P6-7. Term structure of interest rates
LG 1; Intermediate
a.
b. and c.
d. Five years ago, the 10-year bond was paying 9.5%, which would result in approximately 95% in
P6-8. Risk-free rate and risk premiums
LG 1; Basic
a. Risk-free rate: RF r* IP
Security r*IP RF
A 3% 6% 9%
b. Because the expected inflation rates differ, it is probable that the maturity of each security differs.
c. Nominal rate: r r* IP RP
Security r*IP RP r
© 2015 Pearson Education, Inc.
P6-9. Risk premiums
LG 1; Intermediate
a. RFt r* IPt
b. Risk premium:
c. ri r* IP RP or r1 rF risk premium
P6-10. Bond interest payments before and after taxes
LG 2; Intermediate
P6-11. Bond prices and yields
LG 4; Basic
a. 0.97708 $1,000 $977.08
b. (0.05700 $1,000)
¸
$977.08 $57.000
¸
$977.08 0.0583 5.83%
c. The bond is selling at a discount to its $1,000 par value. The bond is selling at a discount because its
d. The yield to maturity is higher than the current yield because the former includes $22.92 in price
P6-12. Personal finance: Valuation fundamentals
LG 4; Basic
a. Cash flows: CF15$1,200
b.
3 5
1 2 4
01 2 3 4 5
(1 ) (1 ) (1 ) (1 ) (1 )
CF CF
CF CF CF
Vr r r r r
= + + + +
+ + + + +
01 2 3 4 5
$1,200 $1,200 $1,200 $1,200 $6,200
(1 0.06) (1 0.06) (1 0.06) (1 0.06) (1 0.06)
V= + + + +
+ + + + +
0
$8,791V=
Using Calculator:
N 5, I 6, PMT $1,200, FV $5,000
Solve for PV: $8791
The maximum price you should be willing to pay for the car is $8,791 because, if you paid more than that
amount, you would be receiving less than your required 6% return.
P6-13. Valuation of assets
LG 4; Basic
Present Value of
Asset End of Year Amount Cash Flows
A 1 $ 5,000 N 3, I 18 $10,871.36
2 $ 5,000 PMT $5,000
3 $ 5,000
P6-14. Personal finance: Asset valuation and risk
LG 4; Intermediate
a.
N PMT
@ 10%
Low Risk
@ 15%
Average Risk
@ 22%
High Risk
CF1–4 $3,000 $ 9,510 $ 8,565 $ 7,481
b. The maximum price Laura should pay is $13,030.92. Unable to assess the risk, Laura would use the
c. By increasing the risk of receiving cash flow from an asset, the required rate of return increases,
which reduces the value of the asset.
P6-15. Basic bond valuation
LG 5; Intermediate
a. I 10%, N 16, PMT $120, FV $1,000
b. Because Complex Systems’ bonds were issued, there may have been a shift in the supply-demand
c. I 12%, N 16, PMT $120, FV $1,000
P6-16. Bond valuation—annual interest
LG 5; Basic
Bond Calculator Inputs Calculator Solution
A N 20, I 12, PMT 0.14 $1,000 $140, FV 1,000 $1,149.39
$1,000
P6-17. Bond value and changing required returns
LG 5; Intermediate
a.
Bond Calculator Inputs Calculator Solution
(1) N 12, I 11%, PMT $110, FV $1,000 $1,000.00
b.
c. When the required return is less than the coupon rate, the market value is greater than the par value,
d. The required return on the bond is likely to differ from the coupon interest rate because either
P6-18. Bond value and time—constant required returns
LG 5; Intermediate
a.
Bond Calculator Inputs Calculator Solution
(1) N 15, I 14%, PMT $120, FV $1,000 $877.16
b.
c. From the graph we can conclude that, all else remaining the same, when the required return differs
from the coupon interest rate and is assumed to be constant to maturity, the bond value approaches the
par value.
P6-19. Personal finance: Bond value and time—changing required returns
LG 5; Challenge
a.
Bond Calculator Inputs Calculator Solution
(1) N 5, I 8%, PMT $110, FV $1,000 $1,119.78
b.
Bond Table Values Calculator Solution
(1) N 15, I 8%, PMT $110, FV $1,000 $1,256.78
c.
Value
Required Return Bond A Bond B
8% $1,119.78 $1,256.75
d. If Lynn wants to minimize interest rate risk in the future, she would choose Bond A with the shorter
P6-20. Yield to maturity
LG 6; Basic
P6-21. Yield to maturity
LG 6; Intermediate
a. Using a financial calculator, the YTM is 12.685%. The correctness of this number is proven by putting
b. The market value of the bond approaches its par value as the time to maturity declines. The yield to
maturity approaches the coupon interest rate as the time to maturity declines.
P6-22. LG 6: Yield to maturity
LG 6; Intermediate
a.
Calculator
Bond Approximate YTM Solution
A
$90 [($1,000 $820) 8]
[($1,000 $820) 2]
+ – ¸
+ ¸
12.36%
12.71%
[($1,000 $900) 2]
+ ¸
b. The market value of the bond approaches its par value as the time to maturity declines. The
P6-23. Personal finance: Bond valuation and yield to maturity
LG 2, 5, 6; Challenge
a. N 5, I 12%, PMT 0.06 $1,000 $60; FV $1,000
b. Number of Bond A bonds $20,000 $783.71 25.520
c. Interest income of A 25.520 bonds$60 $1,531.20
d. At the end of the 5 years both bonds mature and will sell for par of $1,000.
e. The difference is due to the differences in interest payments received each year. The principal
P6-24. Bond valuation—semiannual interest
LG 6; Intermediate
P6-25. Bond valuation—semiannual interest
LG 6; Intermediate
Bond Computer Inputs Calculator Solution
A N 24, I 4%, PMT $50, FV $1,000 $1,152.47
P6-26. Bond valuation—quarterly interest
LG 6; Challenge
P6-27. Ethics problem
LG 1; Intermediate
Case
Case studies are available on www.myfinancelab.com.
Evaluating Annie Hegg’s Proposed Investment in Atilier Industries Bonds
a. Annie should convert the bonds. The value of the stock if the bond is converted is
b. Current value of bond under different required returns – annual interest
2. N 25, I 8%, PMT $80, FV $1,000
3. N 25, I 10%, PMT $80, FV $1,000
c. Current value of bond under different required returns – semiannual interest
1. N 50, I 3%, PMT $40, FV $1,000
2. N 50, I 4%, PMT $40, FV $1,000
3. N 50, I 5%, PMT $40, FV $1,000
d. If expected inflation increases by 1%, the required return will increase from 8% to 9%, and the bond price
e. The value of the bond would decline to $924.81 due to the higher required return and the inverse relationship
f. The bond would increase in value and a gain of $110.61 would be earned by Annie.
g. The bond would increase in value and a gain of $91.08 would be earned by Annie.
h. Antilier Industries provides a yield of 8% ($80) and is priced at $983.80 (0.98380 1,000). Hence, the current
i. Annie should probably not invest in the Atilier bond. There are several reasons for this conclusion.
Spreadsheet Exercise
Group Exercise
Group exercises are available on www.myfinancelab.com.