April 3, 2019

B-134 SOLUTIONS

Now we need to find the monthly interest rate in retirement. We can use the same procedure that we

used to find the monthly interest rates for the stock and bond accounts, so:

(1 + R) = (1 + r)(1 + h)

APR = m[(1 + EAR)1/m – 1]

Now we can find the real monthly withdrawal in retirement. Using the present value of an annuity

equation and solving for the payment, we find:

PVA = C({1 – [1/(1 + r)]t } / r )

This is the real dollar amount of the monthly withdrawals. The nominal monthly withdrawals will

increase by the inflation rate each month. To find the nominal dollar amount of the last withdrawal,

we can increase the real dollar withdrawal by the inflation rate. We can increase the real withdrawal

by the effective annual inflation rate since we are only interested in the nominal amount of the last

withdrawal. So, the last withdrawal in nominal terms will be:

FV = PV(1 + r)t

Calculator Solutions

3.

Enter 10 8.75% $75 $1,000

N I/Y PV PMT FV

4.

Enter 9 ±$934 $90 $1,000

N I/Y PV PMT FV

5.

Enter 13 7.5% ±$1,045 $1,000

N I/Y PV PMT FV

Solve for $80.54

CHAPTER 7 B-135

6.

Enter 20 3.70% $34.50 $1,000

N I/Y PV PMT FV

7.

Enter 20 ±$1,050 $42 $1,000

N I/Y PV PMT FV

8.

Enter 29 3.40% ±$924 $1,000

N I/Y PV PMT FV

15. Bond X

P0

Enter 13 6% $80 $1,000

N I/Y PV PMT FV

P1

Enter 12 6% $80 $1,000

N I/Y PV PMT FV

P3

Enter 10 6% $80 $1,000

N I/Y PV PMT FV

P8

Enter 5 6% $80 $1,000

N I/Y PV PMT FV

P12

Enter 1 6% $80 $1,000

N I/Y PV PMT FV

B-136 SOLUTIONS

Bond Y

P0

Enter 13 8% $60 $1,000

N I/Y PV PMT FV

P1

Enter 12 8% $60 $1,000

N I/Y PV PMT FV

P3

Enter 10 8% $60 $1,000

N I/Y PV PMT FV

P8

Enter 5 8% $60 $1,000

N I/Y PV PMT FV

P12

Enter 1 8% $60 $1,000

N I/Y PV PMT FV

16. If both bonds sell at par, the initial YTM on both bonds is the coupon rate, 9 percent. If the YTM

suddenly rises to 11 percent:

PSa

m

Enter 6 5.5% $45 $1,000

N I/Y PV PMT FV

Solve for $950.04

PDave

Enter 40 5.5% $45 $1,000

N I/Y PV PMT FV

Solve for $839.54

If the YTM suddenly falls to 7 percent:

PSa

m

Enter 6 3.5% $45 $1,000

N I/Y PV PMT FV

Solve for $1,053.29

All else the same, the longer the maturity of a bond, the greater is its price sensitivity to changes

in interest rates.

17. Initially, at a YTM of 8 percent, the prices of the two bonds are:

PJ

Enter 18 4% $20 $1,000

N I/Y PV PMT FV

If the YTM rises from 8 percent to 10 percent:

PJ

Enter 18 5% $20 $1,000

N I/Y PV PMT FV

P

K

Enter 18 5% $60 $1,000

N I/Y PV PMT FV

If the YTM declines from 8 percent to 6 percent:

PJ

Enter 18 3% $20 $1,000

N I/Y PV PMT FV

P

K

Enter 18 3% $60 $1,000

N I/Y PV PMT FV

All else the same, the lower the coupon rate on a bond, the greater is its price sensitivity to

changes in interest rates.

B-138 SOLUTIONS

18.

Enter 18 ±$1,068 $46 $1,000

N I/Y PV PMT FV

19. The company should set the coupon rate on its new bonds equal to the required return; the required

return can be observed in the market by finding the YTM on outstanding bonds of the company.

Enter 40 ±$930 $35 $1,000

N I/Y PV PMT FV

22. Current yield = .0755 = $90/P0 ; P0 = $90/.0755 = $1,059.60

23.

Enter 28 ±$1,089.60 $36 $1,000

N I/Y PV PMT FV

25.

a. Po

Enter 50 4.5% $1,000

N I/Y PV PMT FV

b. P1

Enter 48 4.5% $1,000

N I/Y PV PMT FV

P19

Enter 1 4.5% $1,000

N I/Y PV PMT FV

CHAPTER 7 B-139

c. Total interest = $1,000 – 110.71 = $889.29

d. The company will prefer straight-line method when allowed because the valuable interest

deductions occur earlier in the life of the bond.

26. a. The coupon bonds have an 8% coupon rate, which matches the 8% required return, so they will

For the zeroes:

Enter 60 4% $1,000

N I/Y PV PMT FV

b. Coupon bonds: repayment = 30,000($1,080) = $32,400,000

Zeroes:

Enter 58 4% $1,000

N I/Y PV PMT FV

Solve for $102.82

year 1 interest deduction = $102.82 – 95.06 = $7.76

During the life of the bond, the zero generates cash inflows to the firm in the form of the

interest tax shield of debt.

29.

Bond P

P0

Enter 5 7% $120 $1,000

N I/Y PV PMT FV

P1

Enter 4 7% $120 $1,000

N I/Y PV PMT FV

Solve for $1,097.19

Bond D

P0

Enter 5 7% $60 $1,000

N I/Y PV PMT FV