END-OF-CHAPTER STUDY PROBLEMS

7-1.

Value (Vb) =

Using a financial calculator, we find the value of the bond to be $1,105.94: 20 7 80 1,000 ANSWER -1,105.94

If you pay more for the bond, your required rate of return will not be satisfied. In other words, by paying an amount for the bond that exceeds $1,105.94, the expected rate of return for the bond is less than the required rate of return. If you have the opportunity to pay less for the bond, the expected rate of return exceeds the 7 percent required rate of return.

7-2

If interest is paid semiannually:

Value (Vb) =

The value of the bond would be $941.55:

14 2.5 20 1,000 ANSWER -941.55

If interest is paid annually:

Value (Vb) =

The value of the bond would be $942.14

7 5 40 1,000 ANSWER -942.14

7-3.

a. $875 =

20 875 70 1,000 ANSWER 8.30

b. Value (Vb) = = $744.59

20 10 70 1,000 ANSWER -744.59

c. You should sell the bond.

7.4.

The value of the bond is $825.09.

14 7 50 1,000 ANSWER -825.09

7-5. a. Value (Vb) =

The value of the bond was $865.80: 10 8 60 1,000 ANSWER -865.80

b. If the investor also receives $60 interest, then:

$865.80 = +

And the expected rate of return would be 22.43%

1 865.80 60 1,000 ANSWER 22.43

7-6. If the interest is paid semiannually:

Value (Vb) =

The value of the bond is $1,135.78 16 2 30 1,000 ANSWER -1,135.78

If interest is paid annually:

Value (Vb) =

The value of the bond is $1,134.65: 8 4 60 1,000 ANSWER -1,134.65

7-7.

a. Series A:

Value (Vb) =

Value (Vb) =

Value (Vb) =

12 = 4 7 10 55 1,000 ANSWER -1,140.78 -880.86 -693.38

Series B

Value (Vb) = +

Value (Vb) = +

Value (Vb) = +

1 = 4 7 10 55 1,000 ANSWER -1,014.42 -985.98 -959.09

b. Longer-term bondholders are locked into a particular interest rate for a longer period of time and are therefore exposed to more interest rate risk

7-8. $945 =

20 945 60 1,000 ANSWER 6.50 semiannual rate (1.0652 - 1) 13.42 annual rate

7-9. a. $1,085 =

15 1085 55 1,000 ANSWER 4.70

b. Vb =

15 7 55 1,000 ANSWER -863.38

c. Since the expected rate of return, 4.7 percent, is less than your required rate of return of 7 percent, the bond is not an acceptable investment. This fact is also evident because the market price, $1,085, exceeds the value of the security to the investor of $863.38.

7-10. a. Value

Par Value $1,000.00

Coupon $70

Required Rate of Return 7%

Years to Maturity 15 Market Value $1,000

b. Value at Alternative Rates of Return

Required Rate of Return 9% Market Value $838.79

Required Rate of Return 5% Market Value $1,207.59

c. As required rates of return change, the price of the bond changes, which is the result of "interest-rate risk" Thus, the greater the investor's required rate of return, the greater will be his/her discount on the bond. Conversely, the less his/her required rate of return below that of the coupon rate, the greater the premium will be.

d. Value at Alternative Maturity Dates

Years to Maturity 5

Required Rate of Return 7% Market Value $1,000.00

Required Rate of Return 9% Market Value $922.21

Required Rate of Return 5% Market Value $1086.59

e. The longer the maturity of the bond, the greater the interest rate risk the investor is exposed to, resulting in greater premiums and discounts.

7-11. a. Value

Par Value $1,000.00

Coupon $30

Required Rate of Return 4%

Years to Maturity 20

Market Value $864.10

b. Value at Alternative Rates of Return

Required Rate of Return 7%

Market Value $576.24

Required Rate of Return 2%

Market Value $1,163.51

c. As required rates of return change, the price of the bond changes, which is the result of "interest-rate risk" Thus, the greater the investor's required rate of return, the greater