final 2 fundamentals of corporate finance, 4th edition brealey

Remember: every question carries the same weight, so please do NOT spend too much time on one particular question; 2 Read the exam questions carefully; 3 Choose the answers that are clo

Name Section ID #

Professor Alagurajah’s Section A (Fridays, 2.30-5.30 pm), Professor King’s Section G (Internet), Professor Kohen’s Section F (Tuesdays, 2:30-5:30 pm), Professor Li’s Section E (Wednesdays, 2:30-5:30 pm), Professor Okonkwo’s Section B (Tuesdays,

7-10 pm), Professor Patterson’s Section D (Thursdays, 4-7 pm), and Professor Tahani’s Section C (Wednesdays, 7-10 pm)

AP/ADMS 3530.03 Finance

Final Exam Fall 2009 December 16, 2009

Exam - Solution

This exam consists of 50 multiple choice questions 2 points each for a total of 100 points Choose the response which best answers each question Circle your answers

below, and fill in your answers on the bubble sheet Only the bubble sheet is used to determine your exam score BE SURE TO BLACKEN THE BUBBLES

CORRESPONDING TO YOUR STUDENT NUMBER

Please note the following eight points:

1) Please use your time efficiently and start with the questions that you are most

comfortable with first Remember: every question carries the same weight, so

please do NOT spend too much time on one particular question;

2) Read the exam questions carefully;

3) Choose the answers that are closest to yours, because of possible rounding;

4) Keep at least 2 decimal places in your calculations and final answers, and at least

4 decimal places for interest rates;

5) Interest rates are annual unless otherwise stated;

6) Bonds pay semi-annual coupons unless otherwise stated;

7) Bonds have a par value (or face value) of $1,000;

8) Assume cash flows or payments occur at the end of a period or year, unless

otherwise stated; and

9) You may use the back of the exam paper as your scrap paper

10) Non-programmable financial and/or scientific calculators are allowed

TYPE A TYPE A Answer Keys TYPE B TYPE B Answer Keys Corresponding in A

Numerical Questions

1 You have agreed to pay $1,500 per month on a one-year loan with a principal of

$16,300 What is the EAR of this loan?

A) 9.09%

B) 16.80%

C) 18.72%

D) 20.42%

E) 22.82%

Solution D

Using your calculator:

PMT = 1500, n=12, PV = -16,300, FV = 0, COMP I/Y Æ Im = 015603

EAR = (1.015603)12-1 = 20.4165%

2 You are planning to buy a $320,000 home with a 20% deposit You finance the remainder with a 25 year mortgage that has a stated rate of 5.40% (APR compounded semi-annually) What is your monthly payment?

A) $1,470.49

B) $1,547.70

C) $1,738.78

D) $1,946.24

E) $2,145.87

Solution B

is = 5.40%/2 = 2.70%

EAR = (1+.0270) 2 -1 = 5.4729%

im = (1+0.054729)1/12 - 1 = 0.004450 = 0.4450%

n = 25 years x 12 = 300

Monthly Payment using your calculator:

n=300, I/Y=0.4450%, PV= -$256,000, FV=0, COMP PMT

PMT=$1,547.70

3 A 10-year bond was issued four years ago with a coupon rate of 5% and a face value of $1,000 The coupons are paid semi-annually What is the yield to maturity if the bond is selling at $876.00 today?

E) 7.61%

Solution E

Time remaining = 10 – 4 = 6 years = 12 semi-annual periods

FV= $1000

PMT = 5% x 1000/2 = $25

PV= -$876

Comp I/Y Æ I/Y = 3.8065

YTM = 3.8065 x2 = 7.6129%

4 How much would an investor lose if she purchased a 20-year zero-coupon bond with

a $1,000 par value and 4% yield to maturity, then sold it one year later when market interest rates increased to 6%?

C) $155.98

D) $167.70

E) $170.51

Solution A

The bond was purchased for $1,000/(1+.04)20 = $456.39

The 19-year bond is worth $1,000/(1+.06)19 = $330.51

This is a decline of $125.88

5 A stock that will pay a $5 dividend next year sells today for $80 If the stock’s required return is 14%, what should investors expect to pay for the stock one year from now?

A) $80.00

B) $84.30

C) $86.20

D) $91.20

E) $95.59

Solution C

r = Div1/P0 + (P1 – P0)/P0

14% = $5/80 + (P1 - 80)/80

Î P1 = $86.20

6 Lacey Inc.’s common stock is expected to have extraordinary growth of 20% per year for two years, after which time the growth will settle into a constant 5% rate If the discount rate is 11% and the most recent dividend was $1.50, what should be the current share price?

A) $21.27

B) $22.20

C) $30.68

D) $34.05

E) $37.80

Solution D

DIV1 = $1.50 x (1.20) = $1.80

DIV2 = $1.80 x (1.20) = $2.16

DIV3 = $2.16 x (1.05) = $2.268

P2= $2.268/ (.11-.05) = $37.80

P0= 1.80/(1.11) + 2.16/(1.11)2 + 37.80/(1.11)2

= 1.6216 + 1.7531 + 30.6793 = $34.0541

7 What is the minimum number of years that an investment costing $400,000 must return $48,000 per year at a discount rate of 12 percent in order to be an acceptable investment?

A) 4.29 years

B) 7.40 years

C) 9.26 years

D) 27.01 years

E) An infinite number of years

Solution E

NPV = ($48,000 / 0.12) - $400,000 = 0

8 Cranberry Inc has been presented with an investment opportunity which will yield cash flows of $36,000 for Year 1, $27,000 for Year 2, $34,000 for Year 3 and $X for year 4 This investment will cost the firm $120,000 today and the payback period for this investment is 3.215 years What is the approximate projected cash flow for Year

4 if the company’s opportunity cost of capital is 4%?

Solution D

3.215 = 3 + 120 – (36 + 27 + 34) Î X = $106,977

X

9 A firm is considering the following project Its opportunity cost of capital is 8%

Cash Flow -3000 2000 400 1900 3200

What is the discounted payback period of the project?

A) 2.29 years

B) 2.53 years

C) 2.72 years

D) 2.95 years

E) 3.15 years

Solution B

0 -$3,000 -$3,000

3 $1,508.28 $703.07

Discounted payback occurs between the 2nd and 3rd years

Discounted payback period = 2 years + $805.21/1,508.28 = 2.53 years

10 As the Director of Finance for Bozo Corporation, you are evaluating two mutually exclusive projects with the net cash flows given below If Bozo's cost of capital is 13 percent, which project would you choose?

Year Project A Project B

1 11,000 9,000

2 12,000 10,000

3 21,000 15,000

4 17,000 22,000

A) Project A, since it has the higher IRR

B) Project A, since it has the higher NPV

C) Project B, since it has the higher IRR

D) Project B, since it has the higher NPV

E) Neither project

Solution E

NPV (A) = -$5,887.25

NPV (B) = -$315.17

Therefore both projects should be rejected

11 You have a choice between using your old machine at a cost of $5,500 annually for the next five years Alternatively, you can purchase a new machine for $8,000 plus

$3,500 in annual maintenance for the next five years If the cost of capital is 14%, you should:

A) Buy the new machine and save $400 in equivalent annual costs

B) Buy the new machine and save $330 in equivalent annual costs

C) Keep the old machine and save $400 in equivalent annual costs

D) Keep the old machine and save $330 in equivalent annual costs

E) None of the above statements are correct

Solution D

The PV of total costs of the new machine is $20,015.78:

n = 5 ; i = 14% ; PMT = 3,500 Solve for PV = 12,015.78 + $8,000 upfront cost

This translates into an equivalent annual cost of $5,830.27:

n = 5 ; I = 14% ; PV = 19,015.78 Solve for PMT = $5,830.27

This is $330 higher than the annual cost associated with the old machine.

12 If a project has a cost of $70,000 and a profitability index of 0.2, then:

A) Its NPV is $14,000

B) The present value of its cash inflows is $25,000

C) Its IRR is 15%

D) Its cash inflows are $70,000

E) None of the above are correct

Solution A

PI = NPV/Cost, this gives NPV= $14,000

Please use the following information to answer Questions 13 – 16

Jensen Industries is considering purchasing a new numerically controlled drilling press The press costs $100,000, and belongs to a 15% CCA rate asset class (declining balance method) and the half-year rule applies The press is estimated to have before-tax cash flow savings of $34,000 per year for six years and will require an immediate increase in net working capital of $5,000, which will be recovered when the machine is sold at the end of Year 6 Initially assume there is zero salvage value The discount rate

is 10% and the tax rate is 40%

13 What is Jensen’s CCA in Year 1 and Year 2?

A) $7,500; $12,750

B) $7,500; $13,875

C) $7,500; $15,000

D) $15,000; $12,750

E) $15,000; $13,875

Solution B

CCA in Year 1 = $100,000 × ½ × 0.15 = $7,500

CCA in Year 2 = ($100,000 - $7,500) × 0.15 = $13,875

14 What is the present value of Jensen’s CCA tax shield?

A) $5,367

B) $11,667

C) $19,419

D) $22,909

E) $23,609

Solution D

909 , 22

$

% 10 1

0%

1 0.5 1

% 15 10%

40%

% 15

$100,000

= +

× + +

×

×

=

⎥⎦

⎤

⎢⎣

⎡

⎥⎦

⎤

⎢⎣

⎡

PVCCATS

15 Should Jensen accept the project?

A) Yes, because the NPV is positive, and it exceeds $10,000

B) Yes, because the NPV is positive, although it is less than $10,000

C) No, because the NPV is negative, and it is between 0 and -$10,000

D) No, because the NPV is negative, and it is between -$10,000 and -$100,000 E) None of the above

Answer B

NPV = -$105,000 + $34,000(1-0.40)(PVIFA6yr,10%) + $5,000 (PVIF 6yr,10%)

+ $22,909

= $9,578.69

16 By how much will the NPV increase if Jensen is able to obtain a $10,000 salvage value at the end of Year 6?

A) $1,824

B) $4,290

C) $5,645

D) $6,000

E) $7,123

Answer B

NPV increase = PV of salvage value – PV of lost CCATS due to salvage value

290 , 4 6

%) 10 (1

1

% 15 10%

40%

% 15

$10,000 6

%) 10 (1

$10,000 increase

+ +

×

×

− +

=

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎥⎦

⎤

⎢⎣

⎡

⎥

⎦

⎤

⎢

⎣

⎡

17 Calculate the NPV break-even level of sales for a project requiring an investment of

$3,000,000 and providing as annual cash flows: (0.15 × sales - $250,000) Assume the project will last 10 years and that the discount rate is 10%

A) $3,254,890

B) $3,504,630

C) $4,536,150

D) $4,921,504

E) $4,998,405

Solution D

504 , 921 , 4 9217

0

150 , 536 , 4 Sales 150

, 536 , 4 sales 9217 0

000 , 000 , 3 1446 6 ) 000 , 250

$ sales 15 0 (

0 000 , 000 , 3 ] ) 1 1 ( 1 0

1 1

0

1 )[

000 , 250

$ sales 15 0 (

0 investment )

flows cash ( PV NPV

10

=

=

⇒

=

⇒

=

×

−

×

⇒

=

−

−

−

×

∴

=

−

=

18 What percentage change in sales occurs if profits increase by 3 percent when the firm's degree of operating leverage is 4.5?

A) 0.33 percent

B) 0.67 percent

C) 1.50 percent

D) 3.33 percent

E) 3.67 percent

Solution B

DOL = (% Change in profits) / (% Change in sales)

4.5 = 3% / (% Change in sales)

Î % Change in sales = 0.67%

19 Approximately how much was paid to invest in a project that has a NPV break-even level of sales of $8 million, an eight-year life, a 10 percent discount rate, and annual cash flows determined by (0.28 × sales – $450,000)?

Solution C

PV (cash flows) = investment, so that NPV breaks even

20 A decision tree shows a 30% probability of $2 million in returns and a 70% chance of

$1 million in returns occurring one year in the future What is the maximum amount you would invest today in this project if the discount rate is 10%?

A) $1,181,818

Solution A

818 , 181 , 1 1

1

1 7 0 2 3 0

0 1

1

1 7 0 2 3 0

=

× +

×

=

∴

=

−

× +

×

=

M M

Investment

investment M

M NPV

Please use the following information to answer Questions 21 – 24

State Probability Return on A Return on B

21 What is the expected return on security B?

Solution D

E(RB) = 0.6*8% + 0.4*20% = 12.8%

22 What is the standard deviation of security A?

Solution C

Var(RA) = 0.6*(0.15-0.11)2 + 0.4*(0.05-0.11)2 = 0.0024

Std Dev(RA) = (0.0024)1/2 = 0.0490

23 What is the expected return on a portfolio that is 40% invested in A and 60% invested in B?

Solution E

E(RP) = 0.4*11% + 0.6*12.8% = 12.1%

24 What is the correlation between securities A and B?

A) -1

B) -0.5

C) 0

D) 0.5

E) 1

Solution A

Var(RB) = 0.6*(0.08-0.128)2 + 0.4*(0.2-0.128)2 = 0.0035

Std Dev(RB) = (0.0035)1/2 = 0.0592

Cov(RA,RB) = 0.6*(0.15-0.11) (0.08-0.128)+ 0.4*(0.05-0.11) (0.2-0.128)= -0.0029 Corr(RA,RB) = -0.0029/(0.0592*0.0490) = -0.9997

25 The return on the market portfolio is 12% and the risk-free rate of return is 6% The standard deviation of the market portfolio is 24% What is the standard deviation of a stock that plots on the Security Market Line (SML) with an expected return of 10% and a correlation to the market portfolio of 2/3?

A) 5%

B) 8%

C) 10%

D) 16%

E) 24%

Solution E

Using CAPM: 10% = 6% + Beta (12% – 6%)

Solving for the stock’s Beta = (10% - 6%) / (12% - 6%) = 0.667

Therefore the stock’s standard deviation equals 0.667 x 24% / 0.667 = 24%

26 Where will the following two projects plot in relation to the security market line (SML)

if the risk-free rate is 6% and the market risk premium is 9%? Which project should

be undertaken?

Project A: Beta =2; Actual rate of return = 25%

Project B: Beta =1.1; Actual rate of return = 15%

A) Project A plots above the SML and should be accepted; Project B plots below the SML and should be rejected

B) Project A plots above the SML and should be rejected; Project B plots below the SML and should be accepted

C) Project A plots below the SML and should be accepted; Project B plots above the SML and should be rejected

D) Project A plots below the SML and should be rejected; Project B plots above the SML and should be accepted

E) None of the above

Solution A

Project A: using CAPM E(r) = 0.06 + 2 × 0.09 = 0.24 < 0.25

Project A plots above the SML and should be accepted

Project B: using CAPM E(r) = 0.06 + 1.1 × 0.09 = 0.159 > 0.15

Project B plots below the SML and should be rejected

27 The historical relationship between stock A and the market portfolio can be stated as follows When stock A has gone up by 1.6% the market portfolio has gone up by 1.2%; and when stock A has gone down by 1.6% the market portfolio has gone down by 1.2% The expected return associated with stock A for the upcoming year is 13% The prevailing market risk premium is 3% Based on the above information, what is the prevailing rate of return on a t-bill if all financial instruments are priced correctly?

A) 7.6%

B) 8.2%

C) 9%

D) 9.4%

E) Cannot be determined without additional information

Solution C

We can use the CAPM to answer this question as the t-bill is the proxy for risk free rate of return

re = rf + Beta x (rm - rf) Î rf = re - (Beta x market risk premium)

Or Beta = % change in the stock / % change in the market portfolio

= 1.6/1.2 = 1.3333

Therefore rf = 13% – 1.3333 x 3% = 13% – 4% = 9%

28 What is the beta of the following portfolio?

Amount Invested $5,000 $10,000 $15,000

Solution B

Portfolio Beta is simply the weighted average of the individual betas

Portfolio Beta = (5,000 / 30,000) x 1.2 + (10,000 / 30,000) x 1.8

+ (15,000 / 30,000) x 0.7

= 1.1503

29 Calculate the weighted average cost of capital (WACC) for Julia Corp Julia has both debt and common equity financing The market value of debt represents 40% of its capital structure Julia has 8 year bonds outstanding with a 9% annual coupon which currently trade at par The company’s tax rate is 40% T-bills currently provide a rate

of return of 5.5% and the rate of return on the market portfolio is 10.5% The equity beta of the stock is 1.4

A) 8.31%

B) 9.66%

C) 11.10%

D) 11.18%

E) 11.96%

Solution B

D/V = 0.4; E/V = 0.6; rd = 0.09; Tc = 0.40

re = 0.055 + 1.4 x (0.105 – 0.055) = 0.125

Then WACC = 0.4 x 0.09 x (1 - 0.4) + 0.6 x 0.125 = 0.0966 or 9.66%

30 Kamal Ltd finances its operations using $1.50 of debt for every $2 of common stock The pre-tax cost of debt is 7.5%, the cost of equity is 11%, and the tax rate is 34% Currently, the firm is considering a small project that it considers to be equally as risky as the overall firm The project has an initial cash outlay of $18,500 (non-depreciable) and is expected to have a single cash inflow of $25,000 at the end of year two What is the net present value of this project?