final 4 fundamentals of corporate finance, 4th edition brealey

TD Bank’s earnings and dividends are expected to grow at a rate of 10% during the next 2 years, at 8% in the third year, and at a constant rate of 6% thereafter.. A proposed nuclear powe

Name Section _ ID #

Prof King’s section C & Prof Alagurajah’s sections A and D)

AK/ADMS 3530 Final Exam

Summer 2007 August 14th 7 -10 pm

Type A Exam

50 Multiple Choice Questions (Total of 164 marks) made up a follows

32 Calculation Questions (4 marks each for a total of 128 marks)

18 Conceptual Questions (2 marks each for a total of 36 marks)

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 points:

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

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 least4 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; and

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

Good Luck.

32 Calculation Questions (4 marks each)

1 The common stock of Robin's Tools sells for $24.50 The firm's beta is 1.2, the free rate is 4%, and the return on the market portfolio is 12% Next year's dividend is expected to be $1.50 Assuming that dividend growth is expected to remain constant for Robin’s Tools over the foreseeable future, what is the firm's anticipated dividend growth rate?

3 Consider the following monthly cash flows (see the diagram below):

Cash flows of an amount X are made for months 1, 3, 5, …, 17 and 19 (the ten

odd-numbered months) and cash flows of an amount Z are made for months 2, 4, 6, …, 18

and 20 (the ten even-numbered months) The APR is 6% and is compounded on a

monthly basis What is the present value of these cash flows today if X = $2,000 and

The monthly interest rate is 0.5% but since the X’s cash flows are made every two

months, we need to calculate the 2-months equivalent interest rate:

I2m =r=(1+0.5%)2 −1=1.0025%

The present value of the Z’s cash flows is given by:

Using your calculator:

I2m = 1.0025%, n=10, PMT = -700, FV=0, COMP PV

PVz0 = -$6629.02 at t=0 (Since fist payment begins at t=2 and “i" is calculated for every

2 month period, and last payment is at t=20)

And the present value of the X’s is given by:

Since X begins at t=1, using your calculator for a regular annuity will give PV at t =-1:

I2m = 1.0025%, n=10, PMT = 2000, FV=0, COMP PV

PVx 1 = -$18,940.07 at t= -1 (Since fist payment begins at t=1 and “i" is calculated for

every 2 month period, and last payment is at t=19, you are really calculating PV of an

annuity at t= -1)

To adjust for PVx at t=0-> 18,940.07 x (1.005)1 = $19,034.77

The total present value (Z + X) is equal to:

75.405,12

$02.629,677.034

4 TD Bank’s earnings and dividends are expected to grow at a rate of 10% during the next 2 years, at 8% in the third year, and at a constant rate of 6% thereafter If last dividend paid was $2.00 and the required rate of return on its common stock is 12% How much should you pay today for one share of TD Bank?

6 What is the minimum cash flow that could be received at the end of year two to make the following project "acceptable"? Initial cost = $100,000; cash flow at end of year one

= $35,000, cash flow at the end of year three = $52,250; opportunity cost of capital = 8% A) $20,917

Project is acceptable when NPV is equal to or greater than 0

For a 0 NPV, PV of CFs must be equal to the initial investment

i.e 100,000 = 35,000/ (1.08) + X/(1.08^)2 + 52,250/(1.08)^)3

solve for X to get: X = $30,229

7 A proposed nuclear power plant will cost $22 million to build and then will produce cash flows of $3 million at the end of each year for 15 years At the end of year 15, it must be decommissioned (closed) at a cost of $9 million If the discount rate is 9%, should the plant be built?

A) Yes, because the NPV is positive

B) Yes, because the IRR is positive

C) Yes, because both NPV and IRR are positive

D) No, because the NPV is negative

E) No, because the cash flows sign change over the project’s life

Solution: D

NPV = −22 + 3 × annuity factor(r, 15 years) − 9/(1 + r)15

When r = 9%, NPV = −288,777

IRR = 8.74 % (which is less than the discount rate)

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

9 Below are the cash flows for two for two mutually exclusive projects The projects’ discount rate is 10%

Project C0 C1 C2 C3

A -18 10 10 10

B -50 25 25 25

Which of the following statements is/are true?

A) Project A should be chosen because it has the higher NPV

B) Project A should be chosen because it has the higher IRR

C) If funds are limited, Project B should be chosen because it has the higher profitability index

D) If the firm has unlimited funds, both projects should be chosen

E) None of the above statements is true

Detailed Solution E:

NPVA = –18 + 10 × annuity factor(10%, 3 periods) = $ 6.87

NPVB = –50 + 25 × annuity factor(10%, 3 periods) = $12.17

Thus Project B has the higher NPV if the discount rate is 10%

Project A has the higher profitability index

Project PV ment NPV (= NPV/Investment)

A 24.87 18 6.87 0.38

B 62.17 50 12.17 0.24

A firm with a limited amount of funds available should choose Project A since it has a

higher profitability index of 0.38, i.e., a higher “bang for the buck.”

For a firm with unlimited funds, the possibilities are:

i If the projects are independent projects, then the firm should choose both projects

ii However, if the projects are mutually exclusive(!), then Project B

should be selected It has the higher NPV

10 Sequel Catering is considering a second store that has an up-front cost of $X The project will generate a positive cash flow of $65,000 a year Assume that these cash flows are paid at the end of each year and that the project will last for 20 years Sequel uses a 9% annual discount rate The project has a 12 percent IRR What is the project's NPV?

Then solve for NPV = $107,841.63

11 What is the amount of operating cash flow for a firm with $500,000 profit before tax,

$100,000 depreciation expense, and a 35% corporate tax rate?

12.An investment today of $25,000 promises to return $10,000 annually for the next three years What is the approximate real rate of return on this investment if inflation averages

6 percent annually during the 3 years?

Solving with financial calculator, the IRR = 9.701%

Then, 1.09701/1.06 = 1.0349 or approx 3.5% real return

13 At what discount rate would you be indifferent between accepting or rejecting a project which costs $6,000 today with annual cash flows of $1,200 for the next nine years?

Calculate the IRR; the point at which the NPV of the project equals “0”

(indifference point) Using your calculator IRR = 13.70%

14.A project anticipates net cash flows of $10,000 at the end of year one, this amount will grow at a 5 percent rate of inflation over the subsequent four years Calculate the real present value of this five-year cash stream if the firm employs a nominal discount rate of

1 0952

= 12,315.37

where PVCCATS = [(.4)(.3)(100,000)/.14+.30][1.07/1.14] = 25,598.09

16 Consider the following example of Fairways Driving Range Rental income is expected to be 20,000 buckets a year at $3 per bucket Equipment costs are $20,000, depreciated straight-line over 5 years with no salvage value Variable costs are 10% of rentals and fixed costs are $45,000 per year Assume no increase in working capital nor any additional capital outlays The required return is 15% and the tax rate is 15% What

17.What is the break-even level of revenues for a firm with $6 million in sales, variable costs of $3.9 million, fixed costs of $1.2 million, and depreciation of $1 million?

18 What is the maximum percentage of variable costs in relation to sales that a firm could experience and still (accounting) break even with $5 million revenue, $1million fixed costs and $500,000 depreciation?

profit margin = $1.5 million / $5 million = 0.3

The percentage of variable costs = 1 – 0.3 = 0.7 = 70%

19 A firm with $600,000 fixed costs and $200,000 depreciation is expected to produce

$225,000 in pretax profits What is its Degree of Operating Leverage (DOL)?

20.If pretax profits decrease by 13.8 percent when the DOL is 3.8, then the decrease in sales is:

profits in

X = 3.63% therefore sales decreased by 3.63%

21.What is the approximate variance of returns if over the past three years an investment returned 8.0%, -12.0%, and 15.0%? (please use “n” as your divisor)

12 3.67

128.37 245.55

= 130.89

22 What should be the beta of stock C if an investor wishes to achieve a portfolio beta of

1 in the following equally weighted portfolio: stock A (beta = 0.9), stock B (beta = 1.1), and stock C?

23 You are provided with the following information about two perfectly negatively correlated stocks in a portfolio What is the standard deviation of the portfolio return?

0

27.013.0)1(57.043.0227.057.013.043.0

2

2 2

2 2

2 1 2 , 1 2 1

2 2

2 2

2 1

2 1

×+

×

=

++

00765.0

),(Cov

B A B

A

r r

ρ

σσρ

25 Given the following information, what is WBM Corporation's WACC?

Common Stock: 1 million shares outstanding, $40 per share, $20 par value, beta = 1.3 Bonds: 10,000 bonds outstanding, $1,000 face value each, 8% annual coupon, 22 years to maturity, market price = $1,101.23 per bond Semi-annual coupon payments

Market risk premium = 8.6%, risk-free rate = 4.5%, marginal tax rate = 34%

The Market Value of debt is D = 10,000 x $1,101.23 = $11,012,300

The market value of common shares is E = 1 million x $40 = $40 million

So the total market value of the firm is V = D + E = $51,012,300

r debt = 7.078% (YTM as calculated by a financial calculator)

The weights are: D/V = $11,012,300 / $51,012,300 = 0.2159, E/V = 0.7841

WACC = (D/V) x (1 – T C ) × r debt + (E/V) x r equity

= 0.2159 x (1 - 0.34) x 0.0708 + 0.7841 x 0.1568 = 13.30%

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 Beta IRR

I 2.0 25%

II 1.1 15%

A) Project I plots above the SML and should be accepted; Project II plots below

the SML and should be rejected

B) Project I plots above the SML and should be rejected; Project II plots below

14 the SML and should be accepted

C) Project I plots below the SML and should be accepted; Project II plots above

the SML and should be rejected

D) Project I plots below the SML and should be rejected; Project II plots above

the SML and should be accepted

E) None of the above

Project I: expected return = 0.06 + 2 × 0.09 = 0 24 < IRR of 0.25

Project I plots above the SML and should be accepted

Project II: expected return = 0.06 + 1.1 × 0.09 = 0 159 > IRR of 0.15

Project II plots below the SML and should be rejected

27.A project is determined to have equal probability of generating $1 million annually or

$500,000 annually, for each of four years The initial outlay is $2 million The expected return on Treasury bills is 6 percent and the market risk premium is 8 percent What isthe highest project beta that will justify acceptance of the project?

18.45% = I (Re)

Using CAPM Re = Rf + B (Rm – Rf) Solving for Beta we get 1.56

28 Stone Industries is expected to pay a dividend of $2.10 per share in one year This dividend, along with the firm's earnings, is expected to grow at a rate of 5% forever The current market price for a share of Stone’s common stock is $38.62 If the T-bill return is 4% and the market risk premium is 6%, then what is the beta of Stone’s common stock?

%6

%4

%44.10)(

CAPM,

By the

%

44.10

%5

1.262.38

$DDM,

=

⇒

−+

r r

r r

g r

DIV P

29 Consider the following information for Alex Computers Total book value of the firm’s equity is $10 million; book value per share is $20 The stock sells for a price of

$30 per share The firms’ beta is 1.5 and the market risk premium is 7.33% and the free rate is 4% The firm’s bonds have a par value of $5 million and sell at a price of 110% of par The yield to maturity on the bonds is 9% and the firm’s tax rate is 40% What is the firm’s WACC?

Security Market value Explanation

Debt $ 5.5 million 1.10 × par value of $5 million

Equity $15.0 million $30 per share × 500,000 shares*

Total $20.5 million

*Number of shares = Error!= 500,000

WACC = Error! × rdebt + Error!× requity

= Error!× (1 – 4) × 9% + Error!× 15% = 12.42%

30 Evan Sports Inc has two issues of debt outstanding One is a 9% coupon bond with

a face value of $20 million, a maturity of 10 years, and a yield to maturity of 10% The second bond issue has a maturity of 15 years, and a coupon rate of 10% The face value

of the second issue is $25 million and the issue sells for 92.8% of par Both bonds pay

coupons annually The firm’s tax rate is 35% What is Evan Sports Inc.’s after-tax cost

The 9% coupon bond has a yield to maturity of 10% and sells for 93.86% of face value:

Using your calculator:

The market value of the issue is 928 × $25 million = $23.20 million

The weighted average before-tax cost of debt is therefore

Error!× 10% + Error!× 11% = 10.55%

The after-tax cost of debt is (1 – 35) × 10.55% = 6.86%

31 What is the after-tax cost of 6% preferred stock that has a par value of $20, a total book value of $20 million, sells for $15 per share in the market, and the firm’s tax rate is 40%?

= 6% x 20 = $1.20 per share annual dividend

After-tax cost of preferred =required rate of return = $1.20/15 = 8.00%

Taxes have no impact on the cost of preferred stock!

32 Cocoa Industries has a cost of equity of 12% and a cost of debt of 8%

If the target debt/equity ratio is 60%, and the tax rate is 35%, what is Cocoa's

weighted average cost of capital (WACC)?

If Equity = $100, then Debt = $60 and V = $160

Weight of equity = 100/160 = 625 Weight of debt = 60/160 =.375

WACC = 625 x 12% + (.375 x 08) x (1-.35) = 9.45%

18 Conceptual Questions (2 marks each)

33 Stock prices are said to follow a “random walk,” which means that if a stock’s price decreased during the past week, then

A) this week’s price will reverse last week’s loss and go up

B) this week’s price will continue last week’s decline

C) this week’s price will remain constant until new information is released

D) this week’s price will change in either direction with equal likelihood

E) Only technical analysts can determine this week’s price

Solution: D

34 What happens when a bond's expected cash flows are discounted at a rate lower than the bond's coupon rate?

A) The price of the bond increases

B) The coupon rate of the bond increases

C) The par value of the bond decreases

D) The coupon payments will be adjusted to the new discount rate

E) The maturity of the bond will be increased

Solution: A

35 The book value of a firm's equity is determined by:

A) multiplying current share price by number of shares outstanding

B) multiplying share price of any new equity issue by number of shares outstanding C) the difference between the book values of assets and liabilities

D) the book value of firm's assets divided by shares outstanding

E) the market value of it’s debt

Solution: C

36 A firm is considering the purchase of an asset whose risk is greater than the current risk of the firm, based on any method for assessing risk In evaluating this asset, the decision maker should

A) Increase the IRR of the asset to reflect the greater risk