Division of Business and Economics

F301 Financial Management

Fall 2000

Test 2

a. True

b. False

2. Suppose someone offered you your choice of two equally risky annuities, each paying $5,000 per year for 5 years. One is an annuity due, while the other is a regular (or deferred) annuity. If you are a rational wealth maximizing investor which annuity would you choose? (Hint: Which annuity is worth more today?)

a. The annuity due.

b. The deferred annuity.

c. Either one, because as the
problem is set up, they have the same present value.

d. Without information about
the appropriate interest rate, we cannot find the values of the two annuities,
hence we cannot tell which is better.

e. The annuity due; however,
if the payments on both were doubled to $10,000, the deferred annuity would
be preferred.

3. At an effective annual interest rate of 20 percent, how many years will it take a given amount to triple in value? (Round to the closest year.)

a. 5 years

b. 8 years

c. 6 years

d. 10 years

e. 9 years

4. Assume that you will receive $2,000 a year in Years 1 through 5, $3,000 a year in Years 6 through 8, and $4,000 in Year 9, with all cash flows to be received at the end of the year. If you require a 14 percent rate of return, what is the present value of these cash flows?

a. $ 9,851

b. $13,250

c. $11,714

d. $15,129

e. $17,353

5. If $100 is placed in an account that earns a nominal 4 percent, compounded quarterly, what will it be worth in 5 years?

a. $122.02

b. $105.10

c. $135.41

d. $120.90

e. $117.48

6. South Penn Trucking is financing a new truck with a loan of $10,000 to be repaid in 5 annual end-of-year installments of $2,504.56. What annual interest rate is the company paying?

a. 7%

b. 8%

c. 9%

d. 10%

e. 11%

7. Gomez Electronics needs to arrange financing for its expansion program. Bank A offers to lend Gomez the required funds on a loan where interest must be paid monthly, and the quoted rate is 8 percent. Bank B will charge 9 percent, with interest due at the end of the year. What is the difference in the effective annual rates charged by the two banks?

a. 0.25%

b. 0.50%

c. 0.70%

d. 1.00%

e. 1.25%

8. Your company is planning to borrow $2,500,000 on a 10-year, 9 percent, annual payment, fully amortized term loan. What fraction of the payment made at the end of the third year will represent repayment of principal?

a. 29.83%

b. 50.19%

c. 35.02%

d. 64.45%

e. 72.36%

9. Your father, who is 60, plans to retire in 2 years, and he expects to live independently for 3 years. He wants a retirement income which has, in the first year, the same purchasing power as $40,000 has today. However, his retirement income will be of a fixed amount, so his real income will decline over time. His retirement income will start the day he retires, 2 years from today, and he will receive a total of 3 retirement payments. Inflation is expected to be constant at 5 percent. Your father has $100,000 in savings now, and he can earn 8 percent on savings now and in the future. How much must he save each year, starting today , to meet his retirement goals?

a. $1,863

b. $2,034

c. $2,716

d. $5,350

e. $6,102

10. A 20-year original maturity bond with 1 year left to maturity has more interest rate risk than a 10-year original maturity bond with 1 year left to maturity. (Assume that the bonds have equal default risk and equal coupon rates.)

a. True

b. False

11. A call provision gives bondholders the right to demand, or "call for," repayment of a bond. Typically, calls are exercised if interest rates rise, because when rates rise the bondholder can get the principal amount back and reinvest it elsewhere at higher rates.

a. True

b. False

12. If the required rate of return
on a bond is greater than its coupon interest rate (and k_{d} remains
above the coupon rate), the market value of that bond will always be below
its par value until the bond matures, at which time its market value will
equal its par value. (Accrued interest between interest payment dates should
not be considered when answering this question.)

a. True

b. False

13. You intend to purchase a 10-year, $1,000 face value bond that pays interest of $60 every 6 months. If your nominal annual required rate of return is 10 percent with semiannual compounding, how much should you be willing to pay for this bond?

a. $ 826.31

b. $1,086.15

c. $ 957.50

d. $1,431.49

e. $1,124.62

14. Four years ago you bought a 10 percent, 10-year bond that paid interest annually. However, this bond was callable at the end of Year 5 at a price of $1,200. If the current price is $1,050, what is the bond's yield to call at the present time?

a. 14.74%

b. 18.35%

c. 26.19%

d. 23.81%

e. 32.50%

15. Tony's Pizzeria plans to issue bonds with a par value of $1,000 and 10 years to maturity. These bonds will pay $45 interest every 6 months. Current market conditions are such that the bonds will be sold to net $937.79. What is the YTM of the issue as a broker would quote it to an investor?

a. 11%

b. 10%

c. 9%

d. 8%

e. 7%

16. The common stock valuation model, as shown below, gives no consideration to expected capital gains.

P = D (1 + g) / (ks - g)

a. True

b. False

17. According to the basic stock valuation model, the value an investor assigns to a share of stock is dependent upon the length of time the investor plans to hold the stock.

a. True

b. False

18. The last dividend on Spirex Corporation's common stock was $4.00, and the expected growth rate is 10 percent. If you require a rate of return of 20 percent, what is the highest price you should be willing to pay for this stock?

a. $44.00

b. $38.50

c. $40.00

d. $45.69

e. $50.00

19. You are considering the purchase of a common stock that just paid a dividend of $2.00. You expect this stock to have a growth rate of 30 percent for the next 3 years, then to have a long-run normal growth rate of 10 percent thereafter. If you require a 15 percent rate of return, how much should you be willing to pay for this stock?

a. $71.26

b. $97.50

c. $82.46

d. $79.15

e. $62.68

20. The Textbook Production Company has been hit hard due to increased competition. The company's analysts predict that earnings (and dividends) will decline at a rate of 5 percent annually forever. Assume that k s = 11 percent and D = $2.00. What will be the price of the company's stock three years from now?

a. $27.17

b. $ 6.23

c. $28.50

d. $10.18

e. $20.63

ANSWER KEY FOR TEST-

1. b

Amortization

Chapter:6 QUESTION: 19 OBJECTIVE:

2. a. The annuity due.

Annuities

Chapter:6 QUESTION: 33 OBJECTIVE:

PAGE 2

3. c. 6 years

Time for a sum to triple

Tabular solution:

$1 = $3(PVIF %,n )

PVIF %,n = 0.3333

n = 6 periods (years).

Financial calculator solution:

Inputs: I = 20; PV = -1; PMT = 0; FV = 3. Output: N = 6.026 6 years.

Chapter:6 QUESTION: 42 OBJECTIVE:

4. c. $11,714

PV of an uneven CF stream

Time line:

0 1 2 3 4 5 6 7 8 9 years

14%

PV = ? 2,000 2,000 2,000 2,000 2,000 3,000 3,000 3,000 4,000

Tabular solution:

PV = $2,000(PVIFA 14%,5 ) + $3,000(PVIFA 14$,3 )(PVIF 14%,5 ) +

$4,000(PVIF 14%,9 )

= $2,000(3.4331) + $3,000(2.3216)(0.5194) + $4,000(0.3075)

= $6,866.20 + $3,617.52 + $1,230.00 = $11,713.72 $11,714.

Financial calculator solution:

Using cash flows

Inputs: CF = 0; CF = 2,000; N j = 5; CF = 3,000; N j = 3;

CF = 4,000; I = 14.

Output: NPV = $11,713.54 $11,714.

Chapter:6 QUESTION: 49 OBJECTIVE:

PAGE 3

5. a. $122.02

Quarterly compounding

Tabular solution:

$100(FVIF 1%,20 ) = 100(1.2202) = $122.02.

Financial calculator solution:

Inputs: N = 20; I = 1; PV = -100; PMT = 0. Output: FV = $122.02

Chapter:6 QUESTION: 52 OBJECTIVE:

6. b. 8%

Interest rate

Time line:

0 1 2 3 4 5 Years

i = ?

10,000 -2,504.56 -2,504.56 -2,504.56 -2,504.56 2,504.56

Tabular solution:

$10,000 = $2,504.56(PVIFA i,5 )

PVIFA i,5 = $10,000/$2,504.56 = 3.9927

i = 8%.

Financial calculator solution:

Inputs: N = 5; PV = 10,000; PMT = -2,504.56; FV = 0. Output: I = 8%.

Chapter:6 QUESTION: 55 OBJECTIVE:

7. c. 0.70%

Effective annual rate

Bank A: 8%, monthly.

K Nom m

EAR A = 1 + - 1

m

0.08

= 1 + - 1 = 8.30%.

12

Bank B: 9%, interest due at end of year

EAR B = 9%.

9.00% - 8.30% = 0.70%.

Chapter:6 QUESTION: 56 OBJECTIVE:

PAGE 4

8. b. 50.19%

Amortization

Tabular solution: $2,500,000 = PMT(PVIFA 9%,10 )

PMT = $2,500,000/6.4177 = $389,547.66.

Construct amortization table

Year Beg Balance Payment Interest Principal End Balance

1 $2,500,000 $389,548 $225,000 $165,548 $2,335,452

2 2,335,452 389,548 210,191 179,357 2,156,095

3 2,156,095 389,548 194,049 195,499 1,960,596

Principal fraction of PMT = $195,499/$389,548 = 0.5019 50.19%.

Financial calculator solution:

Calculate the principal portion of PMT using amortization function:

( Note: The steps below are specific to the Hewlett-Packard 17B II but the basic

steps generalize to a variety of calculators.)

Inputs: N = 10; I = 9; PV = -2,500,000. Output: PMT = $389,550.22.

Inputs: [AMORT], #P = 3, [NEXT] or [AMORT].

Output: [=] or [PRIN] = 195,502.12.

Principal fraction = $195,502.12/$389,550.22 = 0.5019 50.19%.

Note: Difference in amortization payment and principal calculation

due to rounding. Answer is unaffected.

Chapter:6 QUESTION: 93 OBJECTIVE:

PAGE 5

9. c. $2,716

Required annuity payments

Goes on

Retires welfare

Infl.=5%

0 1 2 3 4 5

i=8%

40,000 44,100 44,100 44,100

122,742

100,000 ( 116,640 )

PMT PMT 6,102

Step 1 : The retirement payments, which begin at t = 2, must be:

$40,000(1 + Infl.) = $40,000(1.05) = $44,100.

Step 2 : There will be 3 retirement payments of $44,100, made at

t = 2, t = 3, and t = 4. We find the PV of an annuity due at

t = 2 as follows:

Set calculator to "Begin." Then enter:

N = 3; I = 8; PMT = 44,100; FV = 0. Solve for PV = $122,742.

If he has this amount at t = 2, he can receive the 3

retirement payments.

Step 3 : The $100,000 now on hand will compound at 8% for 2 years:

$100,000(1.08) = $116,640.

Step 4 : So, he must save enough each year to accumulate an additional

$122,742 - $116,640 = $6,102:

Need at t = 2 $122,742

Will have ( 116,640 )

Net additional needed $ 6,102

Step 5 : He must make 2 payments, at t = 0 and at t = 1, such that

they will grow to a total of $6,102 at t = 2.

This is the FV of an annuity due found as follows:

Set calculator to "Begin." Then enter:

N = 2; I = 8; PV = 0; FV = 6,102. Solve for PMT = $2,716.

Chapter:6 QUESTION: 99 OBJECTIVE:

10. b

Interest rate risk

Chapter:7 QUESTION: 4 OBJECTIVE:

PAGE 6

11. b

Call provision

Chapter:7 QUESTION: 11 OBJECTIVE:

12. a

Bond value

Chapter:7 QUESTION: 18 OBJECTIVE:

PAGE 7

13. e. $1,124.62

Bond value - semiannual payment

Tabular solution:

V B = $60(PVIFA 5%,20 ) + $1,000(PVIF 5%,20 )

= $60(12.4622) + $1,000(0.3769) = $1,124.63.

Financial calculator solution:

Inputs: N = 20; I = 5; PMT = 60; FV = 1,000.

Output: PV = -$1,124.62; V B = $1,124.62.

Chapter:7 QUESTION: 64 OBJECTIVE:

PAGE 8

14. d. 23.81%

Yield to call

Numerical solution:

You will receive $100 + $1,200 maturity value in one year if the bonds are called.

Therefore, the present yield-to-call is,

$1,050 = $1,300/(1 + k d )

YTC = k d = (1,300 - $1,050)/$1,050 = 23.81%.

Financial calculator solution:

Inputs: N = 1; PV = -1,050; PMT = 100; FV = 1,200. Output: I = 23.81%

Chapter:7 QUESTION: 79 OBJECTIVE:

PAGE 9

15. b. 10%

Yield to maturity

Financial calculator solution:

Inputs: N = 20; PV = -$937.79; PMT = 45; FV = 1,000.

Output: I = 5.0% per period; k d = YTM = 5.0% x 2 periods = 10%.

Chapter:7 QUESTION: 85 OBJECTIVE:

16. b

Constant growth model

Chapter:8 QUESTION: 4 OBJECTIVE:

17. b

Stock valuation

Chapter:8 QUESTION: 6 OBJECTIVE:

18. a. $44.00

Constant growth stock

$4.00(1.1)

P = = $44.00.

0.20 - 0.10

Chapter:8 QUESTION: 46 OBJECTIVE:

PAGE 10

19. a. $71.26

Supernormal growth stock

Tabular solution:

^

P = $2.60(PVIF %, ) + $3.38(PVIF %, ) + $101.054(PVIF %, )

= $2.60(0.8696) + $3.38(0.7561) + $101.054(0.6575) = $71.26.

Financial calculator solution:

Inputs: CF = 0; CF = 2.60; CF = 3.38; CF = 101.054; I = 15.

^

Output: NPV = $71.26. P = $71.26.

Chapter:8 QUESTION: 59 OBJECTIVE:

PAGE 11

20. d. $10.18

Declining growth stock

^ $1.90 $1.90

P = = = $11.875.

0.11 - -0.05 0.16

^ D $1.629

P = = = $10.18.

0.16 0.16

Chapter:8 QUESTION: 61 OBJECTIVE: