To calculate the HPY, we need to find the interest rate that equates the price we paid for the bond
with the cash flows we received. The cash flows we received were $54 each year for two years,
31. The price of any bond (or financial instrument) is the PV of the future cash flows. Even though Bond
M makes different coupons payments, to find the price of the bond, we find the PV of the cash flows.
The PV of the cash flows for Bond M is:
32. In general, this is not likely to happen, although it can (and did). The reason this bond has a negative
YTM is that it is a callable U.S. Treasury bond. Market participants know this. Given the high coupon
33. To find the present value, we need to find the real weekly interest rate. To find the real return, we need
to use the effective annual rates in the Fisher equation. So, we find the real EAR is:
(1 + R) = (1 + r)(1 + h)
1 + .075 = (1 + r)(1 + .032)
r = .0417, or 4.17%
34. To answer this question, we need to find the monthly interest rate, which is the APR divided by 12.
We also must be careful to use the real interest rate. The Fisher equation uses the effective annual rate,
so, the real effective annual interest rates and the monthly interest rates for each account are:
Stock account:
(1 + R) = (1 + r)(1 + h)
1 + .07 = (1 + r)(1 + .04)
r = .0288, or 2.88%
APR = m[(1 + EAR)1/m – 1]
APR = 12[(1 + .0288)1/12 – 1]
APR = .0285, or 2.85%
Now we can find the future value of the retirement account in real terms. The future value of each
account will be:
Stock account:
FVA = C {(1 + r )t – 1]/r}
Bond account:
FVA = C {(1 + r )t – 1]/r}
The total future value of the retirement account will be the sum of the two accounts, or:
Account value = $1,196,731.96 + 170,316.78
Account value = $1,367,048.74
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:
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 )
35. In this problem, we need to calculate the future value of the annual savings after the five years of
operations. The savings are the revenues minus the costs, or:
Savings = Revenue – Costs
Since the annual fee and the number of members are increasing, we need to calculate the effective
growth rate for revenues, which is:
The revenue will grow at 9.18 percent, and the costs will grow at 2 percent, so the savings each year
for the next five years will be:
Year
Revenue
Costs
Savings
1
$305,704.00
$127,500.00
$178,204.00
2
333,767.63
130,050.00
203,717.63
3
364,407.50
132,651.00
231,756.50
4
397,860.10
135,304.02
262,556.08
5
434,383.66
138,010.10
296,373.56
Now we can find the value of each year’s savings using the future value of a lump sum equation, so:
FV = PV(1 + r)t
Year
1
$178,204.00(1 + .09)4 =
2
$203,717.63(1 + .09)3 =
3
$231,756.50(1 + .09)2 =
4
5
Total future value of savings =
He will spend $500,000 on a luxury boat, so the value of his account will be:
Value of account = $1,373,279.31 – 500,000
1.
a.
Enter
40
3%
$1,000
N
I/Y
PV
PMT
FV
Solve for
b.
Enter
40
4%
$1,000
N
I/Y
PV
PMT
FV
Solve for
Enter
40
5%
$1,000
Solve for
2.
a.
Enter
30
3.5%
$35
$1,000
N
I/Y
PV
PMT
FV
Solve for
b.
Enter
30
4.5%
$35
$1,000
N
I/Y
PV
PMT
FV
Solve for
Enter
30
2.5%
$35
$1,000
N
I/Y
PV
PMT
FV
Solve for
3.
Enter
26
±$980
$31
$1,000
N
I/Y
PV
PMT
FV
Solve for
4.
Enter
23
$1,000
N
I/Y
PV
PMT
FV
Solve for
$37.49
$37.49 2 = $74.97
5.
6.
Enter
Solve for
16.
P0
Enter
40
2.85%
$1,000
N
I/Y
PV
PMT
FV
Solve for
Enter
38
2.85%
$1,000
N
I/Y
PV
PMT
FV
Solve for
17. Miller Corporation
P0
Enter
26
2.65%
$32.50
$1,000
N
I/Y
PV
PMT
FV
Solve for
$1,111.71
P1
Enter
24
2.65%
$32.50
$1,000
N
I/Y
PV
PMT
FV
Solve for
$1,105.55
P3
Enter
20
2.65%
$32.50
$1,000
N
I/Y
PV
PMT
FV
Solve for
$1,092.22
P8
Enter
10
2.65%
$32.50
$1,000
N
I/Y
PV
PMT
FV
Solve for
$1,052.11
Enter
2.65%
$32.50
$1,000
N
I/Y
PV
PMT
FV
Solve for
$1,011.54
Enter
Solve for
Modigliani Company
P0
Enter
26
3.25%
$26.50
$1,000
N
I/Y
PV
PMT
FV
Solve for
$895.76
18. If both bonds sell at par, the initial YTM on both bonds is the coupon rate, 5.8 percent. If the YTM
suddenly rises to 7.8 percent:
PLaurel
Enter
6
3.90%
$29
$1,000
N
I/Y
PV
PMT
FV
Solve for
$947.41
PHardy
Enter
40
3.90%
$29
$1,000
N
I/Y
PV
PMT
FV
Solve for
PLaurel
Enter
6
1.90%
$29
$1,000
N
I/Y
PV
PMT
FV
Solve for
P1
Enter
24
3.25%
$26.50
$1,000
N
I/Y
PV
PMT
FV
Solve for
$901.07
P3
Enter
20
3.25%
$26.50
$1,000
N
I/Y
PV
PMT
FV
Solve for
$912.76
P8
Enter
10
3.25%
$26.50
$1,000
N
I/Y
PV
PMT
FV
Solve for
$949.47
P12
Enter
3.25%
$26.50
$1,000
N
I/Y
PV
PMT
FV
Solve for
$988.56
19. Initially, at a YTM of 9 percent, the prices of the two bonds are:
PFaulk
Enter
24
4.5%
$35
$1,000
N
I/Y
PV
PMT
FV
Solve for
$855.05
PYoo
Enter
24
4.5%
$55
$1,000
N
I/Y
PV
PMT
FV
Solve for
Enter
N
I/Y
PV
PMT
FV
Solve for
PYoo
Enter
Solve for
Enter
Solve for
PYoo
Enter
24
3.5%
$55
$1,000
N
I/Y
PV
PMT
FV
Solve for
Enter
Solve for
20.
21. 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
$28.50
$1,000
N
I/Y
PV
PMT
FV
Solve for
24. Current yield = .0842 = $90/P0 ; P0 = $1,068.88
Enter
7.81%
±$1,068.88
$90
$1,000
N
I/Y
PV
PMT
FV
Solve for
25.
Enter
24
±$964.12
$36.20
$1,000
N
I/Y
PV
PMT
FV
Solve for
27.
a. Po
Enter
50
5.9%/2
$1,000
N
I/Y
PV
PMT
FV
Solve for
b. P1
Enter
48
5.9%/2
$1,000
N
I/Y
PV
PMT
FV
Solve for
P24
Enter
2
5.9%/2%
$1,000
N
I/Y
PV
PMT
FV
Solve for
Enter
26
$29.50
$1,000
N
I/Y
PV
PMT
FV
Solve for
28. a. The coupon bonds have a 7% coupon rate, which matches the 7% required return, so they will
sell at par; # of bonds = $50,000,000/$1,000 = 50,000.
For the zeroes:
Enter
60
7%/2
$1,000
N
I/Y
PV
PMT
FV
Solve for
$126.93
$50,000,000/$126.93 = 393,905 will be issued.
Enter
58
7%/2
$1,000
N
I/Y
PV
PMT
FV
Solve for
$135.98
Year 1 interest deduction = $135.98 – 126.93 = $9.04
29.
Bond P
P0
Enter
10
6.5%
$80
$1,000
N
I/Y
PV
PMT
FV
Solve for
$1,107.83
P1
Enter
6.5%
$80
$1,000
N
I/Y
PV
PMT
FV
Solve for
$1,099.84
P0
Enter
N
I/Y
PV
PMT
FV
Solve for
$892.17
30.
a.
Enter
10
±$940
$54
$1,000
N
I/Y
PV
PMT
FV
Solve for
6.22%
Enter
5.22%
N
I/Y
PV
PMT
FV
Solve for
Enter
Solve for
9.37%
31.
PM
CFo
$0
C01
$0
F01
12
C02
$800
16
C03
$1,000
11
C04
$30,000
1
I = 2.8%
NPV CPT
$21,915.52
P1
Enter
Solve for
PN
Enter
40
2.8%
$30,000
N
I/Y
PV
PMT
FV
Solve for
$9,940.24
Enter
7.69%
12
NOM
EFF
C/Y
Solve for
Enter
2.88%
12
NOM
EFF
C/Y
Solve for
2.85%
Enter
3.85%
12
NOM
EFF
C/Y
Solve for
3.78%
Stock portfolio value:
Enter
12 × 30
7.43%/12
$900
N
I/Y
PV
PMT
FV
Solve for
$1,196,731.96
Enter
12 × 30
2.85%/12
$300
N
I/Y
PV
PMT
FV
Solve for
Retirement withdrawal:
Enter
25 × 12
3.78%/12
$1,367,048.74
N
I/Y
PV
PMT
FV
Solve for
$7,050.75
Enter
30 + 25
$7,050.75
N
I/Y
PV
PMT
FV
Solve for
35.
Future value of savings:
Year 2:
Enter
3
9%
$203,717.63
N
I/Y
PV
PMT
FV
Solve for
$263,820.24
Year 3:
Enter
2
9%
$231,756.50
N
I/Y
PV
PMT
FV
Solve for
$275,349.89
Enter
1
9%
$262,556.08
N
I/Y
PV
PMT
FV
Solve for
$286,186.13
Enter
9%
$873,279.31
N
I/Y
PV
PMT
FV
Solve for
Enter
4
9%
N
I/Y
PV
PMT
FV
Solve for
$251,549.49