ASSIGNMENT 5- PROBLEMS 1

Assignment 5 – Problems

Ziad Y. Mazboudi

California Southern University

Corporate Finance

FIN 86505

Dr. Conrad Francis

ASSIGNMENT 5- PROBLEMS 2

Assignment 5 – Problems

Chapter 4, Question 10: Calculating Present Values. Imprudential, Inc. has an unfunded

pension liability of $750 million that must be paid in 25 years. To assess the value of the firm’s

stock, financial analysts want to discuss this liability back to the present. If the relevant discount

rate is 7 percent, what is the present value of this liability?

P=FVt/(1+r)^t (Jordan, Westerfield, & Ross, 2011, p. 143)

P= $750,000,000/(1+0.07)^25

P= $138,186,883.1

ASSIGNMENT 5- PROBLEMS 3

Chapter 4, Question 16: Calculating Rates of Return. Referring to the KVP security we

discussed at the very beginning of the Chapter:

a. What was the annual rate of return on investment in KVP in early January, 2010?

$1,000 on January 25, 2010 yields $2,000 on August 24, 2018

t = 8 years 7 months = 8.583 years

F =2 P

FVt = PVt (1+r)^t (Jordan et al., 2011, p. 133)

2= 1x(1+r)^8.583, solving for r

r = 8.41%

b. Suppose an investor invested Rs 1,000 in KVP on January 25, 2010, and

redeemed it three years later on January 24, 2013 , for Rs 1,100. What annual rate of return did

she earn?

FVt = PVt (1+r)^t

1,100 = 1000 (1+r)^3

1.1 = (1+r)^3 Solving for r

r = 3.23%

c. What would have been the value of the investment in KVP on January 24, 2013 if

she would have earned the annual rate of return calculated in part a?

FVt = PVt (1+r)^t

FV = 1000 (1.0841)^3

FV = 1,274.11 Rs

ASSIGNMENT 5- PROBLEMS 4

Chapter 4, Question 20: Calculating the Number of Periods. You expect to receive

$25,000 at graduation in two years. You plan on investing it at 9 percent until you have

$160,000. How long will you wait from now?

FV = $160,000

PV = $25,000

FVt = PVt (1+r)^t

$160,000 = $25,000 (1.09)^t

6.4 = 1.09^t solving for t

t = log 6.4/log 1.09

t = 21.54 years in 2 years

From now, it is T = 23.54 years

ASSIGNMENT 5- PROBLEMS 5

Chapter 5, question 4: Calculating Annuity Present Values. An investment offers $8,500

per year for 15 years, with the first payment occurring 1year from now. If the required return is 9

percent, what is the value of the investment?

PV = C x{1-[1/(1+r)^t]}/r (Jordan et al., 2011, p. 174)

C = $8,500

t = 15

r = 9%

PV15 = $8,500 x {1-[1/(1+0.09)^15]}/0.09

PV15 = $68,515.85

What would the value be if the payments occurred for 40 years?

PV40 = $8,500 x {1-[1/(1+0.09)^40]}/0.09

PV 40 = $91,437.56

What would the value be if the payments occurred for 75 years?

PV75 = $8,500 x {1-[1/(1+0.09)^75]}/0.09

PV75 = $94,297.15

What would the value be if the payments occurred forever?

PV = C/r (Jordan et al., 2011, p. 174)

PV = $8,500/0.09

PV = $94,444.44

ASSIGNMENT 5- PROBLEMS 6

Chapter 5, question 10: Calculating Perpetuity Values. Dawa Financial is trying to sell

you an investment policy that will pay you and your heirs $35,000 per year forever. If the

required return on investment is 7 percent, how much will you pay for the policy?

PV = C/r

PV = $35,000/0.07

PV = $500,000.00

ASSIGNMENT 5- PROBLEMS 7

Chapter 5, question 20: Calculating Loan Payments. You want to buy a new sports coupe

for $73,800, and the finance office at the dealership has quoted you a 6.1 percent APR loan for

60 months to buy the car. What will your monthly payments be?

PV = C x {1-[1/(1+r)t]}/r (Jordan et al., 2011, p. 174)

APR = 6.1%

r = 6.1/12 = 0.508% monthly

$73,800 = C x {1-[1/1.00508]^60]}/0.0058 solving for C

C = ($73,800 x 0.00508)/(1- [1/1.00508]^60)

C = 374.904/0.262

C= $1,430.93

What is the effective annual rate on this loan?

EAR = (1 + Quoted rate/m)m – 1 (Jordan et al., 2011, p. 176)

EAR = (1 + 0.061/12)12 – 1

EAR = 6.27%

ASSIGNMENT 5- PROBLEMS 8

Chapter 6, question 6: Bond Prices. App Store Co. issued 15-year bonds one year ago at a

coupon rate of 6.1 percent. The bonds make semiannual payments. If the YTM on these bonds is

5.4 percent, what is the current bond price?

Bond value = C x [1-1/(1+r)t]/r + F/(1+r)t (Jordan et al., 2011, p. 202)

Since App Store Co. issued the bonds a year ago, then we have 14 years remaining, hence

28 semiannual payments. t = 28

Since we have semiannual payments, then r= 5.4/2 = 2.7%

Since we have semiannual payments, then each coupon is 6.1/100 /2* 1,000 = $30.5

Solving for Bond Value = C x [1-1/(1+r)t]/r + F/(1+r)t (Jordan et al., 2011, p. 202)

Bond Value = $30.5 x [1 – 1/(1+0.027)28]/0.027 + $1,000/(1+0.027)28

Bond Value = $30.5 x 0.5257/0.027 + $474.27

Bond Value = $1,068.15

ASSIGNMENT 5- PROBLEMS 9

Chapter 6, question 16: Interest Rate Risk. Both Bond Xin and Bond Qan have 9 percent

coupons, make semiannual payments, and are priced at par value. Bond Xin has 3 years to

maturity, whereas Bond Qan has 20 years to maturity. If interest rates suddenly rise by 2 percent,

what is the percentage change in the price of Bond Xin? Of Bond Qan?

Coupon = 9 % with semiannual payments, means each payment is equal to $45

Since the bonds are priced at par value, this means that YTM=coupon rate = 9%

If interest rates suddenly rise by 2 percent, then the following is the new value of the

bonds, with YTM = 11%

PXin = $45 [1-1/(1+0.055)6]/0.055 + 1,000/1.0556

PXin = $45 * 4.9955 + $725.24

PXin = $950.04

Percentage change in price = (950.04-1000)/1,000 = -0.049956

Percentage price change for Bond Xin is -5%

PQan = $45 [1-1/1.05540/0.055 + 1,000/1.05540

PQan = $45 * 16.0461 + 117.46

PQan = $839.53

Percentage change in price = (839.53-1000)/1,000 = -0.16046

Percentage price change for Bond Qan = 16.05 %

If rates were to suddenly fall by 2 percent instead, what would the percentage change in

the price of Bond Xin be then? Of Bond Qan?

PXin = $45 [1-1/(1+0.035)6]/0.035 + 1,000/1.0356

PXin = $239.78 + $813.50

PXin = $1,053.28

ASSIGNMENT 5- PROBLEMS 10

Percentage change in price = (1,053.28-1000)/1,000 = 0.053

Percentage price change for Bond Xin is 5.3%

PQan = $45 [1-1/1.03540/0.035 + 1,000/1.03540

PQan = $960.98 + $252.57

PQan = $1,213.55

Percentage change in price = (1,213.55-1000)/1,000 = 0.2135

Percentage price change for Bond Qan = 21.35%

YTM 9 11 7 Δ(11-9)% Δ (7-9) %Xin $ 1,000.00 $ 950.04 $ 1,053.28 -4.996 5.33Qan $ 1,000.00 $ 893.53 $ 1,213.55 -10.647 21.36

One notices that the Qan bond with the longer maturity is more sensitive to interest rate

changes, in both direction, upward or downward.

ASSIGNMENT 5- PROBLEMS 11

Chapter 6, question 22: Using Bond Quotes. Suppose the

following bond quote for IOU Corporation appears in the financial

page of today’s newspaper. Assume the bond has a face value of

$1,000, and the current date is April 15, 2010. What is the yield

to maturity of the bond? What is the current yield?

Company (Ticker)

Coupon Maturity Last Price Last Yield EST Vol (000s)

IOU (IOU) 9.75 April 15, 2022 91.535 ?? 1,975

The Bond has 12 years to maturity so 24 payments of $48.75

The Bond price equation is: P = 48.75 [1-1/(1+ r)24]/r + 1000/(1+ r)24

Using Excel to calculate the YTM gives the following:

Settlement date 4/15/2010Maturity date 4/15/2022Annual coupon rate 0.0975Bond price (% of par) 91.535Face value (% of par) 100Coupons per year 2Yield to maturity 0.1104

So, the YTM = 11.04 %

The current yield is the annual coupon payment divided by the Bond price.

Current yield = $97.5/$91.35

Current yield =1.067%

ASSIGNMENT 5- PROBLEMS 12

Chapter 7, question 8. Valuing preferred stock. Gesto, Inc. has an issue of preferred

stock outstanding that pays a $4.50 dividend every year, in perpetuity. If this issue currently sells

for $84.70 per share, what is the required return?

P0 = D/R (Jordan et al., 2011, p. 241)

R = D/P = 4.5/84.70

R = 0.053

R = 5.3%

ASSIGNMENT 5- PROBLEMS 13

Chapter 7, question 14: Hot Wings, Inc., has an odd dividend policy. The company has

just paid a dividend of $8 per share and has announced that it will increase the dividend by $6

per share for each of the next four years, and then never pay another dividend. If you require a 15

percent return on the company’s stock, how much will you pay for a share today?

Since the company will not be paying any dividend after 4 years, then P4 = 0, then the

share today is equal to the total of the dividends over the next 4 years.

P0 = D1/(1+R) + D2/(1+R)2 + D3/(1+R)3 + D4/(1+R)4 (Jordan et al., 2011, p. 240)

P0 = $14/1.15 + $20/1.152 + $26/1.153 + $32/1.154

P0 = $62.69

ASSIGNMENT 5- PROBLEMS 14

Chapter 7, question 18: Finding the Dividend. Gontier Corporation stock currently sells

for $74.25 per share. The market requires an 11 percent return on the firm’s stock. If the

company maintains a constant 5.5 percent growth rate in dividends, what was the most recent

dividend per share paid on the stock?

Dividend grows at a steady rate, g, then the price can be written as:

P0 = D1/(R-g) = D0(1+g)/(R-g) (Jordan et al., 2011, p. 247)

D0 = P0 (R-g)/ (1+g) = $74.25 (0.11 – 0.055)/(1.055)

D0 = $3.87

ASSIGNMENT 5- PROBLEMS 15

References

Jordan, B. D., Westerfield, R. W., & Ross, S. A. (2011). Corporate Finance Essentials (7th ed.).

Singapore: The McGraw-Hill Companies.