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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
