financial management assignment no.1 mba aiou sum spring 2010

Q. 1 Read the following case carefully, then give the answer of the questions given

below. The case:

Management Vs Shareholders

The annual shareholders meeting at the Mustafa Company brought some shock to

the management and the board of directors, when a group of shareholders

complained vigorously about the companies financial policies. However,

expressions of dissatisfaction by one or two shareholders had not been uncommon

in the past, the company’s senior executives were surprised by the degree of support

for the protest group voice by other stockholders.

Shareholder Complaints:

The initial target of the complaints was the company’s policy of not paying dividend

in almost two years. The chairman of the board, Mr. Salman Mustafa, responded that

the company had been experiencing poor profitability and had needed all available

funds to maintain its investments. Other shareholders rose to complain that the

company’s policy of not using borrowed money limited its ability to make

investments and pay dividends. Again the chairman responded, this time citing the

need for caution in the way the company was financed. He gave several examples of

multinational companies that had been heavy borrowers and had recently gone

bankrupt. To this another shareholder complained that, if the company were more

aggressive in its investment policies, there would be enough money for everything.

“Until you start taking some chances of new ideas and new products, our stock prices

will continue to go down instead of up. I could have earned more by putting my

money in government bonds”, complained the shareholder.

“Admit it”, another shareholder shouted, “You increase your wealth with your

fancy salaries and fancy offices couldn’t careless about us little investors. But then

why would you? Most of you don’t even own stock in the Company.” Loosing his

temper, the Chairman replied angrily that his own ancestors had founded the

Muhammad Waqas ~ Roll # AD511602 ~ MBA - 1-Financial Management ~ 562 ~ 1st Assignment

business and still owned almost 10 percent of the shares outstanding. He added that

the company, adding, “And I’m not saying that just because my son, Ahmed is

president. After all, nobody forced you to buy your stock and nobody’s forcing you

to keep it. In fact, I would personally be more than happy to buy your stock from

you with my own money. Now I ask the rest of you shareholders”, concluded the

Chairman broadly, “would you rather have your company be safe and secure or

bankrupt?”

1. Identify the principal financial policies being debated.

2. Considering the perspective of management only, what tendencies do you see

in each of these financial policies?

3. Considering the perspective of shareholders only, what tendencies do you see

in each of these financial policies?

4. The Mustafa Company’s creditors are not directly mentioned in the case, but

what do you think their preferences would be with regard to each of the

financial policies?

5. Use some ideas of your own to indicate how Mustafa Company’s shareholders

might persuade management to move in the direction of shareholders’

preferences.

Answer Q. 1

The essence of the debate is whether economic recovery and stabilisation of the financial

system are two distinct and unconnected events. The prevailing view is something like

the framework within which we need to engineer a global economic recovery is

macroeconomics. Since current macroeconomic theory deals only with Keynesian policy

(fiscal and monetary policy), the only tools we have are fiscal and monetary expansion.

The disposal of non-performing assets and injection of capital are necessary steps in

stabilising the financial system, but to the best of our knowledge there is no clear link


between this and a macroeconomic recovery. However, if we achieve an economic

recovery through fiscal and monetary policy, the volume of non-performing assets will

ease, eliminating the need for policies specifically designed to dispose of bad assets.

Signs of economic recovery are now emerging and fears of the crisis overwhelming the

world economy are starting to fade. Yet if the policy responses of US and European

governments toward the disposal of non-performing assets begin to falter, the financial

systems of Europe and the US will once again be vulnerable to recurring financial crises,

There have been those who have recognized that cleaning up banks’ balance sheets and

rehabilitating debtors are necessary preconditions for an economic recovery, but this

recognition has been based purely on empirical principles. The existing theoretical

structure of macroeconomics is incapable of addressing macroeconomic performance and

the stability of the financial system in an integrated context. For example, in the standard

New Keynesian or Neoclassical macroeconomic models, the economic agents are the

household, corporate, and government sectors, and the financial sector is simply treated

as an innocuous veil between these three sectors. The issue of non-performing assets is

invariably viewed as a microeconomic issue related to the banking industry.

In fact, the crisis we are currently experiencing may call for a change in the theoretical

structure of macroeconomics. In my view, a macroeconomic approach that encompasses

financial intermediaries and places them at the centre of its models is necessary. The new

approach should satisfy three requirements:

The focus should be on the function of financial institutions as media of exchange

and the conditions that might cause payment intermediation to malfunction.

Perhaps this kind of macro model can be built on the framework of the monetary

theory of Lagos and Wright (2005), which explicitly considers the role of money

as a medium of exchange.

The new macroeconomic approach should provide a unified framework for

discussing the cost and effectiveness of various policy responses to the current


global crisis in an integrated context, in which fiscal policy, monetary policy, and

bad asset disposal can be compared and relative weightings can be given to all

three.

To provide a unified framework for policy analysis, the new approach should

make it easy to embed a model of financial crises into the standard business cycle

models (i.e., the dynamic stochastic general equilibrium models).

I have elsewhere attempted to construct a theoretical model that satisfies these

requirements, in which I assume that assets such as real estate now function as media of

exchange given the development of liquid asset markets but are unable to fulfil this

function during a financial crisis (see Kobayashi 2009a). With a model like this, we can

regard a financial crisis as the disappearance of media of exchange, which triggers a

sharp fall in aggregate demand. In this case, both macroeconomic policy (fiscal and

monetary policy) and bad asset disposals can be understood as responses targeting the

same goal – restoring the amounts of media of exchange (inside and outside monies).

Thus we can compare and analyse these policies in an integrated context.

Article I.Article II. Bad asset Disposal should not be left to Financial Community Insiders

If macroeconomic policy and financial stabilisation through bad asset disposals are

designed to eradicate the same externality, financial stabilisation is not just a problem for

the financial community – it is crucial for the recovery of the overall economy.

Therefore, the design and execution of policies capable of disposing of non-performing

assets are not tasks that should be left to financial community insiders. We need to openly

discuss what financial stabilisation policies should look like (for practical lessons on the

policy package from Japan’s experience, see Kobayashi 2008, 2009b). Bad asset

disposals including capital injections for financial institutions (or temporary

nationalisation) and the rehabilitation of debt-ridden borrowers must be considered

alongside fiscal stimuli and monetary easing, with a new awareness that they also


constitute macroeconomic policies. Perhaps, we need to adopt a new paradigm of

economic thought.

Shareholders or stockholders own parts or shares of companies. In large corporations,

shareholders are people and institutions that simply invest money for future dividends

and for the potential increased value of their shares, whereas in small companies they

may be the people who established the business or who have a more personal stake in it.

When investors buy shares of companies, they receive certificates that say how many

shares they own. Owning shares of a company often entitles an investor to a part of the

company's profits, which is issued as a dividend. In addition, shareholders are typically

offered a fixed payout per share if the company is bought out. Because they are partial

owners of a company, shareholders are allowed to vote at shareholder meetings for

certain company actions (such as approving or rejecting a merger proposal), review

company accounts, and receive periodic reports on company performance. If shareholders

cannot attend annual meetings, they are permitted to vote by proxy by mailing in their

vote. Furthermore, if a company decides to issue more shares, current shareholders have

the option to buy shares before they are offered to the public.

Shareholders are entitled to vote on a variety of issues, although the specific areas where

shareholders have a say are determined by state laws and corporate bylaws. Generally,

shareholders have the right to appoint a corporate president, elect members to a board of

directors, and vote on significant changes in a corporation. These significant changes

might include changes in the line of business, change of company name, and company

divestments, acquisitions, and mergers. Boards of director’s act on behalf of the share-

holders and, in practice, make most decisions such as appointing corporate officers and

reviewing corporate policies, finances, and strategies. Shareholders may vote only during

a corporation's annual shareholder meeting or at a special shareholder meeting, which

would normally be called by the board of directors. A notice of the meeting and a notice

of the agenda (the major points of the meeting) must be provided before each shareholder

meeting. Shareholder voting power is proportionate to the number of shares each

shareholder owns. For example, if a corporation had two shareholders one with 400


shares and one with 100 shares the one with 400 shares would wield far greater voting

power.

Shareholders may own two kinds of stock: common stock and preferred stock. Owners of

common stock have the last claim to company profits and assets and they may receive

dividends at the discretion of a company's board of directors. In addition, common stock

does not have a fixed value. Holders of common stock, therefore, profit when a company

performs well and suffer losses when a company does not perform well. Nonetheless,

common stockholders are typically the bulk of a publicly traded firm's shareholders and

in many cases enjoy voting privileges that preferred stockholders lack. On the other hand,

owners of preferred stock have first claim to a company's profits and assets. Investors

may own three different kinds of preferred stock:

1. Stock with preferred dividends that entitles them to a fixed dividend rate,

2. Stock with preferred assets that allow them to receive to the first cut of the money

from a company's sale, and

3. Stock with both preferred dividends and preferred assets. Shareholders also may

own redeemable and convertible stock.

Redeemable stock allows a company to repurchase it at some point, whereas convertible

stock enables stockholders to exchange preferred stock for common stock. Companies

sell their stocks to raise money. While they have other financing options such as loans

and bonds, companies may choose to issue stocks because they need to raise more capital

than they can readily borrow, because equity capital may be viewed as less costly than

debt financing, or because favorable stock market conditions may present an opportunity

for private owners to receive cash for part or all of their shares. Companies may sell their

stocks either through private placement or public offerings. Private placement is usually

limited to large institutions or a small group of individuals.

Before the rise of the publicly traded corporation, often the families that founded

companies were the shareholders, managers, and members of the board of directors. But

because these companies needed to raise increasing amounts of capital to expand, they


eventually had to turn to outside investors. As a result, outside parties quickly became

managers and members of the board. After offering shares to the public, founding family

members still retained control of their corporations in many cases; however, shares also

were dispersed among a variety of investors who had small holdings.

Mustafa Company’s shareholders might persuade management to move in the

direction of shareholder’s preferences.

Managers of a company that focuses on shareholder value will strive to remain abreast of

share-holder interests. Consequently, Andrew Black et al. suggest in In Search of

Shareholder Value that managers must think like entrepreneurs in order to meet

shareholders' needs and add to shareholder value, which may require some refocusing if

managers are accustomed to simply following the directions of their superiors. To create

additional shareholder value, managers must concentrate on a company's primary

revenue-generating functions and running a company as efficiently as possible, which

should help a company become a product or service leader and establish closer ties with

consumers. Consequently, managers must begin their effort to increase shareholder value

by identifying the key revenue-generating functions and then by promoting them.

Furthermore, managers must distinguish between the interests of shareholders who have

long-term interests in a company's worth and those who have short-term interests. Then

they must strive to implement growth strategies that will benefit both kinds of investors

insofar as possible, even though these interests may be in conflict with each other,

according to J.P. Donlon and John Gutfreund.

However, this approach has come under the attack of employee advocates and other

critics. In corporate theory, companies traditionally have been viewed according to the

stakeholder model. This model suggests that a company can improve its financial

conditions by attending to the needs and desires of its stakeholders, which include not

only shareholders but also employees, distributors, customers, and so on. Shareholder and

employee interests are sometimes viewed as being at odds with each other, especially


around issues such as layoffs. According to the stake-holder model, managers should

weigh the interests of one group of stakeholders against the interests of another in order

to manage a company fairly. Hence, the shareholder value approach is controversial in

that it gives priority to shareholder needs.

Supporters of the shareholder value approach defend their position by arguing that if a

company is beholden to more than one interest group, then it will face the dilemma of

having to decide between the different groups. If it must decide between competing

interests, then the company must base this decision on some additional reason, but

companies are hard-pressed to determine what the deciding criterion should be if not

increasing shareholder value. The stakeholder model offers no suggestions. Without a

decisive criterion, a company would constantly face this kind of dilemma, which would

drastically slow-down the decision-making process. Such a dilemma could manifest

itself, for example, as a proposal that would increase shareholder value and meet

customer needs, but would result in the reducing the workforce. However, a company

does not ignore the interests of other stakeholders while concentrating on shareholder

value. For example, employees will quit if their interests are not attended to and

customers will patronize the competition if their needs are not met, and so management

inevitably must take their needs into consideration. Finally, advocates of this approach

contend that if a company fails to be profitable, then it will have to close, which would

benefit none of the stakeholders.

Q. 2 (a) Critically examine the relationship between ROE and ROA. Give example in support

of your answer.

Answer Q. 2 (a)


Since ROE = ROA (Equity Multiplier) in order for ROE to equal ROA the equity

multiplier must be one. In other words, the total assets to total shareholders' equity ratio

must be one. The return on assets (ROA) percentage shows how profitable a company's

assets are in generating revenue.

ROA can be Computed as:

This number tells you what the company can do with what it has, i.e. how many dollars

of earnings they derive from each dollar of assets they control. It's a useful number for

comparing competing companies in the same industry. The number will vary widely

across different industries. Return on assets gives an indication of the capital intensity of

the company, which will depend on the industry; companies that require large initial

investments will generally have lower return on assets.

Return on Equity:

Return on equity (ROE) measures the rate of return on the ownership interest

(shareholders' equity) of the common stock owners. It measures a firm's efficiency at

generating profits from every unit of shareholders' equity (also known as net assets or

assets minus liabilities). ROE shows how well a company uses investment funds to

generate earnings growth.

The Formula:

ROE is equal to a fiscal year's net income (after preferred stock dividends but before

common stock dividends) divided by total equity (excluding preferred shares), expressed

as a percentage. As with many financial ratios, ROE is best used to compare companies

in the same industry. High ROE yields no immediate benefit. Since stock prices are most

strongly determined by earnings per share (EPS), you will be paying twice as much (in

Price/Book terms) for a 20% ROE company as for a 10% ROE company. The benefit

comes from the earnings reinvested in the company at a high ROE rate, which in turn


http://en.wikipedia.org/wiki/Earnings_per_share

http://en.wikipedia.org/wiki/Financial_ratio

http://en.wikipedia.org/wiki/Net_income

http://en.wikipedia.org/wiki/Fiscal_year

http://en.wikipedia.org/wiki/Shareholders'_equity

http://en.wikipedia.org/wiki/Capital_intensity

gives the company a high growth rate. ROE is presumably irrelevant if the earnings are

not reinvested.

Q. 2 (b) What are the five groups of ratios? Give two or three examples of each kind.

Answer Q. 2 (b)

These essential financial ratios give you a powerful insight into how your business is

doing. Financial ratios help you to measure where your business stands, where it’s been

and where it’s heading. They also help you measure yourself against industry

benchmarks, and see how you’re tracking against your business plans. There are plenty of

ratios to choose from. Here are our top five.

Gross profit margin

Net profit margin

Current ratio

Inventory turnover

Return on owner’s equity

Your gross profit margin tells you the average gross profit on each dollar of sales before

operating expenses. The equation is simple:


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Your gross profit margin will depend on the industry you’re in, so it’s important to

measure yourself against industry benchmarks. It’s an essential starting point for

assessing the profitability of each product but it still doesn’t tell you whether your

business is making a profit over all. For that you need the net profit margin.

Net profit margin

Your net profit margin is the percentage profit your business makes for every dollar of

revenue whether you’re making a profit after covering all of your costs.

Again, your target net profit margin will be at least partly determined by your industry.

Some retailers, for example, run high-volume, low-margin businesses, while others sell a

small number of expensive items with plenty of margin built in.

Current ratio

You’re making profitable sales but are they enough to cover short term liabilities? To

answer that, you need the current ratio. It helps to measure the solvency of your business

by comparing your current assets (like unpaid invoices) to your current liabilities (unpaid

bills and the like):

As a rule of thumb, you want your current ratio to be 2 or more. In other words, your

assets should be at least double your liabilities, meaning you have plenty of capacity to

meet them. If sales are growing and you have a short operating cycle, a lower number


may be OK. But if you have a long operating cycle, you might want your current ratio to

be higher, to make sure liabilities don’t get out of control.

Inventory turnover

If you have trading stock, then inventory turnover is an incredibly useful number. It

shows you how many times your business’ inventory is sold and replaced over a

particular period:

So, if you’ve spent $200,000 buying stock over the year, and you keep an average of

$20,000 worth of stock on hand, then your inventory turnover is 10 times a year.

Inventory turnover varies by industry but as a rule of thumb the higher it is the better. A

low turnover indicates you have a lot of money tied up in stock for long periods of time,

which is not good for cash flow. Too high a figure could indicate you’re not keeping

enough stock on hand!

Return on owner’s equity compares your net business income to the equity you’ve

invested in the business. It reveals how much you’re making from your investment:

So if you’ve invested $200,000 of your own money in the business, but it’s generating a

net income of $100,000 a year, then your return on owner’s equity is 50%. This ratio is a

great way to compare what you’ve earned from your business to what you might have


earned from another investment. If you’re just starting up, it might not be as high as

you’d like, but it tends to increase over time as your business grows, especially if your

personal investment remains the same.

Q. 2 (c) The most recent income statement of Allied Chemical Ltd is given below.

Prepare a common-size income statement based on this information. Give

interpretation to the standardized net income. What percentage of sales goes to

cost of goods sold?

Allied Corporation

2008 Income Statement

(Rs. In millions)

Sales Rs. 4,053

Cost of goods sold 2,780

Depreciation 550

Earning before interest and taxes Rs. 723

Interest paid 502

Taxable income Rs. 221

Taxes (34%) 75

Net income Rs. 146

Dividends Rs. 47

Addition to retained earnings 99

Answer Q. 2 (c)


Allied Corporation

Income Statement

For the period Ended 2008

Sale 4053 100%

-C.G.S 2780 68.59%

=G.P 1273 31.41%

-Depreciation 550

=Earning before Interest Tax 723

-Interest 502

-Taxable Income 221

-Taxes (34%) 75

=Net Income 146

-Dividends 47

=Addition to Retained Earning 99

Q. 3 (a) Find the amount to which Rs.500 will grow under each of the following

conditions:

i. 12 percent compounded semi-annually for 5 years.

ii. 12 percent compounded quarterly for 5 years.

iii. 12 percent compounded monthly for 5 years.

Answer Q. 3 (a)


===

PV = 500i = 12%n = 5%Fv = Pv (1 + i)n

i. 12% Compounded Semi-Annually for 5 year

Fv - Pv (1 + i %)nx2

n

=500 (1.06)10

ii. 12% Compound quarterly for 5 Year

Fv - Pv (1 + i %)nx4

n

=500 (1.03)20

iii. 12% Compounded Monthly for 5 Year

Fv - Pv (1 + i %)nx12

n

=500 (1 – 01)60

Q. 3 (b) Setup an amortization schedule for Rs.25000 loan to be repaid in equal installments at

the end of the next 5 years. The interest rate is 10 percent.

Answer Q. 3 (b)


Pv = 25000

i = 10%

n = 5%

PvA = FvA (Pvi FAi% ny)

25000 = FvA (Fvi FA10% 5y)

25000 = FvA (3.791)

25000 = FvA

3.791

6595 = FVA

Year Installment Interest Principle Ending

Balance

0 25000

1 6595 2500 4095 20905

2 6595 2090 4505 16400

3 6595 1640 4955 11445

4 6595 1144 5451 5994

5 6595 601 5994 0

Q. 3 (c) The Moonless Corporation has just paid a dividend of Rs.3 per share. The dividend

of this company grows at a steady rate of 8 percent per year. Based on this

information, what will the dividend be in 5 years?


Answer Q. 3 (c)

Div = 3

g = 8%

What will the dividend be in 5 Year.

Do = 3

D1 = 3 (1.08) = 3.24

D2 = 3.24 (1.08) = 3.50

D3 = 3.50 (1.08) = 3.78

D4 = 3.78 (1.08) = 4.08

D5 = 4.08 (1.08) = 4.41

Q. 4 (a) Stock A and B have the following probability distributions of expected future

returns:

Probability km kj

0.3 15% 20%

0.4 9 5

0.3 8 12

i. Calculate the expected rate of return for the market and Stock A.

ii. Calculate the standard deviations for the market and Stock A.

iii. Calculate the coefficients of variation for the market and Stock A.


===

Answer Q. 4 (a)

i. Expected Rate of Return

Ki Probability Ki x Pn

0.20 0.30 0.06

0.05 0.40 0.02

.12 0.30 0.036

0.116

ii. Standard Deviation

Ki K K1 - K (K1 - K)2 Pn (Ki - K) x Pn

0.20 .116 0.084 .0071 0.30 .00213

0.05 .116 -0.066 .0044 0.40 .00176

0.12 .116 0.004 .000016 0.30 .000048

.0038948

Ỏ = 0.0624


Ỏ = ∑ ( Ki – K x Pn−

−−

iii. Coefficient of Variance

= S.D x 100

X

= 0.0624 x 100

.116

= 5.40

Q. 4 (b)

Rehman has Rs.100,000 to invest in a portfolio containing stock A, stock B, and a risk free asset.

He must invest all of his money. Rehman’s goal is to create a portfolio that has an expected return

of 13% and that has only 70% of the overall market. If A has an expected return of 20%, a beta of

1.3 and the risk-free rate is 7%, how much money will he invest in stock A? Also give

interpretation to the answer.

Answer Q. 4 (b)

Investment 100000

Expected Return 13%

20%

B = 1.30


===

R7 = 7%

Ki = Rf + B ( Rm - Rf )

20% = 7% + 1.30 ( Rm - 7%)

20% - 7% = 1.30 ( Rm – 9.1% )

13% + 9.1% = 1.30 Rm

22-1% = Rm

1.30

20.8% = 20.8% = Rm

Expected Return is small differed from the Market Rate of Return. In stock A invest

Rs. 100000.

Q. 5 (a)

What is the relationship between the required rate of return on an investment and the cost

of capital associated with that investment?

Answer Q. 5 (a)

Return on capital calculated in a way that takes into account the risks associated with

income. Example: Being able to compare a high-risk, potentially high-return investment

with a low-risk, lower-return investment helps to answer a key question that confronts

every investor: is it worth the risk? There are several ways to calculate risk-adjusted

return. Each has its strengths and shortcomings. All require particular data, such as an

investment's rate of return, the risk-free return rate for a given period, and a market's

performance and its standard deviation. The choice of calculation depends on an

investor's focus: whether it is on upside gains or downside losses. The two most-used


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measures for evaluating an investment are the net present value and the internal rate of

return. (Two earlier tutorials discussed these concepts. See the tutorials list for links to

tutorials for discounting future income and the internal rate of return.) It is often assumed

that higher is better for both of the net present value and the internal rate of return. In

particular, it is usually stated that investments with higher internal rates of return are

more profitable than investments with lower internal rates of return. However, this is not

necessarily so. In some situations, an investment with a lower internal rate of return may

be better, even judged on narrow financial grounds, than an investment with a higher

internal rate of return. This interactive lecture explores why and when this reversal takes

place. To review, both the net present value and the internal rate of return require the idea

of an income stream, so let's start there. An income stream is a series of amounts of

money. Each amount of money comes in or goes out at some specific time, either now or

in the future. The income stream represents the investment; the income stream is all you

need to know for financial evaluation purposes. In real life, individuals, charitable

institutions, and even for-profit businesses have social or other goals when selecting

investments. For businesses, the benefits of community good will are no less real for

being difficult to measure precisely. For enterprises with social as well as financial goals,

the measures discussed here are still useful: They tell you how much it costs you to

advance your social goals. Here is an income stream example, from the interactive lecture

about the internal rate of return.

Year 0 1 2 3 4 5 6

Income amounts -$1000 $200 $200 $200 $200 $200 $200

Here we see seven points in time and, for each, a dollar inflow or outflow. At year 0

(now), the income amount is negative. Negative income is cost, or outgo. In this

example, the negative income amount in year 0 represents the cost of buying and

installing the machine. In the future, at years 1 through 6, there will be net income of

$200 each year. All of the amounts in the income stream are net income, meaning that

each is income minus outgo, or revenue minus cost. In year 0, the cost exceeds the


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revenue by $1000. In years 1 though 6, the revenue will exceed the cost by $200. This

investment evidently has no salvage value. That is, there is nothing that can be sold in

year 6, the last year. If there were, the amount that could be realized from the sale would

be added to the income amount for year 6. For simplicity, all my examples have the

incomes and outgoes at one-year intervals. Real-life investments can have income and

expenses at irregular times, but the principles of evaluation are the same. Now let's

discuss our two measures in connection with this income stream:

Net Present Value

The net present value of an income stream is the sum of the present values of the

individual amounts in the income stream. Each future income amount in the stream is

discounted, meaning that it is divided by a number representing the opportunity cost of

holding capital from now (year 0) until the year when income is received or the outgo is

spent. The opportunity cost can either be how much you would have earned investing the

money someplace else, or how much interest you would have had to pay if you borrowed

money. See the interactive lecture on discounting future income for more explanation.

That tutorial has a nifty spreadsheet setup for calculating present values that you can copy

and use in your own spreadsheet. The word "net" in "net present value" indicates that our

calculation includes the initial costs as well as the subsequent profits. It also reminds

us that all the amounts in the income stream are net profits, revenues minus cost. In other

words, "net" means the same as "total" here. The net present value of an investment tells

you how this investment compares either with your alternative investment or with

borrowing, whichever applies to you. A positive net present value means this investment

is better. A negative net present value means your alternative investment, or not

borrowing, is better.

Consider again this income stream:

Year 0 1 2 3 4 5 6


http://hadm.sph.sc.edu/courses/econ/dis/Dis.html#spreadsheet

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Income amounts -$1000 $200 $200 $200 $200 $200 $200

Let's assume that the discount rate (the interest rate that you could earn elsewhere or at

which you could borrow) will not change over the life of the project. This makes the

calculation simpler. With this assumption, we can use the usual formula:

Present Value of any one income amount = (Income amount) / ( (1 + Discount Rate)

to the a power)

a is the number of years into the future that the income amount will be received (or spent,

if the income amount is negative). The net present value (NPV) of a whole income stream

is the sum of these present values of the individual amounts in the income stream. If we

still assume that income comes or goes in annual bursts and that the discount rate will be

constant in the future, then the NPV has this formula:

Varying Future Interest Rates

The future interest rate does not have to be constant for this theory to apply. The interest

rate can vary, but that makes the formulas messier. For example, if r1 is the expected

interest rate next year, and r2 is the expected interest rate the year after that, then the

present value today of I2 income in year 2 is I2/(1+r1)(1+r2). The I 's are income

amounts for each year. The subscripts (which are also the exponents in the

denominators) are the year numbers, starting with 0, which is this year. The discount rate

assumed to be constant in the future is r. The number of years the investment lasts is n.

Three properties of the net present value of an income stream are:

1. Higher income amounts make the net present value higher. Lower income

amounts make the net present value lower.


2. If profits come sooner, the net present value is higher. If profits come

later, the net present value is lower.

Internal Rate of Return

In the example we've been using, if you keep the income amounts at their original -1000,

200, 200, 200, 200, 200, and 200, and set the discount rate to 0.0547, the net present

value becomes 0. This discount rate, 0.0547 or 5.47%, is the internal rate of return for

this investment -- it is the discount rate that makes the net present value equal 0. You can

try this below, by setting the discount rate to 0.0547. If you now raise any of the income

amounts in years 1 through 6 (feel free to edit an income amount and see for yourself),

you will need a higher discount rate to bring the net present value back to 0. That would

seem to imply that projects with higher incomes have higher internal rates of return.

Similarly, if you lower any of the income amounts in years 1 through 6, then a lower

discount rate will be needed to bring the net present value back up to 0. That would seem

to imply that projects with lower incomes have lower internal rates of return. These

seeming implications are actually often true, if the projects being compared have about

the same shape, with the costs coming early and the benefits coming late, and if the

projects being compared switch from net outgo to net income at about the same time.

Otherwise, though, the implications might not be true.

The NPV Curve

One way to understand how the net present value and the internal rate of return can give

seemingly different advice is to use what I will call the net present value curve, or NPV

curve. The NPV curve shows the relationship between the discount rate and the net

present value for a range of discount rates. The present value at a given discount rate,

such as 5%, and the internal rate of return are each points on the NPV curve. The NPV

curve, the relationship between the discount rate and the net present value has a formula

that can be written like this:


This, of course, is the formula we saw already for the net present value, for annualized

costs and revenues and a constant discount rate. Each I is an income amount for a

specific year. The subscripts (which are also the exponents in the denominators) are the

year numbers, starting with 0, which is this year. The constant discount rate is r. The

number of years the investment lasts is n. In Weeks's study of professionals' incomes, n

was about 44, because costs and incomes were calculated from age 21 to age 65.

We'll use an example with an n of 6, so the formula fits on your screen:

This is our machine investment example that we have been using all along. The NPV is a

function of r. Graphed, it looks like this:


The blue curve shows the net present value for discount rates (r) from 0 to 0.1 (0% to

10%). The red dots are the two points we get from our measures. The left red dot shows

the net present value at the discount rate of 0.05 (5%). The right red dot shows the

internal rate of return, because it is where the curve crosses the horizontal line indicating

an NPV of 0. That right red dot is between the 0.05 and 0.06 marks on the r axis, so the

internal rate of return is between 0.05 and 0.06. (The actual internal rate of return is

about 0.0547, as we saw earlier.) Imagine we have another possible investment, which

has this NPV equation:

This investment is like the first, except that the net profit in years 1 through 6 is $220 per year, rather than $200. I would say that this investment has a similar "shape" to the first, because the costs and profits come at the same times. Also, the size of the initial outlay is the same for both. The only difference is the amount of profit. Here's a graph with both investments on it:


The green curve is the second investment. It is above and parallel to the first investment's

blue curve. The left orange dot shows the net present value of the second investment at

the discount rate of 0.05. The net present value there is a little over $100. This is higher

than the left red dot, so the net present value at r=5% of the green-line investment is

higher than the net present value at r=5% for the blue-line investment. The right orange

dot shows where the second investment's curve crosses the NPV=0 line. This is well to

the right of the first investment's internal rate of return dot. The internal rate of return for

the second investment is much higher (further to the right).

Q. 5 (b)

The earnings, dividends and stock price of Ehsaan technologies Inc. are expected to grow at 7%

per year in the future. Ehsaan’s common stock sells for Rs.23 per share, its last dividend was

Rs.2.00, and the company will pay a dividend of Rs.2.14 at the end of the current year.

i. What is company’s cost of equity?

ii. If the firm’s beta is 1.6, the risk-free rate is 9%, and the expected return on the market

is 13%, what will be the firm’s cost of equity using the CAPM approach?

Answer Q. 5 (b)

i. Do = 2

Po = 23

g = 7

D1 = D ( 1 + g ) Di = 2.147


= 2(1.07) =

Ke = Dividend1 + g

Po

=2.14 + 7%

23

= 9.3% + 7%

= 16.30%

ii. CAPM

Ki = Rf + B ( Rm – Rf )

= 9% + 1.20 ( 13% - 9% )

= 9% + 1.20 ( 4% )

= 9% + 4.8%

= 13.8%

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financial management assignment no.1 mba aiou sum spring 2010

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