# Fin 571 Problems Sets

Chapter 5

A1. (Bond valuation) A $1,000 face value bond has a remaining maturity of 10 years and a required return of 9%. The bond’s coupon rate is 7.4%. What is the fair value of this bond? Calculating PV factor:

i= required return = 9% = 0.09

n= 10 years

Using Cash Flow of $1000 to calculate present value,

Cash flow= $1000

PV factor = 1/(1+i)^n = 0.42241

PV = $1000*0.42241= 422.41

Using Coupon Rate to calculate present value of Annuity

Cash flow= $1000 * 7.4/100 = $74

PV factor = (1/i)*(1- 1/(1+i)^n) = 6.4176

So, PV = $74*6.4176 = 474.90|

So the fair value of bond = 474.90+422.41 = $897.31

A10. (Dividend discount model) Assume RHM is expected to pay a total cash dividend of $5.60 next year and its dividends are expected to grow at a rate of 6% per year forever. Assuming annual dividend payments, what is the current market value of a share of RHM stock if the required return on RHM common stock is 10%? Current market value = D1/(Required return – growth rate)

= 5.60/(10%-6%) = $140

A12. (Required return for a preferred stock) James River $3.38 preferred is selling for $45.25. The preferred dividends is now growing. What is the required return on James River preferred stock? Required Return = Dividend/Market Price

Dividend = $3.38

Market Price = $45.25

Required Return = $3.38 / $45.25

Required Return = 7.47%

A14.(Stock Valuation) Suppose Toyota has nonmaturing (perpetual) preferred stock outstanding that pays a $1.00 quarterly dividend and has a required return of 12% APR (3% per quarterly). What is the stock worth? Perpetual Quarterly Preferred Dividend (D) = $1.00

Annual Dividend ($1.00 x 4.00) = $4.00

Annual Percentage Rate (APR) = 12%

Preferred Stock Value (P0) = (D / R)

Preferred Stock Value (P0) = ($4.00 / 0.12)

Preferred Stock Value (P0) = $33.33

B16 Interest-rate risk) Philadelphia Electric has many bonds trading on the New York Stock Exchange. Suppose PhilEl’s bonds have identical coupon rates of 9.125% but that one issue matures in 1 year, one in 7 years, and the third in 15 years. Assume that a coupon payment was made yesterday. If the yield to maturity for all three bonds is 8%, what is the fair price of each bond? 1 Year Maturity

n = 1 x 2 = 2

r = 8% / 2 = 4%

PV = ?

PMT = 9.125% x 1,000 / 2 = $45.62

FV = $1,000

PV = $1,010.61

7 Year Maturity

n = 7 x 2 = 14

r = 8% / 2 = 4%

PV = ?

PMT = 9.125% x 1,000 / 2 = $45.625

FV = $1,000

PV = $1,059.42

15 Year Maturity

n = 15 x 2 = 30

r = 8% / 2 = 4%

PV = ?

PMT = 9.125% x 1,000 / 2 = $45.625

FV = $1,000

PV = -$1,097.27

Suppose that the yield to maturity for all of these bonds changed instantaneously to 7%. What is the fair price of each bond now? 1Year Maturity

n = 1 x 2 = 2

r = 7% / 2 = 3.5%

PV = n/a

PMT = 9.125% x 1,000 / 2 = $45.625

FV = $1,000

PV = $1,020.18

7 Year Maturity

n = 7 x 2 = 14

r = 7% / 2 = 3.5%

PV = n/a

PMT = 9.125% x 1,000 / 2 = $45.625

FV = $1,000

PV = $1,116.03

15 Year Maturity

n = 15 x 2 = 30

r = 7% / 2 = 3.5%

PV = n/a

PMT = 9.125% x 1,000 / 2 = $45.625

FV = $1,000

PV = $1,195.42

Suppose that the yield to maturity for all of these bonds changed instantaneously again, this time to 9%. Now what is the fair price of each bond? 1 Year Maturity

n = 1 x 2 = 2

r = 9% / 2 = 4.5%

PV = n/a

PMT = 9.125% x 1,000 / 2 = $45.625

FV = $1,000

PV = $1,001.17

7 Year Maturity

n = 7 x 2 = 14

r = 9% / 2 = 4.5%

PV = n/a

PMT = 9.125% x 1,000 / 2 = $45.625

FV = $1,000

PV = $1,006.39

15 Year Maturity

n = 15 x 2 = 30

r = 9% / 2 = 4.5%

PV = n/a

PMT = 9.125% x 1,000 / 2 = $45.625

FV = $1,000

PV = $1,010.18

B18. (Default risk) You buy a very risky bond that promises a 9.5% coupon and return of the $1,000 principal in 10 years. You pay only $500 for the bond. You receive the coupon payments...

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