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Homework# A1. (Bond valuation) A $1,000 face value bond has a remaining

maturity of 10 years and...

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?The Price of the Bond is equal to the sum of the present values of all future cash flows (PV of coupon payments + PV of the Face Amount). Coupon Payment = $1,000 × 3.7% = $37. Number of periods = 10 years × 2 = 20 periods

Price =

= $481.29 + $414.64= $895.94

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%?

P0 = D1 / (r - g) = $5.60 / (0.10 - 0.06) = $140.00

A12. (Required return for a preferred stock) James River $3.38 preferred is selling for $45.25. The preferred dividend is non-growing. What is the required return on James River preferred stock?

PVPerpetuity = D / r = D / PV = $3.38 / $45.25 = 7.47%

A14. (Stock valuation) Suppose Toyota has non-maturing (perpetual) preferred stock outstanding that pays a $1.00 quarterly dividend and has a required return of 12% APR (3% per quarter). What is the stock worth?

PVPerpetuity = D / r = $1.00 / 0.03 = $33.33

A16. (Growth rate) Suppose Toshiba has a payout ratio of 55% and an expected return on its future investments of 15%. What is Toshiba’s expected growth rate?

A. 1. CALC: n = 1 x 2 = 2 r = 8% / 2 = 4% PV = ? PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000

PV = -$1,010.61

2. CALC: 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

3. CALC: 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

B. 1. CALC: n = 1 x 2 = 2 r = 7% / 2 = 3.5% PV = ? PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000

PV = -$1,020.18

2. CALC: n = 7 x 2 = 14 r = 7% / 2 = 3.5% PV = ? PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000

PV = -$1,116.03

3. CALC: n = 15 x 2 = 30 r = 7% / 2 = 3.5% PV = ? PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000

PV = -$1,195.42

C. 1. CALC: n = 1 x 2 = 2 r = 9% / 2 = 4.5% PV = ? PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000

PV = -$1,001.17

2. CALC: n = 7 x 2 = 14 r = 9% / 2 = 4.5% PV = ? PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000

PV = -$1,006.39

3. CALC: n = 15 x 2 = 30 r = 9% / 2 = 4.5% PV = ? PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000

PV = -$1,010.18

D. Interest-rate risk varies directly with maturity. The longer maturity of bonds, the larger the price change is when interest rates change.

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.

a. You receive the coupon payments for three years and the bond defaults. After liquidating

the firm, the bondholders receive a distribution of $150 per bond at the end of 3.5 years. What is the realized return on your investment?

b. The firm does far better than expected and bondholders receive all of the promised interest and principal payments. What is the realized return on your investment?

A. CALC: n = 3.5x2 =7 r = ? PV = -$500 PMT = 9.5%x1,000/ 2= $47.50

FV = $150 - 47.50 = $102.50

r = -2.8746%

APY = (1 + r)m – 1 = (1 - 0.0278)2 – 1 = -5.6666%

YTM = 2x(-2.8746) = -5.7493% APR

B. CALC: n = 10x2 =20 r = ? PV = -$500 PMT = 9.5%x1,000/2 = $47.50

FV = $1,000

r = 11.0489%

APY = (1 + r)m – 1 = (1 + 0.110489)2 – 1 = 23.3185%

YTM = 2x11.0489 = 22.0977% APR

B20. (Constant growth model) Medtrans is a profitable firm that is not paying a dividend on itscommon stock. James Weber, an analyst for A. G. Edwards, believes that Medtrans will

begin paying a $1.00 per share dividend in two years and that the dividend will increase

6% annually thereafter. Bret Kimes, one of James’ colleagues at the same firm, is less optimistic.

Bret thinks that Medtrans will begin paying a dividend in four years that the dividend will be $1.00, and that it will grow at 4% annually. James and Bret agree that the required return for Medtrans is 13%.

a. What value would James estimate for this firm?

b. What value would Bret assign to the Medtrans stock?

a. P1 = D2 / (r - g) = $1.00 / (0.13 - 0.06) = $14.29

P0 = $14.29 / (1 + 0.13)1 = $12.64

b. P3 = D4 / (r - g) = $1.00 / (0.13 - 0.04) = $11.11

P0 = $11.11 / (1 + 0.13)3 = $7.70

¦ LEVEL C (ADVANCED)

C1. (Beta and required return) The riskless return is currently 6%, and Chicago Gear has estimated the contingent returns given here.

a. Calculate the expected returns on the stock market and on Chicago Gear stock.

b. What is Chicago Gear’s beta?

c. What is Chicago Gear’s required return according to the CAPM?

REALIZED RETURN

State of the Market Probability that State Occurs Stock Market Chicago Gear

Stagnant 0.20 (10%) (15%)

Slow growth 0.35 10 15

Average growth 0.30 15 25

Rapid growth 0.15 25 35

A. Expected Return M = 0.20 x -.10% + 0.35 x 10% + 0.30 x 15% + 0.15 x 25% =

9.75%

Expected Return Chicago Gear = 0.20 x -.15% + 0.35 x 15% + 0.30 x 25% + 0.15 x

35% = 15.00%

B. sM2 = 0.20(-0.10 - 0.0975)2 + 0.35(0.10 - 0.0975)2 + 0.30(0.15 - 0.0975)2 + 0.15(0.25

- 0.0975)2 = 0.0121

Cov(Chicago Gear, M) = 0.20(-0.15 - 0.15)(-0.10 - 0.0975) + 0.35(0.15 - 0.15)(0.10 –

0.0975) + 0.30(0.25 - 0.15)(0.15 - 0.0975) + 0.15(0.35 - 0.15)(0.25 - 0.0975) = 0.018

ß = Cov(j,M) / sM2 = 0.018 / 0.0121 = 1.49

C. r = rf + ß(rM - rf) = 0.06 + 1.49(0.0975 - 0.06) = 0.1159 = 11.59%

required return of 9%. The bond’s coupon rate is 7.4%. What is the fair value of this bond?The Price of the Bond is equal to the sum of the present values of all future cash flows (PV of coupon payments + PV of the Face Amount). Coupon Payment = $1,000 × 3.7% = $37. Number of periods = 10 years × 2 = 20 periods

Price =

= $481.29 + $414.64= $895.94

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%?

P0 = D1 / (r - g) = $5.60 / (0.10 - 0.06) = $140.00

A12. (Required return for a preferred stock) James River $3.38 preferred is selling for $45.25. The preferred dividend is non-growing. What is the required return on James River preferred stock?

PVPerpetuity = D / r = D / PV = $3.38 / $45.25 = 7.47%

A14. (Stock valuation) Suppose Toyota has non-maturing (perpetual) preferred stock outstanding that pays a $1.00 quarterly dividend and has a required return of 12% APR (3% per quarter). What is the stock worth?

PVPerpetuity = D / r = $1.00 / 0.03 = $33.33

A16. (Growth rate) Suppose Toshiba has a payout ratio of 55% and an expected return on its future investments of 15%. What is Toshiba’s expected growth rate?

A. 1. CALC: n = 1 x 2 = 2 r = 8% / 2 = 4% PV = ? PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000

PV = -$1,010.61

2. CALC: 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

3. CALC: 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

B. 1. CALC: n = 1 x 2 = 2 r = 7% / 2 = 3.5% PV = ? PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000

PV = -$1,020.18

2. CALC: n = 7 x 2 = 14 r = 7% / 2 = 3.5% PV = ? PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000

PV = -$1,116.03

3. CALC: n = 15 x 2 = 30 r = 7% / 2 = 3.5% PV = ? PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000

PV = -$1,195.42

C. 1. CALC: n = 1 x 2 = 2 r = 9% / 2 = 4.5% PV = ? PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000

PV = -$1,001.17

2. CALC: n = 7 x 2 = 14 r = 9% / 2 = 4.5% PV = ? PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000

PV = -$1,006.39

3. CALC: n = 15 x 2 = 30 r = 9% / 2 = 4.5% PV = ? PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000

PV = -$1,010.18

D. Interest-rate risk varies directly with maturity. The longer maturity of bonds, the larger the price change is when interest rates change.

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.

a. You receive the coupon payments for three years and the bond defaults. After liquidating

the firm, the bondholders receive a distribution of $150 per bond at the end of 3.5 years. What is the realized return on your investment?

b. The firm does far better than expected and bondholders receive all of the promised interest and principal payments. What is the realized return on your investment?

A. CALC: n = 3.5x2 =7 r = ? PV = -$500 PMT = 9.5%x1,000/ 2= $47.50

FV = $150 - 47.50 = $102.50

r = -2.8746%

APY = (1 + r)m – 1 = (1 - 0.0278)2 – 1 = -5.6666%

YTM = 2x(-2.8746) = -5.7493% APR

B. CALC: n = 10x2 =20 r = ? PV = -$500 PMT = 9.5%x1,000/2 = $47.50

FV = $1,000

r = 11.0489%

APY = (1 + r)m – 1 = (1 + 0.110489)2 – 1 = 23.3185%

YTM = 2x11.0489 = 22.0977% APR

B20. (Constant growth model) Medtrans is a profitable firm that is not paying a dividend on itscommon stock. James Weber, an analyst for A. G. Edwards, believes that Medtrans will

begin paying a $1.00 per share dividend in two years and that the dividend will increase

6% annually thereafter. Bret Kimes, one of James’ colleagues at the same firm, is less optimistic.

Bret thinks that Medtrans will begin paying a dividend in four years that the dividend will be $1.00, and that it will grow at 4% annually. James and Bret agree that the required return for Medtrans is 13%.

a. What value would James estimate for this firm?

b. What value would Bret assign to the Medtrans stock?

a. P1 = D2 / (r - g) = $1.00 / (0.13 - 0.06) = $14.29

P0 = $14.29 / (1 + 0.13)1 = $12.64

b. P3 = D4 / (r - g) = $1.00 / (0.13 - 0.04) = $11.11

P0 = $11.11 / (1 + 0.13)3 = $7.70

¦ LEVEL C (ADVANCED)

C1. (Beta and required return) The riskless return is currently 6%, and Chicago Gear has estimated the contingent returns given here.

a. Calculate the expected returns on the stock market and on Chicago Gear stock.

b. What is Chicago Gear’s beta?

c. What is Chicago Gear’s required return according to the CAPM?

REALIZED RETURN

State of the Market Probability that State Occurs Stock Market Chicago Gear

Stagnant 0.20 (10%) (15%)

Slow growth 0.35 10 15

Average growth 0.30 15 25

Rapid growth 0.15 25 35

A. Expected Return M = 0.20 x -.10% + 0.35 x 10% + 0.30 x 15% + 0.15 x 25% =

9.75%

Expected Return Chicago Gear = 0.20 x -.15% + 0.35 x 15% + 0.30 x 25% + 0.15 x

35% = 15.00%

B. sM2 = 0.20(-0.10 - 0.0975)2 + 0.35(0.10 - 0.0975)2 + 0.30(0.15 - 0.0975)2 + 0.15(0.25

- 0.0975)2 = 0.0121

Cov(Chicago Gear, M) = 0.20(-0.15 - 0.15)(-0.10 - 0.0975) + 0.35(0.15 - 0.15)(0.10 –

0.0975) + 0.30(0.25 - 0.15)(0.15 - 0.0975) + 0.15(0.35 - 0.15)(0.25 - 0.0975) = 0.018

ß = Cov(j,M) / sM2 = 0.018 / 0.0121 = 1.49

C. r = rf + ß(rM - rf) = 0.06 + 1.49(0.0975 - 0.06) = 0.1159 = 11.59%

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