exam solution 10 fundamentals of corporate finance, 4th edition brealey

6 Unless otherwise stated, interest rates are annual, and bonds pay semiannual coupons and have a face value or par value of $1,000.. The mortgage has a five year renewal term for whic

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Professor Alagurajah’s Section M (Thursdays, 4-7 pm), Professor Ho’s Sections R (Fridays, 2:30-5:30 pm) and S (Mondays, 2:30-5:30 pm), Professor King’s Sections P (Mondays,

7-10 pm) and O (Internet), Professor Kohen’s Section T (Wednesdays, 7-7-10 pm), Professor Pestano’s Section Q (Wednesdays, 4-7 pm), and Professor Tahani’s Section N (Tuesdays, 7-10 pm)

AP/ADMS 3530.03 Finance Midterm Exam

Winter 2010 February 21, 2010

Exam - Solution This exam consists of 30 multiple choice questions and carries a total of 100 points Choose the response which best answers each question Circle your answer below, and

fill in your answers on the bubble sheet Only the bubble sheet is used to determine your exam score Please do not forget to write your name and ID # both at the top of this

cover page and on the bubble sheet Also please write the type of your exam (A or B)

on the bubble sheet

Please note the following points:

1) Read the questions carefully and use your time efficiently

2) Choose the answers that are closest to yours, because of possible

rounding

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

and at least 6 decimal places for interest rates

4) The 20 “Numerical questions” are worth 4 points each

5) The 10 “Conceptual questions” are worth 2 points each

6) Unless otherwise stated, interest rates are annual, and bonds pay

semiannual coupons and have a face value (or par value) of $1,000

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

Notations

We may denote the PV and FV annuity factors respectively by PVIFA(r,n) and FVIFA(r,n), i.e.:

r

r n

r FVIFA r

r n

r PVIFA

n n

1 ) 1 ( ) , (

; )

1 ( 1 ) ,

≡ +

−

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

Numerical questions (4 points each)

1 You want to buy a house that costs (before down payment) $450,000 You make a 10% down payment and finance the rest with a 30-year mortgage The mortgage has a five year renewal term for which the annual mortgage rate is 5.20% (APR compounded semi-annually) What will the remaining principal of the loan be at the end of the 5-year term if you are making monthly payments?

A) $272,400

B) $310,450

C) $372,662

D) $372,947

E) $414,068

Answer C

The monthly interest rate is given by:

(1 + im)12= 1 + EAR = (1 + 2.60%)2 = 1.052676, that is im= 0.4287%

The monthly payment for the 30-year loan:

405,000 = PMT x PVIFA(0.4287%,360)

Î PMT = $2,210.01

Mortgage remaining at the end of 5 years, i.e 300 months remaining:

PV = $2,210.01 x PVIFA(0.4287% , 300) = 372,661.65

2 In four years from today, the following cash flow stream will have a future value of

$5,104.64: $100 today, $500 at the end of one year, $800 at the end of two years, “X”

at the end of three years, and $2,000 at the end of four years The annual interest rate

is 6% What is X?

A) $1,050

B) $1,200

C) $1,400

D) $1,484

E) $2,150

Answer C

FV = $5,104.64 = 100 x (1.06)4+ $500 x (1.06)3+ $800 x (1.06)2+ X x (1.06)

+ $2,000

FV = $5,104.64 = $126.25 + $595.51 + 898.88 + X x (1.06) + $2,000

Î X x (1.06) = 1484.00

Î X = 1484.00/1.06 = $1,400

3 If $300,000 is borrowed for a home mortgage at a posted rate of 6.10% (APR semi-annually compounded), how much interest can be saved over the life of the mortgage

by agreeing to a 20-year amortization period, rather than a 30-year amortization period? Assume monthly payments and choose the closest answer

A) $73,400

B) $82,824

C) $96,471

D) $110,715

E) $132,353

Answer E

The monthly interest rate is given by:

(1 + im )12 = 1 + EAR = (1 + 3.05%)² = 1.061930, that is im = 0.5020%

The monthly payment for the 20-year loan

300,000 = PMT x PVIFA(0.5020%,240)

PMT = $2,153.45

Total interest paid with the 20-year loan:

240 x 2,153.45 – 300,000 = $216,828

The monthly payment for the 30-year loan

300,000 = PMT x PVIFA(0.5020%,360)

PMT = $1,803.28

Total interest paid with the 30-year loan:

360 x 1,803.28 – 300,000 = $349,180.80

Difference in total interest paid: $349,180.80 - $216,823.33 = $132,352.80

4 You are planning to set up a 30-year trust fund for your niece that will pay $5,000 at the end of the first year and then the payments increase by 2.25% per year The trust fund will earn on average a 5.75% annual rate of return How much money should you invest today in order to provide the correct amount of funds to your niece?

A) $72,645

B) $90,811

C) $142,857

D) $156,980

E) $175,788

Answer B

PV growing annuity = C1/ (r-g) x [1- { (1+g)/(1 +r) } t ]

= 5,000 / (.0575 - 0225) x [1- { (1+.0225)/(1 +.0575) }30 ]

= 142,857.14 x [1 - 0.0364324]

= 142,857.14 x 0.635676

= 90,810.86

5 How much interest is to be earned between the end of Year 4 and the end of Year 6 on

a $7,500 deposit made today that earns 3.20% annual interest, compounded semiannually?

A) $480.00

B) $483.84

C) $553.16

D) $558.21

E) $577.24

Answer D

The difference between the FV12and FV8(time periods are in terms of 6 months) is the interest you earn over these two years:

FV12= $7,500 x (1 + 1.60%)12 = $9,073.73

FV8= $7,500 x (1 + 1.60%)8= $8,515.52

Î Interest earned = $9,073.73 - $8,515.52 = $558.21

6 David deposits $1,500 in a 3-year term deposit that pays 4% interest with quarterly compounding At the end of three years, he transfers the amount to another 3-year term deposit that pays 5% interest with monthly compounding How much will he have 6 years from now?

A) $1,953

B) $1,963

C) $5,420

D) $6,234

E) $14,761

Answer B

$1,500 ×(1 + 4%/4)12

x (1 + 5%/12)36 = $1,963.16

7 Richard wants to invest his money at the local bank Which one of the five accounts below is best for him?

I APR of 5% with semiannual compounding

II APR of 4.97% with quarterly compounding

III APR of 4.89% with monthly compounding

IV APR of 4.95% with weekly compounding

V APR of 4.94% with daily compounding

A) I

B) II

C) III

D) IV

E) V

Answer D

I EAR = (1 + 05/2)2 − 1 = 5.0625%

II EAR = (1 + 0497/4)4 − 1 = 5.0634%

III EAR = (1 + 0489/12)12 − 1 = 5.0011%

IV EAR = (1 + 0495/52)52 − 1 = 5.0721%

V EAR = (1 + 0494/365)365 − 1 = 5.0637%

Therefore, account IV is the best

8 Mr Matsui plans to make the following annual contributions to his investment account for the next 30 years:

6 and thereafter 8,000 per year

If the contributions are made at the end of each year, and the rate of interest is 5%, how much money will he have at the end of 30 years?

A) $449,726.70

B) $467,527.50

C) $475,527.50

D) $480,212.43

E) $499,303.88

Answer C

FV = $5,000 ×(1.05)29

+$4,000 ×(1.05)28

+$6,000 ×(1.05)27

+$7,000 ×(1.05)26 + $3,000 ×(1.05)25 + ($8,000) x FVIFA(5%, 25 years)

= $93,710.71 + $381,816.79

= $475,527.50

9 Maria Tiberini plans to retire soon, on her 65th birthday She wonders if she has enough money to support her retirement Since she had a heart attack 3 years ago, she does not expect she would live longer than 85 years old She plans to spend $40,000 in the first year of retirement She expects her annual expenses will increase at the rate of inflation, expected to be 2% per year Assume that all expenses are paid at the beginning of each year, how much money does she need at 65 to support her post-retirement expenses? Assume that the rate of interest is 6%

A) $458,797

B) $536,675

C) $539,386

D) $543,613

E) $568,875

Answer E

PV of Growth Annuity Due = [($40,000)(1.06)/(.06-.02)]{1- (1.02/1.06)20 }

= $568,875

10 Chris Little owes his friend some money His friend gives him 5 options of payment If the rate of interest is 8%, which option should Chris choose?

I Pay $2,100 today

II Pay $500 per year, at the end of every year for 5 years

III Pay $450 per year, at the beginning of each year for 6 years,

IV Pay $500 at the end of year 1, $400 at the end of year 2, $300 at the end of year

3, and $1,500 at the end of year 4,

V Pay $1,200 at the end of year 3 and $1,500 at the end of year 5

A) I

B) II

C) III

D) IV

E) V

Answer E

PV(I) = $2,100

PV(II) = $500 x PVIFA(8%,5) = $1,996.36

PV(III) = $450 x PVIFA(8%,6) x (1 + 8%) = $2,246.72

PV(IV) = 500/1.08 + 400/1.082 + 300/1.083 + 1,500/1.084 = $2,146.59

PV(V) = 1,200/1.083 + 1,500/1.085 = $1,973.47

Therefore, option V is the cheapest option.

Please use the following information to answer Questions 11 – 14

In 2004, Target Ltd issued $50 million worth of bonds at par with a coupon rate of 6%, with semi-annual interest payments and a maturity of 10 years In 2008, due to the credit crunch, the yield to maturity of the Target bonds increased to 8% In 2009, Buyer Corp announced a friendly takeover of Target Ltd and the yield to maturity of the bonds decreased to 7%

11 What was the current yield of the bonds in 2008?

A) 3.5%

B) 4.4%

C) 6.0%

D) 6.6%

E) 8.0%

Answer D

Price (2008) = 30 x PVIFA(4%,12) + 1,000 x (1 + 4%)-12 = $906.15

Current Yield = 60/906.15 = 6.6%

12 What was the price of the bonds in 2009?

A) $708.92

B) $918.89

C) $958.42

D) $977.43

E) $1020.24

Answer C

Price (2009) = 30 x PVIFA(3.5%,10) +1000 x (1 + 3.5%)-10= $958.42

13 What is the approximate rate of return for a bondholder who purchased the bonds in

2008 and sold them in 2009 if all coupons were spent?

A) 5.8%

B) 8.5%

C) 11.3%

D) 12.4%

E) 14.5%

Answer D

Rate of return = (Income + Capital gain or loss) / Initial price

= [60 + (958.42–906.15)] / 906.15 = 12.39%

14 In order to be able to pay the total face value back in 10 years, Target Ltd had decided

to use a sinking fund in which it will make semi-annual payments that would serve to accumulate the total face value The sinking fund pays an interest rate of 3% compounded semi-annually What is the total semi-annual cash outflow (including coupon payments) for the company?

A) $1,500,000

B) $1,860,785

C) $2,162,287

D) $3,662,287

E) $4,860,785

Answer D

To accumulate the total face value, $50 million, the company must make the

following semi-annual payments to the sinking fund:

$50 million = PMT x FVIFA(1.5%,20) Î PMT = $2,162,286.79

Adding the total semi-annual coupon, that is $50,000,000 x 3% = $1.5 million to the sinking fund payment, the total semi-annual cash outflow for the company is

$3,662,286.79

15 What is the coupon rate for a bond with four years until maturity, semi-annual interest, a face value of $1,000, a price of $1,035.10, and a yield to maturity of 6%?

A) 3.5%

B) 4.5%

C) 5.5%

D) 7.0%

E) 8.0%

Answer D

1,035.10 = C x PVIFA(3%,8) + 1000 x (1 + 3%)-8

C = (1,035.10 - 789.41)/ 7.02 = 35.00

Coupon rate = 2 x C /1,000 = 7%

16 You buy stock in ABC inc today for $70 ABC expects to pay a $2 dividend next year,

no dividend in year 2 and a $5 dividend in year 3 You expect to sell it at the end of year

3 realizing an expected annual return of 0% annually What is your rate of return over the 3 year period?

A) Gain of 10%

B) Loss of 10%

C) Gain of 11.11%

D) Loss of 11.11%

E) There is no capital gain or loss

Answer B

P0 = $70 = $2 / (1+0%) + $5 / (1+0%)3 + P3 / (1+0%)3 ; solving for P3 = $63

Capital Gain/loss = (P3 - P0) / P0 = ($63 - $70) / $70 = -10%

17 The expected EPS (earnings per share) of Kamal inc is $5 and the company usually retains 70% of its earnings Kamal inc has a discount rate of 16%, and a return on equity (ROE) of 20% What is Kamal inc current stock price?

A) $31.25

B) $60.75

C) $70

D) $75

E) $250

Answer D

The next dividend will be $5 × 0.30 = $1.50 per share

The growth rate g = Plowback Ratio × ROE = 0.70 × 20% = 14%

From the dividend growth model, the stock price is:

P0 = Div1/ (r – g) = $1.50 / (0.16 - 0.14) = $75

18 A preferred stock has paid a $5 annual dividend since the company began The stock currently sells for $62.50 What might investors expect to pay for the stock six years from now if the expected rate of return will stay at the same level?

A) $25.45

B) $33.00

C) $45.00

D) $62.50

E) $92.50

Answer D

Since the return stays unchanged in six years or eight years, the price will remain the same The expected rate of return is r = Div / P0 = 8% The price of the stock at

any year will be Div / r = $5 / 0.08 = $62.50

19 The dividends of XYZ corp are forecasted to grow at 20% per year for two years, after which the shares grow at a fixed rate of 6% forever If the discount rate is 15% and a dividend of $2.50 was just paid, what should be the current share price?

A) $31.16

B) $33.23

C) $37.42

D) $47.77

E) $50.61

Answer C

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20 What should be the annual dividend yield for Year 3 of a stock if a $5 dividend per share was just paid, the stock has an annual required rate of return of 20%, and a constant dividend growth rate of 6%?

D) 14%

E) 15%

Answer D

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Conceptual questions (2 points each)

21 You are the financial manager of BC Gold Corporation and are considering different operating strategies for the coming year From a financial management standpoint, which of the following would be your optimal strategy?

A) Undertake the plan that would reduce the overall riskiness of the firm

B) Undertake the plan that would maximize the current stock price

C) Undertake the plan that would result in the largest profits for the year

D) Undertake the plan that would maximize your personal wealth

E) Undertake the plan that would lead to the most stable stock price for the year

Answer B

22 Shareholders attempt to control managerial behavior by:

A) Electing the board of directors who select management

B) The threat of a takeover by another firm

C) Setting compensation contracts and tying compensation to corporate success D) A and B

E) A and C

Answer E

23 In a capital budgeting decision, which of the following must be considered?

I The size of the cash flows

II The timing of the cash flows

III The riskiness of the cash flows

A) I only

B) II only

C) I and II only

D) II and III only

E) I, II and III

Answer E

24 A stream of equal cash payments equally spaced in time and lasting forever is termed:

A) Perpetuity

B) Growing perpetuity

C) Annuity

D) Growing annuity

E) None of the above

Answer A

25 Which of the following is correct about corporate debt?

A) The risk of default is measured by bond ratings, with the higher the rating the lower the risk of default

B) Because debt holders do not own the firm, they normally have a voting power C) Since interest is an obligation, it cannot be treated as an expense and therefore cannot be deducted from taxable income

D) The fund established to retire the debt before its maturity date is called a mutual fund

E) None of the above statements are correct

Answer A

26 The market value of a firm's equity is determined by:

A) the difference between book values of assets and liabilities

B) multiplying share price at issue by the number of shares issued

C) multiplying share market price by the number of shares outstanding

D) multiplying share market price by the number of shares authorized

E) None of the above

Answer C

27 Which of the following statements best describes the real interest rate?

A) Real interest rates exceed inflation rates

B) Real interest rates are always negative

C) Real interest rates can be negative

D) Real interest rates traditionally exceed nominal rates

E) Real interest rates are always positive

Answer C

28 Which of the following is the most correct for a corporate bond, compared to a

government bond?

A) The corporate bond will sell for a lower price