation. What is the decision?

Project CF0 CF1 CF2 NPV10%

K -10,000 +30,000 +5,000

L -5,000 +5,000 +20,000

M -5,000 +5,000 +15,000


Example

A company has found the following independent investment opportunities (all figures in $000s):

Project Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 A -100 -50 -25 100 100 100 B -50 -70 100 100 C -100 -30 150 200 D -10 -20 50 -100 100 100 E -100 -100 200 100 50 F -200 300 100 100

Assume that none of these projects can have the timing of its cash flow brought forward or delayed, and none can be undertaken more than once. All projects exhibit constant returns to scale. The perfect capital market rate of interest is 10% and this rate is expected to remain constant over the next five years, and can be assumed to reflect the capital suppliers’ opportunity cost. In addition, the company has internally imposed capital constraint, such that external finance raised in any one period must not exceed $150,000. Internally generated finance (from projects) cannot be used to increase the amount of capital expenditure. What should be the appropriate capital budgeting decision for this company? There are several ways in which this problem could be formulated into a linear programme, but each alternative formulation would produce a solution giving exactly the same selection of investment projects to undertake. One approach, which fits directly into our NPV approach, is to take as the LP’s objective function the maximization of the total amount of NPV which the company can generate over the next five years, given the imposed constraints. Thus, taking a, b, c, …, f to represent proportion of Projects A, B, C, …, F undertaken: Objective function:

MAX: NPVa a + NPVb b + NPVc c + NPVd d + NPVe e + NPVf f

Constraints: 100a + 50b + 10d + 100e ≤ 150 (Year 0) 50a + 70b + 100c + 20d + 100e ≤ 150 (Year 1) 25a + 30c + 200f ≤ 150 (Year 2) 100d ≤ 150 (Year 3) a, b, c, d, e ≤ 1 a, b, c, d, e ≥ 0 Solutions: a = 0, b = 0, c = 1, d = 1, e = 0.3, f = 0.6 total NPV of $341,000


Illustration to use “Solver” function in Microsoft Excel to solve this example:


Key cells used: Cell Formula K10 J3*K3+J4*K4+J5*K5+J6*K6+J7*K7+J8*K8 C12 K3*C3+K4*C4+K6*C6+K7*C7 D12 K3*D3+K4*D4+K5*D5+K6*D6+K7*D7 E12 K3*E3+K5*E5+K8*E8 F12 K6*F6 C14 C12+C10 D14 D12+D10 E14 E12+E10 F14 F12+F10 G14 G12+G10 H14 H12+H10 Key cells used in “Solver” function: Set Target Cell $K$10

Equal to MAX

By Changing Cells $K$3:$K$8

Subject to the constraints C14≤150

C14≥0 D14≤150 D14≥0 E14≤150 E14≥0 F14≤150 F14≥0 K3≤1 K3≥0 K4≤1 K4≥0 K5≤1 K5≥0 K6≤1 K6≥0 K7≤1 K7≥0 K8≤1 K8≥0


Comparing projects with Unequal Lives • When choosing between two mutually exclusive alternatives with different lives, an

adjustment is necessary. a. Replacement chain method b. Equivalent annual annuity method

Example Suppose a company is planning to modernise its production facilities, and it is considering either a conveyor system or some forklift trucks for moving materials. The expected cash flows of these two mutually exclusive projects are as follow: Project CF0 CF1 CF2 CF3 CF4 CF5 CF6

Conveyor -40,000 +8,000 +14,000 +13,000 +12,000 +11,000 +10,000

Forklift -20,000 +7,000 +13,000 +12,000 Given discount rate 11.50% Example You are evaluating two different pollution control options. A filtration system will cost US$1.1 million to install and US$60,000 annually, before taxes, to operate. It will have to be completely replaced every five years. A precipitation system will cost US$1.9 million to install, but only US$10,000 per year to operate. The precipitation equipment has an effective operating life of eight years. Straight-line depreciation is used throughout, and neither system has any salvage value. Which option should we select if we use a 12 percent discount rate? The tax rate is 34 percent. Economic Life vs. Physical Life Consider another project with a 3-year life. If terminated prior to Year 3, the machinery will have positive salvage value.

Year CF Salvage Value 0 1 2 3

- 5,000 2,100 2,000 1,750

5,000 3,100 2,000

0 Assuming a 10% cost of capital, what is the project’s optimal, or economic life?


Cash Flow and Capital Budgeting

Cash flows – NOT ACCOUNTING NET INCOME

• The cash flows that should be included in a capital budgeting analysis are those that will only occur if the project is accepted - called incremental cash flows

• These cash flows must be relevant to the project • The stand-alone principle allows us to analyze each project in isolation from the

firm simply by focusing on incremental cash flows Example

The Weber-Decker Co. just paid US$1 million in cash for a building, as part of a new capital budgeting project. This entire US$1 million is an immediate cash outflow. However, assuming straight-line depreciation over 20 years, only US$50,000. The remaining US$950,000 is expensed over the flowing 19 years. For capital budgeting purposes, the relevant cash outflow at the time 0 is the full US$1 million, not the reduction in earnings of only US$50,000.

Focusing on Incremental Cash Flows • Cash flows that directly result from a proposed investment. They effectively

represent the marginal costs (MC) and marginal benefits (MB) expected to result from undertaking a proposed investment.

Ignoring Financing costs – both interest and dividends are ignored when developing an investment’s relevant cash flows • Exclude when calculating operating cash flows or cash flows to the firm • Firms typically calculate a project’s cash flows under the assumption that the

project is financed only with equity. Any adjustments for debt financing are reflected in the discount rate, not the cash flows.

Should we build thisplant?


Considering Taxes • All activities that subjected to tax must be calculated on after-tax basis. • Taxes on earnings before interest and taxes – profits (losses) from sales and

profits (losses) from proceeds from sales of assets

Marginal tax rate: the percentage of taxed owned on the next euro of income. Adjusting for Non-cash Expenses • Non-cash expenses include depreciation, amortisation, and depletion. • Even though non-cash expense itself is not cash flows, its tax-deductibility has tax

consequence.

There are two ways to calculate cash flows that take this effect into account.

o Operating Cash Flows = Net Operating Profit after Tax + Non-Cash Expenses o Operating Cash Flows = Net Operating Profit after Tax + Tax Shield

Suppose a firm spends €80,000 in cash to purchase a fixed asset today that it plans to fully depreciate on a straight-line basis over four years to zero salvage. Acquiring this machine, the firm can now produce 15,000 units of some product each year. The product costs €2 to make and sells for €6. Compute the operating cash flows given 40% tax rate. Depreciation • Straight-line depreciation

o Depreciation = (Initial cost – salvage) / number of years o Very few assets are depreciated straight-line for tax purposes

• Double-declining balance (DDB) method

o Depreciation method that calculates depreciation as the net book value multiplied by the DDB rate.

o Depreciation = (Fixed asset – Accumulated depreciation) x (2/asset’s life in years)

• MACRS – Modified Accelerated Cost Recovery System

o Need to know which asset class is appropriate for tax purposes o Multiply percentage given in table by the initial cost o Depreciate to zero o Mid-year convention


US Tax Depreciation Allowed for Various MACRS Asset Classes

Class of Investment

Ownership Year 3-Year 5-Year 7-Year 10-Year 15-Year 20-Year

1 33.33% 20.00% 14.29% 10.00% 5.00% 3.75% 2 44.45% 32.00% 24.49% 18.00% 9.50% 7.22% 3 14.81% 19.20% 17.49% 14.40% 8.55% 6.68% 4 7.41% 11.52% 12.49% 11.52% 7.70% 6.18% 5 11.52% 8.93% 9.22% 6.93% 5.71% 6 5.76% 8.93% 7.37% 6.23% 5.28% 7 8.93% 6.55% 5.90% 4.89% 8 4.45% 6.55% 5.90% 4.52% 9 6.55% 5.90% 4.46% 10 6.55% 5.90% 4.46% 11 3.29% 5.90% 4.46%

12 – 15 5.90% 4.46% 16 2.99% 4.46%

17 – 20 4.46% 21 2.25%

100.00% 100.00% 100.00% 100.00% 100.00% 100.00% Fixed Asset Expenditures • Initial cash outflow for a project (assume paid in full in cash) • Additional factors that influence the cash consequences of fixed asset acquisitions

include installation costs and proceeds from sales of any existing fixed assets that are being replaced.

Advanced Technologies Corporation (ATC) just purchased €105,000 worth of new computers. Installation cost for the new computers equals €5,000. The computers have a life of five years with €7,000 expected salvage value. Compute depreciation expenses using:

• Straight-line method given an accounting salvage value of €10,000. • Double declining method • Five-year MACRS

Operating Working Capital Expenditures • Net operating working capital is the difference between operating current assets

and current operating liabilities


• Firm may find that it must maintain an investment in working capital – purchase of raw materials before production and sale, giving rise to an investment in inventory. Credit sales will generate account receivable – lowering the cash flows compared to total revenues. Conversely, accounts payable reduce cash flows paid compared to cost of goods sold.

Net Operating Working Capital: the difference between a firm’s current operating assets (operating working capital) and its current operating liabilities.

1st Oct 1st Nov 1st Dec 1st Jan 1st Feb

Minimum Cash £0 £1,500 £1,500 £1,500 £0

Accounts Receivable 0 25,000 11,500 2,000 0

Inventory 0 20,000 20,000 2,500 0

Accounts Payable 0 45,000 30,000 15,000 0

Monthly NOWC

Change in NOWC

Compute cash flows associated with changes in net operating working capital. Example

An investment in net working capital arises whenever (1) inventory is purchased, (2) cash is kept in the project as a buffer against unexpected expenditures, and (3) credit sales are made, generating accounts receivable rather than cash. (The investment in net working capital is reduced by credit purchases, which generate accounts payables.) This investment in net working capital represents a cash outflow, because cash generated elsewhere in the firm is tied up in the project. To see how the investment in net working capital is built from its component parts, let’s the managers predict sales to be US$100,000 and operating costs to be US$50,000. If both the sales and costs were cash transactions, the firm would receive US$50,000. Somehow additional information reveals that the managers:

1. Forecast that US$9,000 of the sales will be on credit, implying that cash receipts will be only US$91,000. The accounts receivable of US$9,000 will be collected in the next year.

2. Believe that they can defer payment of US$3,000 of the US$50,000 of costs, implying that cash disbursements will be only


US$47,000. This US$3,000 accounts payable will be paid in the next year.

3. Decide that the inventory of US$2,500 should be left on hand to avoid stockouts – running out of inventory.

4. Decide that cash of US$1,500 should be earmarked for the project

to avoid running out of cash.

Thus, net working capital of the year is:

US$9,000 – US$3,000 + US$2,500 + US$1,500 = US$10,000 Because US$10,000 of cash generated elsewhere in the firm must be used to offset this requirement for net working capital. Managers correctly view the investment in net working capital as a cash outflow of the project. As the project grows over time, needs for net working capital increase. Changes in net working capital from year to year represent further cash flows in the following years. Since US$10,000 net working capital, for the following year, managers can forecast net working capital for the following year assuming at US$16,320. Changes in net working capital for the following year is US$6,320. Again, pulling cash US$6,320 from elsewhere in the firm.

Terminal Value • The value of a project at a given future date. • Some investments have a defined life span due to the physical life of a piece of

equipment or else project the terminal value, commonly take the final year of cash flows projections and make an assumption that all future cash flows form the project will grow at a constant rate.

Suppose that analysts at Aventas were analysing the potential acquisition of Onuri, Inc. They projected that the acquisition of Onuri, Inc. would generate the following new stream of cash flows: Year 1 Year 2 Year 3 Year 4 Year 5 € 2 billion 4 billion 7 billion 10 billion 13 billion In year 6 and beyond, analysts believed that cash flows would continue to grow at 4 percent per year. What is the terminal value of this investment? What is the present value of these future cash flows? Given 12 percent required rate of return.


THE RELEVANT CASH FLOWS • All incremental, after-tax cash flows (initial outlay, operating cash flows, and

terminal value) associated with a proposed investment. Incremental Cash Flow • Cash flows that directly result from a proposed investment. They effectively

represent the marginal costs (MC) and marginal benefits (MB) expected to result from undertaking a proposed investment.

Angelo Bonetti earns €36,000 per year working as an engineer for a car manufacturer, and he pays taxes at a flat rate of 39 percent. He expects salary increases each year of about 4 percent. Lately, Angelo has been thinking about going back to school to earn an MBA. A few months ago, he spent €600 to enroll in a Graduate Management Admission Test (GMAT) study course. He also spent €1,200 visiting various MBA programmes in the European Union. From his research on MBA programmes, Angelo has learnt a great deal about the costs and benefits of the degree. At the beginning of each of the next two years, his out-of-pocket costs for tuition, fees, and textbooks will be €21,000. He expects to spend roughly the same amount on room and board in graduate school that he spends now. At the end of two years, he anticipates that he will receive a job offer with a salary of €54,000, and he expects that his pay will increase by 7 percent per year over his career (about the next 30 years.) Compute the incremental cash flows for the next few periods. Sunk costs

• Costs that have already been paid (occurred) and are therefore not recoverable. • Since sunk costs are in the past, they cannot be changed by the decision to accept

or reject the project • Sunk costs are ignored and not part of incremental relevant cash flows Example

The General Milk Company is currently evaluating the NPV of establishing a line of chocolate milk. As part of the evaluation the company had paid a consulting firm US$100,000 to perform a test-marketing analysis. This expenditure was made last year. Is this cost relevant for the capital budgeting decision now confronting the management of General Milk Company? The answer is NO. The US$100,000 is not recoverable, so the US$100,000 expenditure is a sunk cost or spilled milk. Of course, the decision to spend US$100,000 for a marketing analysis was a capital budgeting decision itself and was perfectly relevant before it was sunk. Our point is that once the company incurred the expense, the cost became irrelevant for any future decision.


Opportunity costs – costs of lost options

• Lost cash flows on an alternative investment that the firm or individual decides not

to make. • Firm may have an asset that it is considering selling, leasing, or employing elsewhere

in the business. If the asset is used in a new project, potential revenues from alternative uses are lost. Those lost revenues can meaningfully be viewed as costs. By taking the project, the firm foregoes other opportunities for using the assets.

Example

Suppose the Weinstein Trading Company has an empty warehouse in Philadelphia that can be used to store a new line of electronic pinball machines. The company hopes to sell these machines to affluent northeastern consumers. Should the warehouse be considered a cost in the decision to sell the machines? The answer is YES. The company could sell the warehouse, if the firm decides not to market the pinball machines. Thus, the sales price of the warehouse is an opportunity cost in the pinball machine decision.

Side Effects • SYNERGY: Positive side effects – benefits to other projects • EROSION / CANNIBALISATION: Negative side effects – costs to other projects Example

Suppose the Innovative Motors Corporation (IMC) is determining the NPV of a new convertible sports car. Some of the customers who would purchase the car are owners of IMC’s compact sedan. Are all sales and profits from the new convertible sports car incremental? The answer is NO because some of the cash flow represents transfers from other elements of IMC’s product line. This is erosion, which must be included in the NPV calculation. Without taking erosion into account, IMC might erroneously calculate the NPV of the sports car to be, say, US$100 million. If half the customers are transfers from the sedan and lost sedan sales have an NPV of – US$150 million, the true NPV is – US$50 million. IMC is also contemplating the formation of a racing team. The team is forecasted to lose money for the foreseeable future, with perhaps the best projection showing an NPV of – US$35 million for the operation. However, IMC’s managers are aware that the team will likely generate great publicity for all of IMC’s products. A consultant estimates that the increase in cash flows elsewhere in the firm has a present value of US$65. Assuming that the consultant’s estimates of synergy are trustworthy, the net present value of the team is US$30 million. The managers should form the team.


Allocated Costs • Frequently a particular expenditure benefits a number of projects. Accountants

allocate this cost across the different projects when determining income. However, for capital budgeting purposes, this allocated cost should be viewed as a cash outflow of a project only if it is an incremental cost of the project.

Example

The Voetmann Consulting Corp. devotes on wing of its suite of offices to a library requiring a cash outflow of US$100,000 a year in upkeep. A proposed capital budgeting project is expected to generate revenue equal to 5 percent of the overall firm’s sales. An executive at the firm, H. Sears, argues that US$5,000 (5% x 100,000) should be viewed as the proposed project’s share of the library’s costs. Is this appropriate for capital budgeting? The answer is NO. The firm will spend US$100,000 on library upkeep whether or not the proposed project is accepted. Since acceptance of the proposed project does not affect this cash flow, the cash flow should be ignored when calculating the NPV of the project. Differentiate the cash flows of the entire firm with the project and the cash flows of the entire firm without the project to identify incremental relevant cash flows.

Cash Flows Estimation Guidance Section I: Initial Investment Outlay • Capital budgeting process starts from project initiation usually be the initial

investments in the project. o Fixed assets investment – land, building, equipment, etc. o Initial net working capital – raw materials for manufacturing process,

minimum safety stock, etc. Section II: Annual Operating Cash Flows • After initial investments, project is ready to start generating revenues, incurring

expenses. Income statements can be generated, or forecasted. • Modified income statement to cash flows basis. Add additional related cash flows:

o Additional (or reduction in) net working capital o Additional fixed assets investments – the capital expenditure (CAPEX)

Section III: Terminal Year Cash Flows • At the end of the projection horizon, either:

o Proceeds from sales of fixed assets are estimated – with tax effect, including return on all net working capital – at the end, all inventory is sold, the cash balance maintained as a buffer is liquidated, and all accounts receivable are collected, or


o Accumulated present value of operating cash flows after horizon After-tax Salvage • If the salvage value is different from the book value of the asset, then there is a

tax effect • Book value = initial cost – accumulated depreciation • After-tax salvage = salvage – T(salvage – book value) CASE I: Regency Integrated Chips – Expansion

Regency Integrated Chips (RIC)’s research and development department has developed a small computer designed to control home appliances. Once programmed, the computer will automatically control the heating and air-conditioning systems, security system, hot water heater, and even small appliances such as a coffee maker. This project has now reached the stage where a decision must be made on whether to go forward with production.

RIC’s marketing vice-president believes that annual sales would be 20,000 units if the units were priced at 3,000 baht each. RIC expects no growth in sales, and it believes that the unit price will rise by 2 percent each year. The engineering department has reported that the project will require additional manufacturing space, and RIC currently has an option to purchase an existing building, at a cost of 12 million baht, which would meet this need. The building would be bought and paid for on 31st December 2004, and for depreciation purposes it would fall into the MACRS 39-year class.

The necessary equipment would be purchased and installed in late 2004, and it would also be paid for on 31st December 2004. The equipment would fall into the MACRS 5-year class, and it would cost 8 million baht, including transportation and installation. Moreover, the project would also require an initial investment of $6 million in net operating working capital, which is also be made on 31st December 2004. Then, each subsequent years, required NOWC equal to 10 percent of the upcoming year’s sales.

The project’s estimated economic life is four years. At the end of that time,

the building is expected to have a market value of 7.5 million baht, whereas the equipment would have a market value of 2 million baht.

The production department has estimated that variable manufacturing costs

would be 2,100 baht per unit, and that fixed overhead costs, excluding depreciation, would be 8 million baht per year. They expect variable costs to rise by 2 percent per


year, and fixed costs to rise by 1 percent per year. Depreciation expenses would be determined in accordance with MACRS rates.

RIC’s tax rate is 40 percent; its cost of capital is 12 percent; and, for capital budgeting purposes, the company’s policy is to assume that operating cash flows occur at the end of each year. Because the plant would begin operations on 1st January 2005, the first operating cash flows would occur on 31st December 2005

Several other points should be noted: (1) RIC is a relatively large corporation, which sales of more than 4,000 million baht, and it takes on many investments each year. Thus, if the computer control project does not work out, it will not bankrupt the company – management can afford to take a chance on the computer project. (2) If the project is accepted, the company will be contractually obligated to operate it for its full four-year life. Management must make this commitment to its component suppliers. (3) Returns on this project would be positively correlated with returns on RIC’s other projects and also with the stock market - the project should do well if other parts of the firm and the general economy are strong.

Assume that you have been assigned to conduct the capital budgeting analysis.

For now, assume that the project has the same risk as an average project, and use the corporate weighted average cost of capital, 12 percent. Depreciation Schedule

Years 1 2 3 4 Building Depr'n Rate 1.3% 2.6% 2.6% 2.6% Building Depr'n Ending Book Value Equipment Depr'n Rate 20.0% 32.0% 19.20% 11.52% Equipment Depr'n Ending Book Value

Net Salvage Values in 2008 Building Equipment Total Estimated Market Value in 2006 Book Value in 2006 Expected Gain or Loss Taxes paid or tax credit Net cash flow from salvage


Projected Net Cash Flows Years (Time line of annual cash flows) 0 1 2 3 4 Investment Outlays: Long-Term Assets Building Equipment Operating Cash Flows over the Project's Life Units sold Sales price per unit Variable costs per unit Sales revenue Variable costs Fixed operating costs Depreciation (building) Depreciation (equipment) Operating income before taxes (EBIT) Taxes on operating income (40%) Net Operating Profit After Taxes (NOPAT) Add back: Depreciation (building) Depreciation (equipment) Cash Flows Due to Net Operating Working Capital Net Operating Working Capital Cash flow due to investment in NOWC Salvage Cash Flows: Long-Term Assets Total salvage cash flows Net Operating Cash Flow


Key Output and Appraisal of the Proposed Project Net Present Value (at 12%) Internal Rate of Return Modified Internal Rate of Return Profitability Index Discounted Payback Period Payback Period

Replacement Analysis • Remember that we are interested in incremental cash flows • If we buy the new machine, then we will sell the old machine • What are the cash flow consequences of selling the old machine today instead of at

the previously expected year? CASE II: Regency Integrated Chips – Replacement

A lathe for trimming molded plastics was purchased 10 years ago at a cost of 7,500 baht. The machine had an expected life of 15 years at the time it was purchased, and management originally estimated, and still believes, that the salvage value will be 1,000 at the end of the 15-year life. The machine is being depreciated on a straight-

line basis.

The R&D manager reports that a new special-purpose machine can be purchased for 12,000 baht (including freight and installation), and, over its five-year life, it will reduce labour and raw materials usage sufficiently to cut annual operating costs from 9,000 to 4,000 baht.

It is estimated that the new machine can be sold for 2,000 baht at the end of

five years; this is its estimated salvage value. The old machine’s actual current market value is 1,000 baht. If the new machine is acquired, the old lathe will be sold to another company rather than exchanged for the new machine.

The company’s tax rate is 40 percent, and the replacement project is of average

risk. Net operating working capital requirements will also increase by 1,000 baht at the time of replacement. By an IRS ruling, the new machine falls into the 3-year MACRS class, and, since the cash flows are relatively certain, the project’s cost of capital is only 11.5 percent versus 12 percent for an average-risk project.

Should the replacement be made?


Replacement Project Net Cash Flow Schedule Year: 0 1 2 3 4 5 Section I. Investment Outlay Cost of new equipment Market value of old equipment Tax savings on old equipment sale Increase in net operating WC Section II. Operating Inflows over the Project's Life Decrease in costs Depreciation on new machine Depreciation on old machine Operating income before taxes (EBIT) Taxes on operating income (40%) Net Operating Profit After Taxes (NOPAT) Add back: Depreciation Less: Depreciation

Annual Operating cash flow Section III.Terminal Year Cash Flows Estimated salvage value of new machine Tax on salvage value (new) Estimated salvage value of old machine Tax on salvage value (old) Return of net operating WC Total terminal cash flows Net Operating Cash Flow


Capital Budgeting Analysis Net Present Value (at 11.5%) Internal Rate of Return Modified Internal Rate of Return Profitability Index Discounted Payback Period Payback Period

Risk Analysis in Capital Budgeting

• Uncertainty about a project’s future profitability. • Measured by σNPV, σIRR, beta.

1. Sensitivity Analysis A tool that allows exploration of the impact of individual assumptions on a decision variable, such as a project’s net present value, by determining the effect of changing one variable while holding all others fixed. 2. Scenario Analysis

A more complex form of sensitivity analysis that provides for calculating the decision variable, such as net present value, when a whole set of assumptions changes in a particular way. 3. Monte Carlo Simulation

A sophisticated risk assessment technique that provides for calculating the decision variable, such as net present value, using a range or probability distribution of potential outcomes for each of a model’s assumptions.


Sensitivity Analysis • Shows how changes in a variable such as unit sales affect NPV or IRR. • Each variable is fixed except one. Change this one variable to see the effect on

NPV or IRR. • Answers “what if” questions, e.g. “What if sales decline by 30%?” % Deviation % Deviation

from NPV from Units NPVBase Case WACC 5,809 Base Case Sold $5,809

-30% 8.4% $9,030 -30% 14,000 -$3,628-15% 10.2% $7,362 -15% 17,000 $1,091

0% 12.0% $5,809 Base Case 0% 20,000 $5,80915% 13.8% $4,363 15% 23,000 $10,52830% 15.6% $3,014 30% 26,000 $15,247

% Deviation % Deviationfrom Variable NPV from Growth NPV

Base Case Cost $5,809 Base Case Rate % $5,809-30% $1.47 $29,404 -30% -30% -$4,923-15% $1.79 $17,607 -15% -15% -$115

0% $2.10 $5,809 Base Case 0% 0% $5,80915% $2.42 -$5,988 15% 15% $12,98730% $2.73 -$17,785 30% 30% $21,556

% Deviation % Deviationfrom Sales NPV from Fixed NPV

Base Case Price $5,809 Base Case Costs $5,809-30% $2.10 -$27,223 -30% $5,600 $10,243-15% $2.55 -$10,707 -15% $6,800 $8,026

0% $3.00 $5,809 Base Case 0% $8,000 $5,80915% $3.45 $22,326 15% $9,200 $3,59330% $3.90 $38,842 30% $10,400 $1,376

GROWTH RATE, UNITSVARIABLE COSTS

1st YEAR UNIT SALESWACC

SALES PRICE FIXED COSTS

Deviationfrom Sales Variable Growth Year 1 Fixed

Base Case Price Cost/Unit Rate Units Sold Cost WACC-30% ($27,223) $29,404 ($4,923) ($3,628) $10,243 $9,030-15% ($10,707) $17,607 ($115) $1,091 $8,026 $7,3620% $5,809 $5,809 $5,809 $5,809 $5,809 $5,80915% $22,326 ($5,988) $12,987 $10,528 $3,593 $4,36330% $38,842 ($17,785) $21,556 $15,247 $1,376 $3,014

Range 66,064 47,189 26,479 18,875 8,867 6,016

NPV at Different Deviations from Base


Table 12-3. Scenario Analysis (Dollars in Thousands) SquaredDeviation

Sales Unit Variable Growth TimesProbability Price Sales Costs Rate NPV Probability

25% $3.90 26,000 $1.47 30% $146,180 3,294,458,65750% $3.00 20,000 $2.10 0% $5,809 327,072,28225% $2.10 14,000 $2.73 -30% ($32,257) 1,012,583,996

4634114935

Expected NPV = sum, prob times NPV $31,385Standard Deviation = Sq Root of column I sum $68,074Coefficient of Variation = Std Dev / Expected NPV 2.17

Scenario

Worst Case Base CaseBest Case

($30,000)

($20,000)

($10,000)

$0

$10,000

$20,000

$30,000

$40,000

-30% -15% 0% 15% 30%Deviation from Base-Case Value (%)

NPV ($)Sales priceVariable costGrowth rateUnits soldFixed costWACC

Results of Sensitivity Analysis • Steeper sensitivity lines show greater risk. Small changes result in large declines in

NPV. • The company should worry about the accuracy of those steeper lines than those

less steep. What are the weaknesses of sensitivity analysis? • Does not reflect diversification. • Says nothing about the likelihood of change in a variable, i.e. a steep sales line is not

a problem if sales won’t fall. • Ignores relationships among variables. Why is sensitivity analysis useful? • Gives some idea of stand-alone risk. • Identifies dangerous variables.

Scenario Analysis • Examines several possible situations, usually worst case, most likely case, and best

case. • Provides a range of possible outcomes.


Portfolio Models Dollar Returns and Percentage Returns Total Return = Income + Capital Gain (Loss) Total percentage return equals the sum of the investment’s yield and its percentage capital gain or loss. Total Percentage Return = Total Return

Initial Investment Example: Dollar Returns and Percentage Returns

Soren purchases 100 shares of Hop-On Air stock for €20 per share. A year later, the stock pays a dividend of €0.80 per share and sells for €24. Meanwhile, Sven purchases 50 shares of Hydro Power Corp. for €12 per share. Hydro Power shares pay no dividends, but at the end of the year, the stock sells for €20. Compute dollar return and percentage return for Soren and Sven. Distribution of Historical Stock Returns Economy Prob. T-Bill Alta Repo Am F. MP

Recession 0.10 8.0% -22.0% 28.0% 10.0% -13.0% Below avg. 0.20 8.0 -2.0 14.7 -10.0 1.0 Average 0.40 8.0 20.0 0.0 7.0 15.0 Above avg. 0.20 8.0 35.0 -10.0 45.0 29.0 Boom 0.10 8.0 50.0 -20.0 30.0 43.0

1.00


Expected Value • A statistical measure of the mean or average value of

the possible outcomes. Operationally, it is defined as the weighted average of the possible outcomes with the weights being the probability of occurrence.

Expected Return • A forecast of the return that an asset will earn over

some period of time.

E [Ri] = expected rate of return

E [Ri]

T-bill

Alta

Repo Men

Am. Foam

Market Portfolio

Variance • A measure of volatility equal to the sum of squared deviations

from the mean divided by one less than the number of observations in the sample.

• A measure of volatility equal to the sum of squared deviations from the mean divided by the number of observations in the population.

Standard Deviation • A measure of volatility equal to the square root of variance

.Px R = ]E[Rn

1=ii i i∑

∑

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RER

n

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1

2

1

2

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][][

Variance deviation Standard 2σσ


σi2 σi

T-bill

Alta

Repo Men

Am. Foam

Market Portfolio

Coefficient of Variation

A standardised measure of the risk per unit of return

CV = Standard deviation

Expected return

C.V.

T-bill

Alta

Repo Men

Am. Foam

Market Portfolio

Statistical Properties of Normal Distribution


Probability distribution

Rate ofreturn (%)50150-20

Stock X

Stock Y

Which stock is riskier? Why?

Example: Which Stock is Riskier? Why?

Investment Risk

• Typically, investment returns are not known with certainty.

• Investment risk pertains to the probability of earning a return less than that expected.

• The greater the chance of a return far below the expected return, the greater the risk.

Covariance (σ1,2) A measure of the direction of relationship between two variables.

( )( )x,y iσ = p x - x y - y∑

T-bill Alta Repo Men Am. Foam Market Port

T-bill

Alta

Repo Men

Am. Foam

Market Port


Correlation (ρ1,2)

Correlation

• The tendency of two variables to move together. Correlation Coefficient

• A measure of the degree of relationship between two variables.

1,2 1 2 1,2 ρ σ σ σ=

T-bill Alta Repo Men Am. Foam Market Port

T-bill

Alta

Repo Men

Am. Foam

Market Port

http://www.zurich.com.ve/site/empresas/i/Juego/risk01.htm

http://www.zurich.com.ve/site/empresas/i/Juego/risk01.htm


Portfolio Theory A group of individual assets held in combination. An asset that would be relatively risky if held in isolation may have little, or even no, risk if held in a well-diversified portfolio. Example:

If you form a two-stock portfolio by investing US$50,000 in Alta and US$50,000 in Repo, what is the portfolio’s expected rate of return and standard deviation? Naive Method

Economy Prob. Alta Repo Portfolio

Recession 0.10 -22.0% 28.0%

Below avg. 0.20 -2.0 14.7

Average 0.40 20.0 0.0

Above avg. 0.20 35.0 -10.0

Boom 0.10 50.0 -20.0

1.00


Portfolio Expected Return E[Rp] E[Rp] is a weighted average: Two-Stock Portfolio Standard Deviation Two-Stock Portfolios • Two stocks can be combined to form a riskless portfolio if ρ = -1.0. • Risk is not reduced at all if the two stocks have ρ = +1.0. • In general, stocks have ρ ≈ 0.65, so risk is lowered but not

eliminated. • Investors typically hold many stocks.

E[Rp] = Σ wi x E[Ri]n

i = 1

2 2 2 21 1 2 2 1 2 1,2 1 2

2 2 2 21 1 1 2 1 1 1,2 1 2

1 2

2

(1 ) 2 (1 )

1

p

p

W W W W

W W W W

w w

σ σ σ ρ σ σ

σ σ σ ρ σ σ

= + +

= + − + −

+ =


Power of Diversification Diversification

• The act of investing in many different assets rather than just a few. Systematic Risk / Non-Diversifiable Risk / Market Risk

• Risk that cannot be eliminated through diversification. Unsystematic Risk / Diversifiable Risk / Company Specific Risk

• Risk that can be eliminated through diversification. Stand-alone risk = Market risk + Diversifiable risk What would happen to the risk of an average 1-stock portfolio as more randomly selected stocks were added? • σp would decrease because the added stocks would not be

perfectly correlated, but E[Rp] would remain relatively constant. • As more stocks are added, each new stock has a smaller risk-

reducing impact on the portfolio. • σp falls very slowly after about 40 stocks are included. The

lower limit for σp is about 20% = σM . • By forming well-diversified portfolios, investors can eliminate

about half the riskiness of owning a single stock.

Number of Securities (Assets) in PortfolioNumber of Securities (Assets) in Portfolio

Port

folio

Ris

k, σ

k p

Nondiversifiable RiskNondiversifiable Risk

Diversifiable RiskDiversifiable Risk

Total riskTotal risk

1 5 10 15 1 5 10 15 20 25 20 25 Number of Securities (Assets) in PortfolioNumber of Securities (Assets) in Portfolio

Port

folio

Ris

k, σ

k p

Nondiversifiable RiskNondiversifiable Risk

Diversifiable RiskDiversifiable Risk

Total riskTotal risk

1 5 10 15 1 5 10 15 20 25 20 25


The Capital Asset Pricing Model (CAPM) The Capital Asset Pricing Model (CAPM) states that the expected return on a specific asset equals the risk-free rate plus a premium that depends on the asset’s beta and the expected risk premium on the market portfolio

ki = kRF + [ kM – kRF ] βi Required rate of return ki

• The rate of return investors require from an investment given the risk of the investment.

Market Portfolio (kM)

• A portfolio that contains some of every asset in the economy. Market Risk Premium [ kM – kRF ] βi

• The additional return earned (or expected) on the market portfolio over and above the risk-free rate.

Beta βi

• A standardised measure of the risk of an individual asset, one that captures only the systematic component of its volatility.

bi = (ρiM σi σM)

σM2

Example

Calculate beta for T-bills, Alta, Repo Men, Am. Foam, and market portfolio.

beta

T-bill

Alta

Repo Men

Am. Foam

Market Portfolio


Assumptions in CAPM

• Investors all think in terms of a single holding period. • All investors have identical expectations. • Investors can borrow or lend unlimited amounts at the risk-free rate. • All assets are perfectly divisible. • There are no taxes and no transactions costs. • All investors are price takers, that is, investors’ buying and selling won’t

influence stock prices. • Quantities of all assets are given and fixed. How are betas calculated?

• In addition to measuring a stock’s contribution of risk to a portfolio, beta also which measures the stock’s volatility relative to the market.

• Run a regression line of past returns on Stock i versus returns on the market.

• The regression line is called the characteristic line. • The slope coefficient of the characteristic line is defined as the

beta coefficient. Using a Regression to Estimate Beta

• Run a regression with returns on the stock in question plotted on the Y axis and returns on the market portfolio plotted on the X axis.

• The slope of the regression line, which measures relative volatility, is defined as the stock’s beta coefficient, or b.

Security Market Line (SML)

• Represents, in a graphical form, the relationship between the risk of an asset as measured by its beta and the required rates of return for individual securities.

ββMM = 1.01.0Systematic Risk (Beta)

RRff

RRMM

Req

uire

d R

etur

nR

equi

red

Ret

urn

RiskRiskPremiumPremium

RiskRisk--freefreeReturnReturn


Example: beta calculation

Security Expected Return beta Required Return Price

T-bill

Alta

Repo Men

Am. Foam

Market Portfolio

Calculating Beta in Practice

• Many analysts use the S&P 500 to find the market return. • Analysts typically use four or five years’ of monthly returns to establish

the regression line. • Some analysts use 52 weeks of weekly returns. How is beta interpreted?

• If b = 1.0, stock has average risk. • If b > 1.0, stock is riskier than average. • If b < 1.0, stock is less risky than average. • Most stocks have betas in the range of 0.5 to 1.5. • Can a stock have a negative beta?

Systematic Risk (Beta)

RRff

Req

uire

d R

etur

nR

equi

red

Ret

urn

Direction ofMovement

Direction ofMovement

Stock Y Stock Y (Overpriced)

Stock X (Underpriced)


Portfolio Beta Calculation

• Beta of a portfolio is the weighted average of individual security beta in the portfolio

P iβ = w βi∑ Example: Portfolio Beta Calculation (1)

Calculate beta for a portfolio that invests US$50,000 in Alta and US$50,000 in Repo.

Example: Portfolio Beta Calculation (2)

Calculate the beta of the portfolio described in the following table. Stock Beta € Invested

Siemens 1.20 €7,500 Unilever 0.74 €9,000 L’ Oreal 0.51 €7,500 Nokia 1.50 €6,000


Impact of Inflation Change on SML Impact of Risk Aversion Change

SML1

Original situation

Required Rate of Return r (%)

SML2

0 0.5 1.0 1.5 2.0

181511

8

New SMLΔ I = 3%

rM = 18%rM = 15%

SML1

Original situation

SML2

After increasein risk aversion

Risk, bi

18

15

8

1.0

Δ RPM = 3%


Advance Contents Interpreting Regression Results • The R2 measures the percent of a stock’s

variance that is explained by the market. The typical R2 is:

o 0.3 for an individual stock o over 0.9 for a well diversified

portfolio • The 95% confidence interval shows the

range in which we are 95% sure that the true value of beta lies. The typical range is:

o from about 0.5 to 1.5 for an individual stock

o from about .92 to 1.08 for a well diversified portfolio

Are there problems with the CAPM tests? • Yes.

o Richard Roll questioned whether it was even conceptually possible to test the CAPM.

o Roll showed that it is virtually impossible to prove investors behave in accordance with CAPM theory.

What are our conclusions regarding the CAPM? • It is impossible to verify. • Recent studies have questioned its validity. • Investors seem to be concerned with both market risk and stand-alone

risk. Therefore, the SML may not produce a correct estimate of ri. • CAPM/SML concepts are based on expectations, yet betas are

calculated using historical data. A company’s historical data may not reflect investors’ expectations about future riskiness.

• Other models are being developed that will one day replace the CAPM, but it still provides a good framework for thinking about risk and return.

What is the difference between the CAPM and the Arbitrage Pricing Theory (APT)? • The CAPM is a single factor model. • The APT proposes that the relationship between risk and return is

more complex and may be due to multiple factors such as GDP growth, expected inflation, tax rate changes, and dividend yield.


Cost of Capital

The cost of capital is used primarily to make decisions which involve raising and investing new capital or marginal costs. • Weighted average cost of capital (WACC) • Weighted average of all required rate of return on each capital component • Depends on

o Component cost o Capital structure o Effective tax rate

What sources of long-term capital do firms use? What costs of long-term capital do firms incur? Component cost of debt

kd(1-T)

• kd is the marginal cost of debt capital. • The yield to maturity on outstanding L-T debt is often used as a measure of kd. • Interest is tax deductible, so After-Tax kd = Before-Tax kd (1-Tax) • Use nominal rate. • Flotation costs involved

Long-Term CapitalLong-Term Capital

Cost of DebtCost of Debt Cost of Preferred StockCost of Preferred Stock Common StockCommon Stock

Cost of Retained EarningsCost of Retained Earnings Cost of New Common StockCost of New Common Stock


Cost of DebtCost of Debt Cost of Preferred StockCost of Preferred Stock Common StockCommon Stock

Cost of Retained EarningsCost of Retained Earnings Cost of New Common StockCost of New Common Stock


Long-Term DebtLong-Term Debt Preferred StockPreferred Stock Common StockCommon Stock

Retained EarningsRetained Earnings New Common StockNew Common Stock


Long-Term DebtLong-Term Debt Preferred StockPreferred Stock Common StockCommon Stock

Retained EarningsRetained Earnings New Common StockNew Common Stock


Component cost of preferred stock (kp) • kp is the marginal cost of preferred stock. • The rate of return investors require on the firm’s preferred stock. • Preferred dividends are not tax-deductible, so no tax adjustments necessary. Just

use kp. • Nominal kp is used. • Our calculation ignores possible flotation costs. Component cost of equity ks and ke

• ks is the marginal cost of common equity using retained earnings. • The rate of return investors require on the firm’s common equity using new equity

is ke. Three ways to determine the cost of common equity, ks • CAPM: ks = kRF + (kM – kRF) β • DCF: ks = D1 / P0 + g ke = D1 / P0(1 – F) + g • Own-Bond-Yield-Plus-Risk Premium: ks = kd + RP

• Subjective • Simply add a judgmental risk premium of 3 to 5 percentage points to the

interest rate on the firm’s own long-term debt

Why is there a cost for retained earnings? • Earnings can be reinvested or paid out as dividends. • Investors could buy other securities, earn a return.

∞∞

+++

++

++

+=

)k(1D ...

)k(1D

)k(1

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Pp

3p

2p

1p

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p

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• If earnings are retained, there is an opportunity cost (the return that stockholders could earn on alternative investments of equal risk).

o Investors could buy similar stocks and earn ks. o Firm could repurchase its own stock and earn ks. o Therefore, ks is the cost of retained earnings.

Cost of retained earnings is cheaper than the cost of issuing new common stock • When a company issues new common stock they also have to pay flotation costs to

the underwriter. • Issuing new common stock may send a negative signal to the capital markets, which

may depress the stock price. Calculating the weighted average cost of capital WACC = wdkd(1-T) + wpkp + wc ks ke • The w’s refer to the firm’s capital structure weights. • The k’s refer to the cost of each component.

Break Point Calculation

Break Point = Maximum amount of fund before the cost increases Optimal percentage of fund

Choosing the Optimal Capital Budget • Finance theory says to accept all positive NPV projects. • Two problems can occur when there is not enough internally generated cash to fund

all positive NPV projects: o An increasing marginal cost of capital. o Capital rationing

Increasing Marginal Cost of Capital • Externally raised capital can have large flotation costs, which increase the cost of

capital. • Investors often perceive large capital budgets as being risky, which drives up the

cost of capital. • If external funds will be raised, then the NPV of all projects should be estimated

using this higher marginal cost of capital.


Illustration Case US Engineering Inc. (UE) has the following capital structure, which it considers to be optimal: Debt US$ 5,000,000 Preferred Stock 3,000,000 Common Equity 12,000,000 US$ 20,000,000 UE’s expected net income this year is US$34,285.72; its established dividend payout ratio is 30 percent; its return on equity is 12.86 percent; its marginal tax rate is 40 percent; and investors expect earnings and dividends to grow at a constant rate in the future. UE paid a dividend of US$3.60 per share last year, and its stock currently sells at a price of US$60 per share. UE can obtain new capital in the following ways: Common: New common stock has a flotation cost of 10 percent for up to US$12,000 of new stock and 20 percent for all common stock over US$12,000. Preferred: New preferred stock with a dividend of US$11 can be sold to the public at a price of US$100 per share. However, flotation costs of US$5 per share will be incurred up to US$7,500 of preferred stock, and flotation costs will rise to 10 percent on all preferred stock over US$7,500. Debt: Up to US$5,000 of 10-year debt can sold at a coupon rate of 8 percent, semi-annually coupon payment at a price of US$770.60;

Debt in the range of US$5,001 to US$10,000 must carry a coupon of 10 percent rate of interest, 10-year semi-annual coupon payment at a price of US$788.12;

For all debts over US$10,000 will be issued at a coupon rate of 12 percent, 10-year semi-annual coupon payment at a price of US$803.64.

UE has the following independent investment opportunities:

Project Cost at t = 0 Annual Net Cash Flows Project Life A US$10,000 US$ 2,191.20 7 years B 10,000 3,154.42 5 C 10,000 2,170.18 8 D 20,000 3,789.48 10 E 20,000 5,427.84 6


a. Find the break-points in the MCC schedule.

Break point (debt1) = Break point (debt2) =

Break point (preferred stock) =

Break point (equity1) =

Break point (equity2) =

Optimal Capital Structure and Range of each capital structure component

Debt 5M

Preferred stock 3M

Equity 12M


b. Determine the cost of debt for each capital structure component.

Cost of debt before tax (kd) = yield-to-maturity (YTM)

New debt

Cumulative new debt

Cost of debt (kd)

c. Determine the cost of preferred stock for each capital structure component.

Cost of preferred stock (kp) = return on preferred stock (kp)

New preferred stock

Cumulative new preferred stock

Cost of preferred stock (kp)


d. Determine the cost of equity for each capital structure component.

Cost of equity1 = cost of retained earnings (ks) = return on existing common share (k) ***** Price is not reduced by flotation cost *****

Cost of equity2+ = cost of new common stock (ke) ***** Price is reduced by flotation cost *****

New equity

Cumulative new equity

Cost of equity ks = Ke1 = ke2 =


e. Calculate the weighted average cost of capital in the interval between each

break in the MCC schedule. WACC = wdkd(1-T) + wpkp + wc ks ke

WACC1 WACC2 WACC3 WACC4 WACC5

Cost of debt

5,000 + 5,000 + 2,500 + 2,500

5,000 10,000 12,500 15,000

Cost of preferred stock

3,000 + 3,000 + 1,500 + 1,500

3,000 6,000 7,500 9,000

Cost of equity

12,000 + 12,000 + 6,000 + 6,000

12,000 24,000 30,000 36,000

New capital 20,000 + 20,000 + 10,000 + 10,000

Cumulative capital 20,000 40,000 50,000 60,000

WACC1 WACC2 WACC3 WACC4 WACC5

Marginal cost of capital


f. Calculate the IRR for all projects.

Project A B C D E

Initial Investment 10,000 10,000 10,000 20,000 20,000


IRR rule: invest in projects ranging from highest IRR to lowest IRR

Project

Initial Investment

Cumulative Investment


g. Construct a graph showing the MCC and IOS schedules. h. Which projects should UE accept? i. What is the average cost of all projects invested?


Firm Valuation: Free Cash Flows Model

Assets Liabilities and Equities

Free Cash Flows to the Firm

FCF is the amount of cash available from operations for distribution to all investors (including stockholders and debtholders) after making the necessary investments to support operations.

A company’s value depends upon the amount of FCF it can generate. Five uses of free cash flows: 1. Pay interest on debt. 2. Pay back principal on debt. 3. Pay dividends. 4. Buy back stock. 5. Buy non-operating assets (e.g., marketable securities, investments in other companies, etc.) Value of operations: Corporate Value Liabilities and Equities

Value of Operating assets +

Value Non-operating assets

Debtholders

Preferred stock holders

Common stock holders

∑∞

= +=

1 )1(tt

tOp WACC

FCFV


CASE: Henley Corporation The Henley Corporation is a privately held company specialising in lawn care products and services. The most recent financial statements are shown below:

Balance Sheets for December 31 (Millions of Dollars)

Assets 2004 Liabilities and Equity 2004Cash 8.0$ Accounts Payable 16.0$ Marketable Securities 20.0 Notes payable 40.0 Accounts receivable 80.0 Accruals 40.0

Inventories 160.0 Total current liabilities 96.0$

Total current assets 268.0$ Long-term bonds 300.0$ Net plant and equipment 600.0 Preferred stock 15.0$

Total Assets 868.0$ Common Stock (Par plus PIC) 257.0$

Retained earnings 200.0

Common equity 457.0$

Total liabilities and equity 868.0$

Income Statement for the Year Ending December 31 (Millions of Dollars)

2004Net Sales 800.0$ Costs (except depreciation) 576.0$ Depreciation 60.0$

Total operating costs 636.0$

Earning before int. & tax 164.0$ Less interest 32.0$

Earning before taxes 132.0$ Taxes (40%) 52.8$

Net income before pref. div. 79.2$ Preferred div. 1.4$

Net income avail. for com. div. 77.9$

Common dividends 31.1$ Addition to retained earnings 46.7$

Number of shares (in millions) 10 Dividends per share 3.11$


The ratios and selected information for the current and projected years are shown below: Inputs Actual Projected Projected Projected Projected

2004 2005 2006 2007 2008

Sales Growth Rate 15% 10% 6% 6%Costs / Sales 72% 72% 72% 72% 72%Depreciation / Net PPE 10% 10% 10% 10% 10%Cash / Sales 1% 1% 1% 1% 1%Acct. Rec. / Sales 10% 10% 10% 10% 10%Inventories / Sales 20% 20% 20% 20% 20%Net PPE / Sales 75% 75% 75% 75% 75%Acct. Pay. / Sales 2% 2% 2% 2% 2%Accruals / Sales 5% 5% 5% 5% 5%Tax rate 40% 40% 40% 40% 40%Weighted average cost of capital (WACC) 10.5% 10.5% 10.5% 10.5% 10.5% a. Forecast the parts of the income statement and balance sheets necessary to calculate free

cash flow.

Actual Projected Projected Projected Projected

2004 2005 2006 2007 2008

Net Sales 800.0$

Costs (except depreciation) 576.0$ Depreciation 60.0$

Total operating costs 636.0$

Earning before int. & tax 164.0$


Operating Assets 2004 2005 2006 2007 2008

Cash 8.0$

Accounts receivable 80.0$

Inventories 160.0$

Net plant and equipment 600.0$

Operating Liabilities

Accounts Payable 16.0$

Accruals 40.0$

Partial Income Statement for the Year Ending December 31 (Millions of Dollars)

Partial Balance Sheets for December 31 (Millions of Dollars)


b. Calculate free cash flow for each projected year. Also calculate the growth rates of free cash flow each year to ensure that there is constant growth (i.e., the same as the constant growth rate in sales) by the end of the forecast period.


Calculation of FCF 2004 2005 2006 2007 2008

Operating current assetsOperating current liabilities

Net operating working capitalNet PPE

Net operating capital

NOPATInvestment in operating capital na

Free cash flow na

Growth in FCF na na

Growth in sales c. Calculate the value of operations. (Hint: first calculate the horizon value at the end of the

forecast period, which is equal to the value of operations at the end of the forecast period. Assume that growth beyond the horizon is 6 percent.)


2004 2005 2006 2007 2008

Free cash flow

Long-term constant growth in FCF

Weighted average cost of capital (WACC) 10.5% 10.5% 10.5% 10.5% 10.5%

Horizon value

FCF + horizon value

Value of operations (PV of FCF + HV) d. Calculate the price per share of common equity as of 12/31/2004.

2004Value of OperationsPlus Value of Mkt. Sec.

Total Value of CompanyLess Value of DebtLess Value of Pref.

Value of Common StockNumber of sharesPrice per share


FINANCIAL ANALYSIS OF LEASEING Who are the two parties to a lease transaction?

• The lessee, who uses the asset and makes the lease, or rental, payments. • The lessor, who owns the asset and receives the rental payments. • Note that the lease decision is a financing decision for the lessee and an investment decision for

the lessor. What are the five primary lease types?

• Operating lease o Short-term and normally cancelable o Maintenance usually included

• Financial lease o Long-term and normally noncancelable o Maintenance usually not included

• Sale and leaseback • Combination lease • "Synthetic" lease How does leasing affect a firm’s balance sheet? • For accounting purposes, leases are classified as either capital or operating. • Capital leases must be shown directly on the lessee’s balance sheet. • Operating leases, sometimes referred to as off-balance sheet financing, must be disclosed in the

footnotes. Classification as Capital Lease Lease must be capitalised; if one or more of the following conditions exist:

1. Under the terms of the lease, ownership of the property is effectively transferred from the lessor to the lessee.

2. The lessee can purchase the property at less than its true market value when the lease expires.

3. The lease runs for a period equal to or greater than 75% of the asset’s life. Thus, if an asset has a ten-year life and the lease is written for eight years, the lease must be capitalised.

4. The present value of the lease payments is equal to or greater than 90% of the initial value of the asset.


ILLUSTRATION CASE Anderson Company plans to acquire equipment, with a 5-year MACRS life (but a 10-year useful life), at a cost of $10 million (delivery and installation included). Anderson can borrow the $10 million at 10%, interest only until the repayment in 5 years. Alternatively, Anderson can lease the equipment for five years at a rental charge of $2.65 million per year, at the beginning of the year. The equipment, when used, will have an estimated net salvage value of $2 million. If Anderson buys, it will own the equipment at the end of five years. If Anderson leases, it will not exercise the option to buy the equipment. The lease includes maintenance service, whereas if bought, the equipment would require maintenance provided by a service contract for $500,000 per year, at the end of the year. The equipment falls into the MACRS five-year class life, and the depreciable basis is the original cost. Anderson's tax rate is 35%. MACRS 5-year Depreciation Schedule

Year 1 2 3 4 5 6 Depr. Rate 20% 32% 19% 12% 11% 6% Depr. Exp. $2,000 $3,200 $1,900 $1,200 $1,100 $600

Starting book value $10,000 $8,000 $4,800 $2,900 $1,700 $600 Remaining book value $8,000 $4,800 $2,900 $1,700 $600 $0

EVALUATION BY THE LESSEE Cost of Owning Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 After-tax loan payments Maintenance Cost Tax savings from maintenance costs Tax savings from depreciation Residual value Tax on residual value Net cash flow

PV ownership cost


Cost of Leasing Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Lease payment Tax savings from lease Net cash flow PV of leasing

PV ownership cost PV of leasing Net Advantage to Leasing

EVALUATION BY THE LESSOR The lessor for Anderson Equipment Company is a wealthy individual whose marginal federal plus state tax rate is 40%. The investor can buy 5-year bonds with a 9% yield to maturity. All other terms of the lease are the same as above. Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Net purchase price Maintenance cost Tax savings from maintenance costs Tax savings from depreciation Lease payment Tax on lease payment Residual value Tax on residual value Net cash flows NPV IRR

MIRR


WORKING CAPITAL MANAGEMENT

Terminology • (Gross) Working capital: Total current assets. • Net working capital: Current assets - Current liabilities. • Working capital policy: Firm’s policies regarding:

o Target level of each current asset. o How current assets are financed.

• Working capital management: Includes both establishing working capital policy and

carry out them to the day-to-day operation and control of: o Cash o Inventories o Receivables o Short-term liabilities

Net working capital (redefined) • Current assets – Current liabilities • Short-term assets that are free from short-term obligation • Short-term assets that are financed by long-term fund Working Capital Management • Short-term financial operations affect the firm’s current assets and current

liabilities. The firm starts with some cash on hand and receives information on the demand for its product. On the basis of this forecast the firm orders materials to produce inventories of finished goods (a current asset,) which it then sells to customers. When the firm orders materials, it creates an account payable (a current liability.) When the firm sells inventory, it either receives cash directly from the sale or receives a promise to pay from the customer – an account receivable. When the firm collects the account receivable, it receives cash. This cycle repeats itself many times during the course of the year, and the course of the year, and the firm typically needs external financing, such as short-term bank loans, to complete each working capital cycle. (In this figure, squares represent accounts, and circles represent actions.)


Accounts Receivable Inventory Accounts

PayableMake Sales

ObtainInformation

aboutDemand

Increases

Retained Earnings(Profit)

Place Order forInventory

CollectReceivables Cash

Loan (Notes Payable)

Repay Loans Borrow

PayAccountsPayable

The Operating Cycle • Operating cycle The time between purchasing the inventory and collecting the cash • Inventory period The time required to purchase and sell the inventory • Accounts receivable period The time to collect on credit sales • Operating cycle = inventory period + accounts receivable period • Accounts payable period The time between purchase of inventory and payment for the inventory Cash Cycle • The time period for which we need to finance our inventory • Difference between when we receive cash from the sale and when we have to pay

for the inventory • Cash cycle = Operating cycle – accounts payable period


Example 1 SK Corp. spends, on average, 50 days to produce goods and sell them on credit. Its average collection time is 40 days and its deferral period is 30 days. What are its operating cycle, cash conversion cycle, and cash turnover? Example 2 DEB Company had sales of 1,825,000 baht in previous year. The gross profit margin was 35%. The ending accounts receivable were 160,000 baht. The ending inventories were 220,000 baht. The ending accounts payable and accruals were 180,000 baht. Find the operating cycle, cash conversion cycle. Assume there are 360 days in a year. Example 3 Assume there are 360 days in a year. Find the operating cycle and cash conversion cycle of the BCC Inc. in the following situations. a) Credit sales 12,000,000 baht

Ending accounts receivable 2,055,000 baht Ending inventories 2,475,000 baht Ending accounts payable 900,000 baht

b) Assume that sales in (a) were cash sales. c) Assume that sales in (a) were cash sales and that the firm bought goods in cash. d) Assume that sales in (a) were made on credit and that the company bought goods in

cash. Example 4 AC Shop is a shoe producer and wholesaler. On average, it pays the suppliers 35 days after purchases. It spends 16 days to produce shoes and sell them. Customers pay AC 60 days after credit sales are made. Currently, AC can produce 10 pairs a day, with a cost of 350 baht each. Assume there are 360 days a year. • Find AC’s cash conversion cycle • If AC produces 10 pairs a day, how much minimum operating cash does it need? • Assume that the additional minimum operating cash can be arranged by short-term

borrowing from the bank, which agrees to lend AC up to 100,000 baht. How should AC do if it - cannot reduce the product cost,

- maintains its production of 10 pairs a day, - cannot extend the time to pay its suppliers, and - cannot reduce its inventory days?


Cash Conversion Cycle Pattern • When cash conversion cycle is positive

o Cash conversion cycle < Operating cycle o Cash conversion cycle = Operating cycle o Cash conversion cycle > Operating cycle

• When cash conversion cycle is negative Cash Budget • A schedule showing cash receipts, cash disbursements, and cash balance for a firm

over a specified period usually done on a monthly basis • Forecast of cash inflows and outflows over the next short-term planning period

o Primary tool in short-term financial planning o Helps determine when the firm should experience cash surpluses and

when it will need to borrow to cover working-capital costs o Allows a company to plan ahead and begin the search for financing before

the money is actually needed Example: Cash Budget Information Financial data from 1st October 2005 to 31st December 2005 are as follows: • The firm’s sales are made on credit. A 2-percent cash discount is given to the

customers if payments are made within 10 days after purchases. The collection policies are as follows: collections within the month of sale, 20%; collections the month following the sale, 70%; collections the second month following the sale, 10%. All collections received within the month of sale are made within 10 days after purchases. Assume that the sale rate is constant and that there is no bad debt.

• The selling price is 50 baht per unit. Monthly sales in units are as follows: Actual sales August 100 units September 100 units Forecasted sales October 200 units November 300 units December 400 units January 2006 200 units • Wages are made in cash during the month they incur, and are expected as follows: October 750 baht November 1,000 baht December 1,250 baht


• The firm buys goods one month before sales are made. The total units bought are

just enough for the expected units sold next month. The gross profit margin (before cash discounts) is 30 percent on average. Payments are made one month after purchases, without cash discounts. Assume a constant monthly buying rate. The firm’s monthly safety stocks are constant at 120 units.

• Monthly rent payments, made in cash, are 250 baht. Income taxes are paid twice in

March and August of every year. Accrued dividends of 2,000 baht will be paid in cash in October. Monthly depreciation allowances are 750 baht. There is no purchase of fixed assets in the last quarter of 2005.

• Other cash expenses are as follows: October 150 baht November 150 baht December 200 baht • A minimum cash balance of 2,500 baht will be maintained during the cash budget

period. If the firm does not have enough cash, it will use a 12-percent short-term loan (overdraft or OD) from the bank. Borrowing, in multiples of 1,000 baht, will be made at the beginning of the month, while the repayment of principal, also in multiples of 1,000 baht, will be made at the end of the month when the firm cash balance is greater than the minimum monthly cash requirement. The interests of all loans are paid at the end of each month. Cash is kept as cash on hand.

• Assume that today is 30th September 2005. The balance sheet at the end of today

is as follows:

Cash Accounts receivable Inventory Net PPE Total assets

2,500 4,500 11,450 24,000 42,450

Accounts payable Accrued taxes Accrued dividends Short-term loan (12%) Long-term loan (15%) Common stock Retained earnings Total L&OE

7,000 2,000 2,000 1,000 10,000 10,700 9,750 42,450

Instructions: • Prepare the monthly cash budget for 3 months ended December 2005. Also

prepare the working paper for cash collection from sales and disbursement for purchases of goods.

• Find the amount of cash, accounts receivable, inventory, accounts payable, and short-term loan at the end of December 2005.

• Find the maximum loan amount needed during the last quarter of 2005.


WORKING PAPER (BAHT) For 3 months ended 31st December 2005

August September October November December January Cash collections from sales Units sold Sales(baht) Collections - within the month of sale - 1 month following the sale - 2 months following the sale

Total cash collected from sales

Cash disbursements for purchases Net units bought Net purchase (baht) Disbursements - 1 month following the purchase

Total cash disbursed for purchases CASH BUDGET (BAHT)

For 3 months ended 31st December 2005 October November December Cash collections

Total cash collections Cash disbursements

Total cash disbursements Net cash received (paid) Beginning cash balance Cash surplus (deficit) Minimum cash balance Principal borrowed (repaid) Interest received (paid) Ending cash balance Cumulative new amount of (ST) loan


Redo: if Net cash received (paid) – 1,325 – 1,630 4,000 Beginning cash balance 2,500 Cash surplus (deficit) 1,175 Minimum cash balance 2,500 2,500 2,500 Principal borrowed (repaid) 2,000 Interest received (paid) – 20 Ending cash balance 3,155 Cumulative new amount of (ST) loan 2,000 Warnings • If cash inflows and outflows are not uniform during the month, we could seriously

understate the firm’s peak financial requirements. Our example shows the situation expected on the last day of each month, but on any given day during the month it could be quite different. For example, if all payments had to be made on the fifth of each month, but collections came in uniformly throughout the month, the firm would need to borrow much larger amount that those calculated. In this case, daily cash budget should be prepared

• Because the cash budget represents a forecast, all the values in the table are

expected values. If actual sales, purchases, and so on are different from the forecasted level, the projected cash deficits and surpluses will be different.

Compensating Balance A minimum checking account balance that a firm must maintain with a bank to compensate the bank for services rendered or to making the loan; generally equal to 10 to 20 percent of the loans outstanding. Example We have a $500,000 line of credit with a 15% compensating balance requirement. The quoted interest rate is 9%. We need to borrow $150,000 for inventory for one year. • How much do we need to borrow? • What interest rate are we effectively paying?


Factoring Example Last year your company had average accounts receivable of $2 million. Credit sales were $24 million. You factor receivables by discounting them 2%. What is the effective rate of interest? Term of Sale • Immediate payment – Cash before delivery (CBD) – Cash on delivery (COD) • Ordinary terms – net 30 (or n/30) – 2/10, net 30 (or 2/10, n/30) • Monthly billing – net 30, EOM – 1/10, net 30, EOM • Seasonal dating – net 60, 1st October dating – 2/30, n/60, 1st October dating Terms of Sale • Basic Form: 2/10 net 45

–2% discount if paid in 10 days –Total amount due in 45 days if discount not taken

• Buy $500 worth of merchandise with the credit terms given above –Pay $500(1 - .02) = $490 if you pay in 10 days –Pay $500 if you pay in 45 days

Implied interest rate when customers do not take the discount Credit Terms SAR (%) Comparison Costs of Trade Credits

1/10, net 30

2/10, net 30

1/15, net 30

1/10, net 45


International Financial Management What is an international corporation? • An international corporation is one that operates in two or more countries. • At one time, most multinationals produced and sold in just a few countries. • Today, many multinationals have world-wide production and sales. Why do firms expand into other countries? • To seek new markets. • To seek new supplies of raw materials. • To gain new technologies. • To gain production efficiencies. • To avoid political and regulatory obstacles. • To reduce risk by diversification. What are the major factors that distinguish international from domestic financial management? • Currency differences • Economic and legal differences • Language differences • Cultural differences • Government roles • Political risk Exchange Rate Quotations • A direct quotations gives the amount of Thai baht required to exchange one unit of

foreign currency • An indirect quotation gives the amount of a foreign currency required to exchange

one Thai Baht.

What is a cross rate? • A cross rate is the exchange rate between any two currencies that calculated from

2 quotations of 3 currencies • Originally, cross rate can be calculated by eliminating US dollars, hence, cross rate

is not involved with US dollars Exchange Rate Risk

Exchange rate risk is the risk that the value of a cash flow in one currency translated from another currency will decline due to a change in exchange rates. Spot Rates and Forward Rates • A spot rate is the rate applied to buy currency for immediate delivery • A forward rate is the rate applied to buy currency at some agreed-upon future date


Forward Premium/Discount • If the Thai Baht buys fewer units of a foreign currency in the forward than in the

spot market, the foreign currency is selling at a premium. • In the opposite situation, the foreign currency is selling at a discount. • The primary determinant of the spot/forward rate relationship is relative interest

rates. International Parity Conditions • Purchasing Power Parity • International Fisher Effect • Interest Rate Parity • Forward Rate as an Unbiased Estimator of Future Spot Rate International Fisher Effect • International Fisher Effect is the relationship between the spot exchange rates

over time and the differentials between comparable interest rates Here, iH = periodic interest rate in the home country. iF = periodic interest rate in the foreign country. Interest rate parity • Interest rate parity is the difference in the national interest rates for securities

of similar risk and maturity should be equal to, but opposite in sign to, the forward rate discount or premium for the foreign currency, except for transaction costs.

Here, iH = periodic interest rate in the home country. iF = periodic interest rate in the foreign country. Example • James Chang, a foreign exchange trader at J.P. Morgan Chase, can invest $5 million

or the foreign currency equivalent of the bank’s short-term funds. He has the following quotes:

o Spot exchange rate: DKr 7.5000/$ o 3-month forward rate: DKr 7.5372/$ o 3-month dollar interest: 3% per year o 3-month krone interest: 5% per year

• Identify James Chang investment opportunities and expected returns.

Future Spot RateSpot rate = 1 + iH

1 + iF.Future Spot Rate

Spot rate = 1 + iH1 + iF

.

Forward rateSpot rate = 1 + iH

1 + iF.Forward rate

Spot rate = 1 + iH1 + iF

.


Covered Interest Arbitrage • When spot and foreign exchange markets are not in equilibrium, the arbitrager who

recognises such an imbalance will move to take advantage of the disequilibrium by investing in whichever currency offers the higher return on a covered basis

Example • Assume that interest rates in the United States increase to 4% per year but all

other rates remain the same. Can James Chang make a 90-day covered interest arbitrage profit?

• Assume that interest rates in the Euro zone increase to 6% per year but all other rates remain the same. Calculate whether James Chang could make a 90-day covered interest arbitrage profit.

Types of Foreign Exchange Exposure • Accounting Exposure

o Changes in reported owners’ equity in consolidated financial statements caused by a change in exchange rates

• Operating Exposure o Change in expected future cash flows arising from an unexpected change

in exchange rates • Transaction Exposure

o Impact of setting outstanding obligations entered into before change in exchange rates but to be settled after change in exchange rates

Comparison of Exposures Translation Exposure Operating Exposure Time |

Moment in time when exchange rate changes

Transaction Exposure FOUR METHODS OF CURRENCY TRANSLATION METHODS • Current/Non-current Method • Monetary/Non-monetary Method • Temporal Method • Current Rate Method


Example: Dayton’s Exposure • Scout Finch is the chief financial officer of Dayton, a US-based manufacturer of

gas turbine equipment.

• She has just concluded negotiations for the sale of a turbine generator to Crown, a British firm, for ฃ1,000,000.

• This single sale is quite large in relation to Dayton’s present business.

• Dayton has no other current foreign customers, so the currency risk of this sale is of particular concern.

• The sale is made in March with payment due three months later in June.

• Scout has collected the following financial and market information for the analysis of her currency exposure problem.

• Spot exchange rate: US$1.7640/ฃ

• 3-month forward rate: US$1.7540/ฃ

• Dayton’s cost of capital: 12.00% p.a.

• UK 3-month borrowing rate: 10.00% p.a.

• UK 3-month investment rate: 8.00% p.a.

• US 3-month borrowing rate: 8.00% p.a.

• US 3-month investment rate: 6.00% p.a.

• June put option in the over-the-counter (bank) market for ฃ1 million: strike price = US$1.75; 1.50% premium

• June put option in the over-the-counter (bank) market for ฃ1 million: strike price = US$1.71; 1.00% premium

• Dayton’s foreign exchange advisory service forecasts that the spot rate in three months will be US$1.76/ฃ

• Like many manufacturing firms, Dayton operates on relatively narrow margins.

• Although Scout Finch and Dayton would be very happy if the pound appreciated versus the dollar, concerns centre on the possibility that the pound will fall.

• When Scout budgeted this specific contract, she determined that its minimum acceptable margin was at a sales price of US$1,700,000.

• The budget rate, the lowest acceptable dollar per pound exchange rate, was therefore established at US$1.70/ฃ.

• At any exchange rate below this budget rate, Dayton is actually losing money on the transaction.

• What are the alternatives for Dayton to manage the exposure?


• Four alternatives are available to Dayton to manage the exposure:

o Remain unhedged

o Hedge in the forward market

o Hedge in the money market

o Hedge in the option market


Comparison of Alternative Hedging Strategies Valuation of Cash Flows Under Various Hedging Alternatives

lecture note for the course - ms.src.ku · differences between these three financial statements?...

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