CHAPTER 7 B- 131
b. To nd our HPY, we need to nd the price of the bond in two years. The price of the bond in
two years, at the new interest rate, will be:
P, = $70(PVIFA,_,) + $1,000(Pv1F5_1,%,) = $1
CHAPTER 7 B- 121
Here we need to nd the coupon rate of the bond. All we need to do is to set up the bond pricing
equation and solve for the coupon payment as follows:
P = $1,045 = C(PVIFA7_5%,13) + $1
B- 120 SOLUTIONS
NOTE: Most problems do not explicitly list a par value for bonds. Even though a bond can have any par
value, in general, corporate bonds in the United States will have a par value of
47.
Enter 18 10% $4,000
Pm
Solve for $32,805.65
Enter 710% $32,805.65
PMT
Solve for $16,834.48
48.
Enter 84 7% / 12 $1,500
1411
Solve for $87,604.36
Enter 96 11%/ 12 $1,500
Pm
Solve for $110,021.35
E
CHAPTER 7
INTEREST RATES AND BOND
VALUATION
Answers to Concepts Review and Critical Thinking Questions
1.
No. As interest rates uctuate, the value of a Treasury security will uctuate. Long-term Treasu
B-130 SOLUTIONS
Now we can use the future value of an annuity equation to nd the annual deposit. Doing so, we
nd:
FVA = Ccfw_[(1+ r): 1] / r
$1,500,000 = $C[(1.06944 1) / .0694]
C = $7,637.76
Chalice
3.70%
3.837%
3.40%
6%
6%
6%
6%
6%
6.
Enter 20
Solve for
7.
Enter 20
Solve for
3.837% >< 2 = 7.67%
8.
Enter 29
Solve for
($29.84 / $1,000)(2) = 5.97%
15. Bend X
Pu
Enter 13
Solve fer
P1
Enter
B-134 SOLUTIONS
Now we need to nd the monthly interest rate in retirement. We can use the same procedure that we
used to nd the monthly interest rates for the stock and bond accounts, so:
(1+R)=(1+ r)
B- 124 SOLUTIONS
16. Any bond that sells at par has a YTM equal to the coupon rate. Beth bends sell at par, so the initial
YTM on both bonds is the coupon rate, 9 percent. If the YTM suddenly rises to
60.
Enter
Selve fer
61.
Enter
Selve fer
Enter
Solve for
Enter
Selve fer
Enter
Solve fer
Enter
Selve fer
HF
7. 72%
$21, 250 i$25,000
17.65%
8% 12
7.72%7 12 $47,000/ 12
$48,699.39
8% $48,6
10.
11.
12.
13.
14.
15.
CHAPTER 7 13-1 19
The term structure is based on pure discount bonds. The yield curve is based on coupon-bearing
issues.
Bond ratings have a subjective factor to them. Split ra
B- 128 SOLUTIONS
26.
(I.
The interest deduction is the price of the bond at the end of the year, minus the price at the
beginning of the year, so:
Year 1 interest deduction = $120.90 110.71 = $10.19
T
Orientation and Direction
Superior
Inferior
Anterior
Posterior
Cranial
Caudal
Ventral
Dorsal
Medial
Lateral
Intermediate
Proximal
Distal
Superficial
Deep
External
Internal
At 65, she is short: $1,112,371.50 295,072.50 = $817,298.80
Enter 30
Solve for
Her employer will contribute $1,500 per year, so she must contribute:
7%
$8,652.25 1,500 = $7,152.25 per year
67. Without
CHAPTER 7 3-127
23. The bond has 14 years to maturity, so the bond price equation is:
P = $1,089.60 = $36(PVIFAR%,23) + $1,000(PVIFR%,23)
Using a spreadsheet, nancial calculator, or trial and error we
14.
15.
CHAPTER 7 3-123
This is a premium bond because it sells for more than 100% of face value. The current yield is:
Current yield = Annual coupon payment 7 Price = $75/$1,351.5625 = 5.978%
The YTM
B-132 SOLUTIONS
The call value is the difference between this implied bond value and the actual bond price. So, the
call value is:
Call value = 115.4730 103.50 = 11.9730
Assuming $1,000 par value, the
B- 122 SOLUTIONS
9.
10.
11.
12.
13.
The approximate relationship between nominal interest rates (R), real interest rates (r), and ination
(h) is:
R=r+h
Approximate r = .07 .038 =.032 or 3.20%
The Fish
31 10 SOLUTIONS
52. Monthly rate = .10 / 12 = .0083; semiannual rate = (1.0083711 1 = 5.11%
Enter 1 0
Solve for
Enter
Solve for
Enter 1 0
Solve for
Enter 1 6
Solve for
53.
:21.
Enter 5
Salve fer
TBG
Ba] 16 SOLUTIONS
Enter 1 12% $1 , 100
pm
Selve fer $15232
Se, at Year 5, the value is: $1,586.11 + 1,416.17 + 1,404.93 + 1,254.40 + 1,232
+ 1,100 = $7,993.60
At Year 65, the value is:
Enter 8% $7,993
CHAPTER 7 B-133
35. To answer this question, we need to nd the monthly interest rate, which is the APR divided by 12.
We also must be careil to use the real interest rate. The Fisher equation uses the
CHAPTER 7 B-137
Pave
Enter 40 3.5% $45 $1.000
PMT
Solve for $1.1213.55
APDM% = ($1.213.55 1.000) / $1.000 = + 21.36%
All else the same. the longer the maturity of a bond. the greater is its price sens
B~136 SOLUTIONS
Bend Y
Pr:
Enter 13 8% $60 $1,000
Solve for $841.92
P1
Enter 12 8% $60 $1,000
Solve for $849.28
P3
Enter 10 8% $60 $1,000
Solve fer $865.80
Ps
Enter 5 8% $60 $ 1 ,000
Solve for $920.
Bwl 12 SOLUTIONS
PV of lease:
Enter 36 7%/ 12 $450
PMT
Solve for $14,573.99
$14,573.91 + 99 = $14,672.91
Buy the car.
You would be indifferent when the PV of the two cash ows are equal. The presen
B- 126 SOLUTIONS
20.
21.
22.
Accrued interest is the coupon payment for the period times the fraction of the period that has passed
since the last coupon payment. Since we have a semiannual coupon bon