P6–8 Risk-free rate and risk premiums The real rate of interest is currently 3%; the inflation expectation and risk premiums for a number of securities follow.

Inflation expectation

Security

Premium

Risk premium

A

6%

3%

B

9

2

C

8

2

D

5

4

E

11

1

a. Find the risk-free rate of interest, RF, that is applicable to each security.

c. Find the nominal rate of interest for each security.

P6–9 Risk premiums Eleanor Burns is attempting to find the nominal rate of interest for each of two securities—A and B—issued by different firms at the same point in time. She has gathered the following data.

Characteristic

Security A

Security B

Time to maturity

3 years

15 years

Inflation expectation premium

9.0%

7.0%

Risk premium for:

Liquidity risk

1.0%

1.0%

Default risk

1.0%

2.0%

Maturity risk

0.5%

1.5%

Other risk

0.5%

1.5%

a. If the real rate of interest is currently 2%, find the risk-free rate of interest applicable to each security.

b. Find the total risk premium attributable to each security’s issuer and issue characteristics.

c. Calculate the nominal rate of interest for each security. Compare and discuss your findings.

P6–16 Bond valuation: Annual interest Calculate the value of each of the bonds shown in the following table, all of which pay interest annually.

Bond

Par value

Coupon interest rate

Years to maturity

Required return

A

$1,000

14%

20

12%

B

1,000

8

16

8

C

100

10

8

13

D

500

16

13

18

E

1,000

12

10

10

P6–21 Yield to maturity The Salem Company bond currently sells for $955, has a 12% coupon interest rate and a $1,000 par value, pays interest annually, and has 15 years to maturity.

a. Calculate the yield to maturity (YTM) on this bond.

b. Explain the relationship that exists between the coupon interest rate and yield to maturity and the par value and market value of a bond.

P7–8 Common stock value: Constant growth Use the constant-growth model (Gordon growth model) to find the value of each firm shown in the following table.

Firm

Dividend expected next year

Dividend growth rate

Required return

A

$1.20

8%

13%

B

4.00

5

15

C

0.65

10

14

D

6.00

8

9

E

2.25

8

20

P7–20 Management action and stock value REH Corporation’s most recent dividend was $3 per share, its expected annual rate of dividend growth is 5%, and the required return is now 15%. A variety of proposals are being considered by management to redirect the firm’s activities. Determine the impact on share price for each of the following proposed actions, and indicate the best alternative.

a. Do nothing, which will leave the key financial variables unchanged.

b. Invest in a new machine that will increase the dividend growth rate to 6% and lower the required return to 14%.

c. Eliminate an unprofitable product line, which will increase the dividend growth rate to 7% and raise the required return to 17%.

d. Merge with another firm, which will reduce the growth rate to 4% and raise the required return to 16%.

e. Acquire a subsidiary operation from another manufacturer. The acquisition should increase the dividend growth rate to 8% and increase the required return to 17%.