brooks problem solutions

Financial Management, Raymond Brooks, Ph.D.Solutions to Selected Problems

Romero 340 Section

Chapter 1

1. The cycle of money is the movement of funds from a lender to a borrower and back to the lender. The participants are the original lender, usually an individual (or household) through direct investment or through a financial institution, the financial institution that matches the lender with a borrower or bundles up a set of lenders for a single borrower, and the borrower such as a company that is using the funds for operating the business or expanding the business. The objective of every financial transaction is to make all parties in the transaction better off.

3. Area One: Corporate Finance – the financial activities that support the operations of a business. A typical financial activity in this area is borrowing funds to support a plant expansion or supplementing short term cash needs.

Area Two: Investments – the activities around the buying and selling of financial assets. A typical activity is the selling of a bond issue such as a school bond for building a new school.

Area Three: Financial Institutions – the organizations that promote and facilitate the cycle of money. A typical financial activity is issuing checking and savings accounts as well as selling securities such as certificates of deposit, stocks and bonds.

Area Four: International Finance – the financial activities performed in foreign countries for a domestic company. A typical financial activity is the changing of currency from one country to another country.

7. The goal of the financial manager is to maximize the current share price or equity value of the firm. This goal encompasses many good business practices such as a good working relationship with the surrounding community. If the firm pollutes local streams, abuses local facilities such as roads, and in general does not participate in the economic advancement of the local community its share price or equity value will suffer. The local community may sue the company for its damages and the best local workforce members may choose not to work for the company. Employees may not be loyal to the company causing high turnover and increased personal costs for recruiting and training. Finally, facilities such as roads and utilities may not be repaired or modernized by the local community impacting the company’s ability to produce a profit. A good community relationship is embedded in the goal of maximizing current share price or the equity value of the company.

Chapter 2

1b. With TVM formula, and table set-up: FV = $400.00 x (1.05)5 = $400.00 x (FVIF5%,5) FV = $17,411.00 x (1.06)30 = $17,411.00 x (FVIF6%,30) FV = $35,000.00 x (1.10)20 = $35,000.00 x (FVIF10%,20)FV = $26,981.75 x (1.16)15 = $26,981.75 x (FVIF16%,15)

1c. Time Value of Money Keys or Spreadsheet

Input 5 5.0 -400 0Variable N I/Y PV PMT FVCompute 510.51

Input 30 6.0 -17,411 0Variable N I/Y PV PMT FVCompute 99,999.92

Input 20 10.0 -35,000 0Variable N I/Y PV PMT FVCompute 235,462.50

Input 15 16.0 -26,981.75 0Variable N I/Y PV PMT FVCompute 249,999.97

Solutions with TVM Keys or SpreadsheetPresent Value Interest Rate Number of Periods Future Value

$400.00 5.0% 5 $510.51$17,411.00 6.0% 30 $99,999.92$35,000.00 10% 20 $235,462.50$26,981.75 16% 15 $249,999.97

3c. Solutions with Calculator TVM Keys or Spreadsheet

Present Value Future Value Number of Periods Interest Rate$500.00 $1,998.00 18 8.00%

$17,335.36 $230,000.00 30 9.00%$35,000.00 $63,214.00 20 3.00%$27,651.26 $225,000.00 15 15.00%

Input 18 500.00 0 -1,998.00Variable N I/Y PV PMT FVCompute 8.00

Input 30 17,335.36 0 -230,000Variable N I/Y PV PMT FVCompute 9.00

Input 20 35,000 0 -63,214Variable N I/Y PV PMT FVCompute 3.00

Input 15 27,651.26 0 -225,000Variable N I/Y PV PMT FVCompute 15.00

5. b. FV = $7,000 x (1.06)5 = $7,000 x (FVIF6%,5) = 9,367.58d. FV = $7,000 x (1.06)15 = $7,000 x (FVIF6%,15) = 16,775.91

7. a. PV = $2,500 x 1/(1.07)2 = $2,500 x (PVIF7%,2) = $2,183.60b. PV = $2,500 x 1/(1.07)5= $2,500 x (PVIF7%,5)= $1,782.47 c. PV = $2,500 x 1/(1.07)9 = $2,500 x (PVIF7%,9)= $1,359.83 d. PV = $2,500 x 1/(1.07)14 = $2,500 x (PVIF7%,14)= $969.54e. PV = $2,500 x 1/(1.07)18 = $2,500 x (PVIF7%,18)= $739.66

13. Present Value of Average Employee:PV = $400,000 x 1/(1.05)22 = $400,000 x (PVIF5%,22)= $136,740

With 240,000 Employees the total obligations are:

PV Obligation of Pension Fund = 240,000 x $136,740 = $32,817,600,000

(Note, the PV was rounded to nearest dollar prior to multiplying times the number of employees.)

15. Fund One’s Rate, r = 11.96%Fund Two’s Rate, r = 15.98%

Fund Two has the higher return but for a shorter period of time. To be appropriate for comparing performance the funds should be measured over the same period of time. The first fund may have had a higher return over the last six years than the second fund but low returns in the earlier years reduced the return below the 16% return rate of the second fund.

17. Answer for 5% growth rate in pedestrian traffic: n = 33 years Answer for 8% growth rate in pedestrian traffic: n = 21 years Ten Years Maximum would require growth rate of: r = 17.46%

Chapter 3

3. FV = $250.00 x [(1 + 0.06)10 – 1] / 0.06 = $250.00 x (FVIFA6%,10) = $3,295.20FV = $1,387.88 x [(1 + 0.12)20 – 1] / 0.12 = $1,387.88 x (FVIFA12%,20)= $100,000.14 FV = $600.00 x [(1 + 0.04)25 – 1] / 0.04 = $600.00 x (FVIFA4%,25)= $24,987.55 FV = $572.25 x [(1 + 0.01)360 – 1] / 0.01 = $572.25 x (FVIFA1%,360)= $1,999,993.23

7. Using TVM Keys from a Texas Instrument BAII Plus Calculator and rounded to two decimal places for interest percent. The P/Y and C/Y variables are set to 1.

INPUT 10 -3,680.04 500.00 0TVM KEYS N I/Y PV PMT FVOUTPUT 6.00

INPUT 20 0 -346.97 25,000TVM KEYS N I/Y PV PMT FVOUTPUT 12.00

INPUT 30 -20,000 1,946.73 0TVM KEYS N I/Y PV PMT FVOUTPUT 9.00

INPUT 100 0 400.00 -1,044,010.06TVM KEYS N I/Y PV PMT FVOUTPUT 5.00

11. FV = $25,000 x 1.106 = $25,000 x (FVIF10%,6) = $44,289.03

13. $25,000 = PMT (PVIFA10%,6) Annual Payment = $5,740.18

15. Part a. FVA = $50 x (FVIFA7%,25) = $3,162.45Part b. FVA = $50 x (FVIFA7%,10) = $690.82 so the rainy day fund is $9.18 short

of being able to cover the medical bill.

19. 30,000 = PMT (PVIFA8.5%,10) PMT= $4,572.23

21. First remember to check if the payment is greater than the interest expense for the period. PMT > PV x R = $3,900 > $15,000 x 0.2 = $3,000 and now, on the calculator:INPUT ? 20.0 $15,000 -$3,900 $0Variables N I/Y PV PMT FV

OUTPUT 8.0426 ≈ 8 payments or 8 years…Note: Most HP calculators get 9, because they round up to nearest integer when solving for n.

Chapter 4

Period APRCompounding

Per Year Periodic RateEffective

Annual RateSemi-Annual 8% 2 4.0% 8.16%Quarterly 9% 4 2.25% 9.31%Monthly 7.5% 12 0.625% 7.76%Daily 4.25% 365 0.01164384% 4.34%

1. Periodic Rate = APR / (C/Y) = 0.08 / 2 = 0.04 = 4.0%Periodic Rate = APR / (C/Y) = 0.09 / 4 = 0.0225= 2.25%Periodic Rate = APR / (C/Y) = 0.075 / 12 = 0.00625= 0.625%Periodic Rate = APR / (C/Y) = 0.0425 / 365 = 0.0001164384 = 0.01164384%

EAR = (1 + Periodic Rate)C/Y - 1 = 1.042 – 1 = 1.0816 – 1 = 0.0816 = 8.16%EAR = (1 + Periodic Rate)C/Y - 1 = 1.02254 – 1 = 1.0931 – 1 = 0.0931= 9.31%EAR = (1 + Periodic Rate)C/Y - 1 = 1.0062512 – 1 = 1.0776 – 1 = 0.0776 = 7.76%EAR = (1 + Periodic Rate)C/Y - 1 = 1.0001164365 – 1 = 1.0434 – 1 = 0.0434 = 4.34%

3. Periodic Rate = 0.0775 / 12 = 0.0064583333EAR = (1 + Periodic Rate)C/Y - 1 = 1.0064583312 – 1 = 1.0803 – 1 = 0.0803 = 8.03%

5. PV = 18,000N = 6 x 4I = 7.5%/4PMT = ? Quarterly Payment = $938.26

Change n to 6 x12 & I to 7.5%/12Monthly Payment = $311.22

Annual Cash Outflow Quarterly Payment = $938.26 x 4 = $3,753.04Annual Cash Outflow Monthly Payment = $3,734.64Difference of $18.04 It is lower for the monthly payment because each payment reduces some of the principal and so over the 3 months between the quarterly payments the average borrowed amount is lower so that the accumulated interest expense is lower.

9. n = 44 x 12I = 6%/12FV = 1,000,000PMT = ?Payment = $386.96

25. The decade of the 80s had the highest interest rates and the decade of the 50s had the lowest rates.

Chapter 5

3. CD Percent Return = ($540 + $0 - $500) / $500 = 0.0800 or 8.00%Stock Percent Return = ($34 + $2 - $23) / $23= 0.5652 or 56.52%Bond Percent Return = ($980 + $80 - $1,040) / $1,040 = 0.0192 or 1.92%Bike Percent Return = ($220 + $0 - $400) / $400 = -0.4500 or -45.00%

InvestmentOriginal Cost or Invested $

Selling Price of Investment

Distributions Received $ Percent Return

CD $500.00 $540.00 $0.00 8.00%Stock $23.00 $34.00 $2.00 56.62%Bond $1,040.00 $980.00 $80.00 1.92%Bike $400.00 $220.00 $0.00 -45.00%

17a. Expected Return A = 0.35 x 0.04 + 0.50 x 0.04 + 0.15 x 0.04 = 0.0140 + 0.0200 + 0.0060 = 0.0040 or 4.0%

Expected Return B = 0.35 x 0.21 + 0.50 x 0.08 + 0.15 x (-0.01)

= 0.0735 + 0.0400 - 0.0015 = 0.1120 or 11.2%

Expected Return C = 0.35 x 0.30 + 0.50 x 0.20 + 0.15 x (-0.26) = 0.1050 + 0.1000 - 0.0390 = 0.1660 or 16.6%

17b. Variance of A = 0.35 x (0.04 – 0.04)2 + 0.50 x (0.04 – 0.04)2 + 0.15 x (0.04 – 0.04)2

= 0.35 x 0.0000 + 0.50 x 0.0000 + 0.15 x 0.0000 = 0.0000+ 0.0000 + 0.0000 = 0.0000 or 0.00%

Variance of B = 0.35 x (0.21 – 0.112)2 + 0.50 x (0.08 – 0.112)2 + 0.15 x (-0.01 – 0.112)2

= 0.35 x 0.0096 + 0.50 x 0.0010 + 0.15 x 0.0149= 0.0034+ 0.0005 + 0.0022 = 0.0061 or 0.61%

Variance of C = 0.35 x (0.30 – 0.166)2 + 0.50 x (0.20 – 0.166)2 + 0.15 x (-0.26 – 0.166)2

= 0.35 x 0.0180 + 0.50 x 0.0012 + 0.15 x 0.1815= 0.0063 + 0.0006 + 0.0272 = 0.0341 or 3.41%

17c. Standard Deviation of A = (0.0000)1/2 = 0.0000 or 0.00%

Standard Deviation of B = (0.0061)1/2 = 0.0781 or 7.81%

Standard Deviation of C = (0.0341)1/2 = 0.1846 or 18.46%

Chapter 6

1. Price = $1,000.00 x 1/(1.06)10 + $80.00 (1 – 1/(1.06)10)/ 0.06Price = $1,000.00 x (PVIF6%,10) + $80.00 x (PVIFA6%,10)Price = $1,147.20

Calculator Keystrokes: FV=1,000 PMT=80 I/Y=6 n=10 PV=?

Price = $1,000.00 x 1/(1.08)10 + $60.00 (1 – 1/(1.08)10)/ 0.08Price = $1,000.00 x (PVIF8%,10)+ $60.00 x (PVIFA8%,10)Price = $865.80


Price = $5,000.00 x 1/(1.07)20 + $450.00 (1 – 1/(1.07)20)/ 0.07Price = $5,000.00 x (PVIF7%,20)+ $450.00 x (PVIFA7%,20)Price = $6,059.40


Price = $5,000.00 x 1/(1.05)30 + $600.00 (1 – 1/(1.05)30)/ 0.05Price = $5,000.00 x (PVIF5%,30)+ $600.00 x (PVIFA5%,30)Price = $10,380.36


2. Check figure for 1st bond: Assuming P/Y = 1, C/Y =1, and periodic adjustments are made to I & n:Calculator Keystrokes: FV=1,000 PMT=40 I/Y=3 n=20 PV=? $1,148.77

Or Assuming that P/Y = 2, C/Y = 2:Calculator Keystrokes: FV=1,000 PMT=40 I/Y=6 n=20 PV=? $1,148.77

5. (TVM Keys) Set Calculator to P/Y = 1 and C/Y = 1INPUT 10 ? -1000.00 80.00 1000.00KEYS N I/Y PV PMT FVCPT 8.0

(TVM Keys) Set Calculator to P/Y = 1 and C/Y = 1INPUT 10 ? -850.00 60.00 1000.00KEYS N I/Y PV PMT FVCPT 8.2619



6. Check figure for 1st bond: Set Calculator to P/Y = 1 and C/Y = 1

INPUT 20 ? -1000.00 40.00 1000.00KEYS N I/Y PV PMT FVCPT 4.0 (then multiply by 2 for annual YTM = 8%)

OR Set Calculator to P/Y = 2 and C/Y = 2INPUT 20 ? -1000.00 40.00 1000.00KEYS N I/Y PV PMT FVCPT 8.0

11a. At five years to maturityPrice = $1,000.00 x 1/(1.05)10 + $40.00 (1 – 1/(1.05)10)/ 0.05Price = $1,000.00 x (PVIF5%,10)+ $40.00 x (PVIFA5%,10)

(TVM Keys) Set Calculator to P/Y = 1 and C/Y = 1INPUT 10 5.0 ? 40.00 1000.00KEYS N I/Y PV PMT FVCPT -922.78

OR Set Calculator to P/Y = 2 and C/Y = 2INPUT 10 10.0 ? 40.00 1000.00KEYS N I/Y PV PMT FVCPT -922.78

At ten years to maturityPrice = $1,000.00 x (PVIF5%,20)+ $40.00 x (PVIFA5%,20)



At fifteen years to maturityPrice = $1,000.00 x (PVIF5%,30)+ $40.00 x (PVIFA5%,30)



At twenty years to maturityPrice = $1,000.00 x (PVIF5%,40)+ $40.00 x (PVIFA5%,40)



11b. The longer the maturity of a bond selling at a discount, all else held constant, the lower the price of the bond!

Chapter 7

1. Use the constant dividend infinite dividend stream model: Price = Dividend / ra. Price = $0.50 / 0.05 = $10.00b. Price = $0.50 / 0.08 = $6.25c. Price = $0.50 / 0.10 = $5.00d. Price = $0.50 / 0.13 = $3.85e. Price = $0.50 / 0.20 = $2.50

5. Use the constant growth dividend model with an infinite dividend stream:

Price = Last Dividend x (1 + g) / (r – g)

a. Price = $0.40 x (1.04) / (0.05 – 0.04) = $0.4160 / 0.01 = $41.60b. Price = $0.40 x (1.04) / (0.08 – 0.04) = $0.4160 / 0.04 = $10.40c. Price = $0.40 x (1.04) / (0.10 – 0.04) = $0.4160 / 0.06 = $6.93d. Price = $0.40 x (1.04) / (0.13 – 0.04) = $0.4160 / 0.09 = $4.62e. Price = $0.40 x (1.04) / (0.20 – 0.04) = $0.4160 / 0.16 = $2.60

11. Use the constant dividend model with infinite horizon

Price = Dividend / r

a. Brad’s Price = $100 x 0.06 / 0.10 = $60.00b. Mike’s Price = $100 x 0.06 / 0.12 = $50.00c. Rick’s Price = $100 x 0.06 / 0.15 = $40.00d. Julius’s Price = $100 x 0.06 / 0.18 = $33.33

15. The Security Market Line equation is: E(r) = rf + β (E(rm) - rf)

The intercept is rf ; The slope is E(rm) - rf ;The market risk premium is E(rm) - rf

a. The SML is E(r) = 3% + β (12% - 3%) = 3% + β 9%b. The SML is E(r) = 5% + β (18% - 5%) = 5% + β 13%c. The SML is E(r) = 4% + β (8%) d. The SML is E(r) = 2% + β (6%) e. The SML is E(r) = 3% + β (9%) f. The SML is E(r) = 4% + β (7%)

17. e. SJN expected return: E(rSJN) = 3% + 0.4 (9%) = 3% + 3.6% = 6.6%f.GFN expected return: E(rGFN) = 3% + 1.6 (9%) = 3% + 14.4% = 17.4%g. JE expected return: E(rJE) = 3% + 1.0 (9%) = 3% + 9% = 12%h. PE expected return: E(rPE) = 3% + 0.0 (9%) = 3% + 0.0% = 3%

19. First find the expected return for the stocks if the betas are correct. Compare with the listed return. For stocks where the expected return is less than the listed return, the stock is underpriced. For stocks where the expected return is greater than the listed return, the stock is overpriced.

CompanyCompany

BetaListed Return

Expected Return

Underpriced orOverpriced

TJB 1.2 15.10% 2.5% + 1.2 (9.25%) = 13.6% UnderpricedMAB 0.6 9.55% 2.5% + 0.6 (9.25%) = 8.05% UnderpricedPMF 0.8 9.60% 2.5% + 0.8 (9.25%) = 9.90% OverpricedCNF 1.4 14.45% 2.5% + 1.4 (9.25%) = 15.45% OverpricedSJN 0.4 5.70% 2.5% + 0.4 (9.25%) = 6.20% OverpricedGFN 1.6 18.80% 2.5% + 1.6 (9.25%) = 17.30% UnderpricedJE 1.0 11.00% 2.5% + 1.0 (9.25%) = 11.75% OverpricedPE 0.0 3.0% 2.5% + 0.0 (9.25%) = 2.50% Underpriced

Chapter 8

1. Expected Return J = 0.30 x 0.05 + 0.40 x 0.05 + 0.20 x 0.05 + 0.10 x 0.05

= 0.0150 + 0.0200 + 0.0100 + 0.0050= 0.0050 or 5.0%

Expected Return K = 0.30 x 0.24 + 0.40 x 0.12 + 0.20 x 0.04 + 0.10 x (-0.10)

= 0.0720 + 0.0480 + 0.0080 - 0.0100 = 0.1180 or 11.80%

Expected Return L = 0.30 x 0.30 + 0.40 x 0.20 + 0.20 x 0.06 + 0.10 x (-0.20)

= 0.0900 + 0.0800 + 0.0120 + 0.0200 = 0.1620 or 16.20%

3. Expected Return Portfolio = 0.10 x 0.05 + 0.50 x 0.118 + 0.40 x 0.162

= 0.0050 + 0.0590 + 0.0648 = 0.1288 or 12.88%

Chapter 9

1. Project A: Year One: -$10,000 + $4,000 = $6,000 left to recover

Year Two: -$6,000 + $4,000 = $2,000 left to recover

Year Three: -$2,000 + $4,000 = fully recovered

Year Three: $2,000 / $4,000 = ½ year needed for recovery

Payback Period for Project A: 2 and ½ years, ACCEPT!

Project B: Year One: -$25,000 + $2,000 = $23,000 left to recover


Year Three: -$15,000 + $14,000 = $1,000 left to recover

Year Four: -$1,000 + $20,000 = fully recovered

Year Four: $1,000 / $20,000 = 1/20 year needed for recovery

Payback Period for Project B: 3 and 1/20 years, REJECT!

Project C: Year One: -$45,000 + $10,000 = $35,000 left to recover


Year Three: -$20,000 + $20,000 = fully recovered

Year Three: $20,000 / $20,000 = full year needed

Payback Period for Project B: 3 years, ACCEPT!

Project D: Year One: -$100,000 + $40,000 = $60,000 left to recover


Year Three: -$30,000 + $20,000 = $10,000 left to recover

Year Four: -$10,000 + $10,000 = fully recovered

Year Four: $10,000 / $10,000 = full year needed

Payback Period for Project B: 4 years, REJECT!

7. a. NPV = $59,859.98 and accept the project.

b. NPV = $22,840.31 and accept the project.

c. NPV = -$7,939.82 and reject the project.

Cash Flows Project M Project N Project O Project PYear one $500,000 $600,000 $1,000,000 $300,000Year two $500,000 $600,000 $800,000 $500,000Year three $500,000 $600,000 $600,000 $700,000Year four $500,000 $600,000 $400,000 $900,000Year five $500,000 $600,000 $200,000 $1,100,000Discount Rate 6% 9% 15% 22%

9. NPV = $106,182 $333,791 $197,127 $-219,414

And the ranking order based on NPVs is,

Project N – NPV of $333,790.77

Project O – NPV of $197,126.53

Project M – NPV of $164,738.34

Project P – NPV of -$219,413.98

Swanson Industries should pick Project N.

11. Enter the keys noted for each project in the CF of a Texas BA II Plus calculator:

Cash Flows Project M Project N Project O Project PCFO -$2,000,000 -$2,000,000 -$2,000,000 -$2,000,000CO1, F1 $500,000, 1 $600,000, 1 $1,000,000, 1 $300,000, 1CO2, F2 $500,000, 1 $600,000, 1 $800,000, 1 $500,000, 1Year three $500,000, 1 $600,000, 1 $600,000, 1 $700,000, 1Year four $500,000, 1 $600,000, 1 $400,000, 1 $900,000, 1Year five $500,000, 1 $600,000, 1 $200,000, 1 $1,100,000, 1CPT IRR 7.93% 15.24% 20.27% 17.72%

15. Find the present value of benefits and divide by the present value of the costs for each project:

Project U’s PI = $2,106,182/ $2,000,000 = 1.05 accept project.

Project V’s PI = $2,333,790.77 / $ 2,500,000 = 0.9335 and reject project.

Project W’s PI = $2,197,126.53 / $2,400,000 = 0.9155 and reject project.

Project X’s PI = $1,780,586.02 / $1,750,000 = 1.0175 and accept project.

17. Payback Period: -$10,400,000 + $2,600,000 + $2,600,000 + $2,600,000 +

$2,600,000 = $0 (Four years but year five is also an outflow so we need to

continue) -$1,200,000 + $7,500,000 + $7,500,000 = $300,000 so we only need

part of year seven, $4,500,000 / $7,500,000 = 0.6 so total Payback is 7.6 years

and project is rejected with six year cut-off.

NPV = -$2,161,656.25 and reject project under NPV rules.

IRR = (discount rate where NPV = 0)

In calculator solve for r, CF0 = -10,400,000

C01 = 2,600,000 and F01 = 4

C02 = - 1,200,000 and F02 = 1

C03 = 750,000 and F03 = 3

CPT IRR = 3.1955%

and reject project as IRR is less than 12%

Profitability Index:

Present Value of Benefits = $8,919,256*

*Calculate the NPV, excluding all costs & cash outflows. (Remember to enter in

0 for CF0 and 0 for CF year 5.)

Present Value of Costs: $10,400,000 + $1,200,000/1.125 = $10,400,000 +

$680,912.23 = $11,080,912.23

Profitability Index = $8,919,255.73 / $11,080,912.23 = 0.8049 and reject.

HONORS ONLY:

19. Discount Rate NPV

0% $120,0005% $71,290.5110% $31,500.5815% -$1,357.74 20% -$28,761.57

IRR = 14.77%

5% 10% 15% 20%

Discount Rates

$120,000

$90,000

$60,000

$30,000

$0

-$30,000

NPV Dollars

NPV ProfileOf Project L-2

Chapter 10

5. Income Statement for the Year Ending 12/13/2004

Sales Revenue $350,000

COGS $140,000

Fixed Costs $ 43,000

SG&A Expenses $ 28,000

Depreciation $ 46,000

EBIT $ 93,000

Interest Expense $ 18,000

Taxable Income $ 75,000

Taxes @ 40% $ 30,000

Net Income $ 45,000

And with a Dividend payment of $30,000 the remainder of Net Income goes to Retained Earnings, $15,000. To complete the balance sheet add up all the asset accounts and subtract off the accumulated depreciation (contra asset account) for a total of $400,000. Now balance the balance sheet by determining the total liabilities and owner’s equity accounts ($353,000) and filling in the difference between this total and total assets as the balance in Retained Earnings, $47,000.

Balance Sheet 12/31/2003

Assets: Liabilities:Cash $ 16,000 Notes Payable $ 14,000Accounts Rec. $ 28,000 Accounts Payable $ 19,000Inventories $ 48,000 Long-Term Debt $190,000Fixed Assets $368,000 Owner’s EquityAcc. Depreciation $142,000 Retained Earnings $ 47,000Intangible Assets $ 82,000 Common Stock $130,000Total Assets $400,000 Total Liab. & OE $400,000

Do the same for the year 2004 but now we must first find accumulated depreciation total. The prior year was $142,000 and the current year’s depreciation from the income statement is $46,000 so the accumulated depreciation for 2004 is $188,000. Also, Retained Earnings went up by Net Income minus dividends paid out so we have an increase of $15,000 ($45,000 - $30,000).

Balance Sheet 12/31/2004Assets: Liabilities:

Cash $ 26,000 Notes Payable $ 12,000Accounts Rec. $ 19,000 Accounts Payable $ 24,000Inventories $ 53,000 Long-Term Debt $162,000Fixed Assets $448,000 Owner’s EquityAcc. Depreciation $188,000 Retained Earnings $ 62,000Intangible Assets $ 82,000 Common Stock $180,000Total Assets $440,000 Total Liab. & O.E. $440,000

10. To create the Sources and Uses of Cash (Cash Flow Statement) we need to compute the changes in the Balance Sheets from 2003 to 2004 (below). (For ease of calculating the changes in the accounts, the balance sheet is shown below in the top/bottom format, where assets are listed up top, and liabilities & OE are below. The balance sheet in the problem is shown as a side by side format, assets on the left; liabs & OE on the right.)

2004 2003 2004-2003

ASSETS

Cash & Equivalents $ 26,000 $ 16,000 $ 10,000 Accounts Receivable 19,000 28,000 (9,000)Inventories 53,000 48,000 5,000 TOTAL CURRENT ASSETS 98,000 92,000 6,000 Gross Fixed Assets 448,000 368,000 80,000 Less: Accumulated Depreciation 188,000 142,000 46,000 Net Fixed Assets 260,000 226,000 Intangible Assets 82,000 82,000 0 TOTAL ASSETS $ 440,000 $ 400,000 $ 40,000

======= =======

LIABILITIES

Accounts Payable $ 24,000 $ 19,000 $ 5,000 Accruals 0 0 0 Short-Term Notes Payable 12,000 14,000 (2,000)TOTAL CURRENT LIABILITIES 36,000 33,000 3,000 Long-Term Debt 162,000 190,000 (28,000)TOTAL LIABILITIES $ 198,000 $ 223,000 $ (25,000)

OWNERS' EQUITYCommon Stock 180,000 130,000 50,000 Retained Earnings 62,000 47,000 15,000 TOTAL OWNERS' EQUITY 242,000 177,000 65,000 TOT LIABILITIES & OWNERS' EQUITY $ 440,000 $ 400,000 $ 40,000

======= =======

This Sources and Uses of Cash ties out to the change in the cash balance for the year, therefore we have a target of $10,000 increase in cash (or source) for 2004.

2004 Sources and Uses of Cash (Cash Flow Statement)

Sources and (Uses): Operating Activities

After Tax Net Income $ 45,000Sources:Depreciation 46,000Decrease in Accounts Receivable 9,000Increase in Accounts Payable 5,000Uses:Increase in Inventory - 5,000Net Cash Flow from Operating Activities $100,000

Sources and (Uses): Investing Activities

Increase in Gross Fixed Assets - 80,000Net Cash Flow from Investing Activities $ - 80,000

Sources and (Uses): Financing Activities

Decrease in Notes Payable* -2,000Decrease in Long Term Debt -28,000Increase in Common Stock 50,000Dividends Paid -30,000Net Cash Flow from Financing Activities $ -10,000

Net Change in Cash Account $ 10,000

*The change in Notes Payable (a current liability) is always included in the financing section.

11. Erosion Cost = ($90 - $35) x 8,000 = $440,000

Net Annual Cash Flow with one bike: ($90 - $35) x 40,000 = $2,200,000

Net Annual Cash Flow with two bikes:

($90 - $35) x (40,000 - 8,000) = $1,760,000

($410 - $360) x 12,000 = $600,000

Net Annual CF = $1,760,000 + $600,000 = $2,360,000

Increase of $160,000 per year so add new off-road bike to production.

15. Annual depreciation is cost of truck divided by five; $29,000/ 5 = $5,800

And for the first and last year we have $5,800 / 2 = $2,900.

a. Depreciation schedule using MACRS;

Year One Depreciation = $29,000 x 0.2000 = $5,800Year Two Depreciation = $29,000 x 0.3200 = $9,280Year Three Depreciation = $29,000 x 0.1920 = $5,568Year Four Depreciation = $29,000 x 0.1152 = $3,340.80Year Five Depreciation = $29,000 x 0.1152 = $3,340.80Year Six Depreciation = $29,000 x 0.0576 = $1,670.40

b. Comparing the two depreciation schedules before and after taxes (at 30%):

Year Straight Line MACRS ∆ Before Tax ∆ After TaxOne $2,900 $5,800 $2,900 $870Two $5,800 $9,280 $3,480 $1,044Three $5,800 $5,568 -$232 -$69.60Four $5,800 $3,340.80 -$2,459.20 -$737.76Five $5,800 $3,340.80 -$2,459.20 -$737.76Six $2,900 $1,670.40 -$1,229.60 -$368.88Total $29,000 $29,000 $0 $0

The difference is that the MACRS moves up the tax shield to the early years of depreciation yet the total tax shield is the same under both depreciation schedules.

17. The accumulated depreciation after three years using MACRS is:

$29,000 x (0.20 + 0.32 + 0.192) = $20,648.

The basis in the truck is therefore $29,000 - $20,648 = $8,352.

a. If the sales price is $15,000 then the truck had a gain on sale of $15,000 - $8,352 = $6,648 and the tax liability is $6,648 x 0.30 = $1,994.40. The after tax cash flow is $15,000 - $1,994.40 = $13,005.60

b. If the sales price is $10,000 then the truck had a gain on sale of $10,000 - $8,352 = $1,648 and the tax liability is $1,648 x 0.30 = $494.40. The after tax cash flow is $10,000 - $494.40 = $9,505.60

c. If the sales price is $5,000 then the truck had a loss on sale of $5,000 - $8,352 = $3,352 and the tax credit is $3,352 x 0.30 = $1,005.60. The after tax cash flow is $5,000 + $1,005.60 = $6,005.60

Chapter 11

1. Total funds borrowed = $2,000 + $1,500 + $800 = $4,300

WACC = ($2,000 / $4,300) x 0.06 + ($1,500 / $4,300) x 0.08 + ($800 / $4,300) x 0.14

WACC = 0.4651 x 0.06 + 0.3488 x 0.08 + 0.1860 x 0.14

WACC = 0.0279 + 0.0279 + 0.0260 = 0.0819 or 8.19%

3. A. If the bond sells for $920 we solve for YTM on the calculator:

Set P/Y = 1; C/Y =1

INPUTS 40 ? -920 40 1000Variables N I/Y PV PMT FVOUTPUT 4.43% x 2 = 8.86%

OR Set P/Y = 2; C/Y =2

INPUTS 40 ? -920 40 1000Variables N I/Y PV PMT FVOUTPUT 8.86%

B. If the bond sells for $1000 we have:

set P/Y = 1; C/Y =1INPUTS 40 ? -1000 40 1000Variables N I/Y PV PMT FVOUTPUT 4.00% x 2 = 8%

OR set P/Y = 2; C/Y =2INPUTS 40 ? -1000 40 1000Variables N I/Y PV PMT FVOUTPUT 8.00%

C. If the bond sells for $1080 we have:

set P/Y = 1; C/Y =1INPUTS 40 ? -1080 40 1000Variables N I/Y PV PMT FVOUTPUT 3.62% x 2 = 7.24%

OR set P/Y = 2; C/Y =2INPUTS 40 ? -1080 40 1000Variables N I/Y PV PMT FVOUTPUT 7.24%

We note that as the price of the bond increases (proceeds from the sale) the lower the cost of debt. This inverse relationship exists between price and the cost of debt as the future cash flows of the bond are fixed at issue and thus buyers will to pay more for the fixed stream of cash flows are lending money at a lower rate to the company.

5. A. If the bond sells for $920 and Kenny pays $25 per bond the net proceeds are $895

set P/Y = 1; C/Y =1


OR set P/Y = 2; C/Y =2


B. If the bond sells for $1000 and Kenny pays $25 per bond the net proceeds are $975

set P/Y = 1; C/Y =1




C. If the bond sells for $1080 and Kenny pays $25 per bond the net proceeds are $1055

set P/Y = 2; C/Y =2




7. A. Using the security market line we have,

E(ri) = rf + βi (E(rm) – rf)

Cost of Equity = E(ri) = 0.04 + 0.75 (0.12 – 0.04)

Cost of Equity = 0.04 + 0.75 (0.08) = 0.04 + 0.06 = 0.10 or 10%

B. Using the security market line we have,

E(ri) = rf + βi (E(rm) – rf)

Cost of Equity = E(ri) = 0.04 + 0.90 (0.12 – 0.04)

Cost of Equity = 0.04 + 0.90 (0.08) = 0.04 + 0.072 = 0.112 or 11.2%

9. What is the cost of preferred stock for Kyle?

The dividend is $100 x 0.06 = $6.00

And with a price of $80 the cost of preferred stock is $6/$80 = 0.075 or 7.5%

11. Market Enterprise Component Weights,Market Value of Debt = $980 x 3,000 = $2,940,000Market Value of Equity = $23.40 x 260,000 = $6,084,000Debt Component = $2,940,000 / ($2,940,000 + $6,084,000) = 0.3258Equity Component = $6,084,000 / ($2,940,000 + $6,084,000) = 0.6742

WACC for Market = 0.3258 x 8% + 0.6742 x 12% = 10.6968%

13. a. Adjusted WACC = 0.35 x 14% + 0.15 x 11% + 0.50 x 10% x (1 – 0.40) =

Adjusted WACC = 4.9% + 1.65% + 3.0% = 9.55%

b. Adjusted WACC = 0.35 x 14% + 0.15 x 11% + 0.50 x 10% x (1 – 0.30) =

Adjusted WACC = 4.9% + 1.65% + 3.5% = 10.05%

19.

Category T0 T1 T2 T3

Investment -$4,000,000NWC Change -$300,000 $300,000OCFs $1,500,000 $1,500,000 $1,500,000Salvage $250,000

At 6% WACC we have,NPV = $171,309 Accept project if WACC is 6% or lower.

At 8% WACC we have,NPV = $2,253 Accept project if WACC is 8%.

At 10% WACC we have,NPV = -$156,499 Reject project if WACC is 10% or higher.

Chapter 12

9. WACC if she borrows $1,000,000 isWACC = 0.4 x 8.5% + 0.6 x 9.25% = 3.40% + 5.55% = 8.95%

a. WACC if she borrows $2,000,000 is

WACC = 0.2 x 8.5% + 0.375 x 9.25% + 0.425 x 17% WACC = 1.7000% + 3.4688% + 7.2250% = 12.3938%

b. She can not borrow $3,000,000 her maximum borrowing is $2,450,000.

WACC at $2,450,000 is,

WACC = 0.1633 x 8.5% + 0.3061 x 9.25% + 0.5306 x 17% WACC = 1.3878% + 2.8316% + 9.0204% = 13.2398%

Chapter 13

1. Business Cycle = Production Cycle + Collection CycleBusiness Cycle = 35 Days + 21 Days = 56 DaysCash Conversion Cycle = Business Cycle – Payment CycleCash Conversion Cycle = 56 Days – 14 Days = 42 Days

Reducing Production Cycle by one week (7 days) reduces cash conversion cycle by one week (7 Days) to 35 days.Reducing Collection Cycle by one week (7 days) reduces cash conversion cycle by one week (7 Days) to 35 days.Increasing Payment by one week (7 days) reduces cash conversion cycle by one week (7 Days) to 35 days.

3. Average Production Cycle:Average Inventory = (Beginning Inventory + Ending Inventory) / 2Average Inventory for Corporate Seasonings = ($55,000 + $59,000) / 2 = $57,000The second step is to determine how quickly we turn over the inventory. To do this, we take the cost of goods sold for the year, COGS, and divide by the average inventory:Inventory Turnover = COGS / Average InventoryInventory Turnover for Corporate Seasonings = $570,000 / $57,000 = 10 timesAverage Production Cycle = Days in Year / Inventory TurnoverAverage Production Cycle = 365/10 = 36.5 Days

5.Average Collection Cycle: Average Accounts Receivable = (Beginning A/R + Ending A/R) / 2Average A/R for Corporate Seasonings = ($38,000 + $46,000) / 2 = $42,000Step two is to determine the Accounts Receivable turnover rate:

Accounts Receivable Turnover Rate = Credit Sales / Average Accounts ReceivableA/R Turnover for Corporate Seasonings = $672,000 / $42,000 = 16 timesThe third and final step is to estimate the collection cycle by dividing the number of days in a year by the Accounts Receivable turnover rate:Collection Cycle = 365 / Accounts Receivable Turnover RateRian’s Collection Cycle = 365 / 16 = 22.8125 Days

7.Average Accounts Payable Cycle: Average Accounts Payable = (Beginning of the year A/P + End of Year A/P) / 2

Average A/P = ($27,000 + $25,000) / 2 = $26,000The second step is to determine the Accounts Payable Turnover and here we use the COGS as the cost of production. Accounts Payable Turnover = COGS / Average A/PRian’s A/P Turnover = $570,000 / $26,000 = 21.9231 timesThe third and final step is to determine the number of days that Corporate Seasonings takes to pay its suppliers:Accounts Payable Cycle = 365 / Accounts Payable Turnover

Rian’s A/P Cycle = 365 / 21.9231 = 16.6491 days

19.Find the incremental cash flows by yearCF0 = $3,500,000 plus $500,000 outflow or -$4,000,000CF1 through CF4 = $1,000,000CF5 = $1,000,000 plus $500,000 plus $250,000 or $1,750,000NPV at 12% NPV = $30,346

And the project is a go!

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