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Chapter 5 CFIN5
Chapter 5 Solutions
5-1
1,000($29-$28)+1,000(4 0.10) $1.40
Return= = =0.05=5.0%
1,000($28) $28
´
5-2
40($9-$10)+40(0.50) -$0.50
Return= = =-0.05=-5.0%
40($10) $10
5-3
($44-$42)+2(0.05) $2.10
Return= = =0.05=5.0%
$42 $42
5-4
$156-$150+0 $6
Return= = =0.04=4.0%
$150 $150
5-5 a.
1,000($45-$50)+1,000[($0.50)(8)] -$1
Return= = =-0.02=-2.0%
1,000($50) $50
b.
Year 1
1,000($45-$50)+1,000[($0.50)(4)] -$3
Return = = =-0.06=-6.0%
1,000($50) $50
Year 2
1,000($45-$45)+1,000[($0.50)(4)] $2
Return = = =0.044=4.4%
1,000($45) $45
5-6 a.
200($32-$28)+200[($0.60+$0.60+$0.60] $5.80
Return= = =0.207=20.7%
200($28) $28
b.
Year 1
200($26-$28)+200($0.60) -$1.40
Return = = =-0.05=-5.0%
200($28) $28
Year 2
200($28-$26)+200($0.60) $2.60
Return = = =0.10=10.0%
200($26) $26
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
Chapter 5 CFIN5
Year 3
200($32-$28)+200($0.60) $4.60
Return = = =0.164=16.43%
200($28) $28
5-7 Remember that the bonds’ yields represent the averages of the expected one-year interest rates for the
remaining lives of the bonds. Thus, the one-year interest rates for Year 2 and Year 3 can be computed as
follows:
Yield on 2-Year bond: (R1 + R2)/2
(4.0% + R2)/2 = 5.0%
R2 = 2(5%) – 4% = 6.0%
5-8 rRF1 = 1.0%; rRF2 = 0.9%; rRF3 = 0.8%
Remember that the bonds’ yields represent the averages of the expected one-year interest rates for the
remaining lives of the bonds. Thus, the one-year interest rates for Year 2 and Year 3 can be computed
as follows:
a. rRF2 averages 0.9% for two years. Thus, R2 in Year 2 is:
2
1.0%+R
0.9%= 2
R2 = 0.9%(2) – 1.0% = 0.8%
b. rRF3 averages 0.8% for three years. Thus, R3 in Year 3 is:
3
1.0%+0.8%+R
0.8%= 3
R3 = 0.8%(3) – (1.0% + 0.8%) = 0.6%
5-9 Remember that the bonds’ yields represent the averages of the expected one-year interest rates for the
remaining lives of the bonds. Thus, the one-year interest rates for Year 2 and Year 3 can be computed as
follows:
a. Year 2 interest rate: (0.4% + R2)/2 = 0.8%
b. Year 3 interest rate: (0.4% + 1.2% + R3)/3 = 1.1%
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
Chapter 5 CFIN5
5-10 Because the bonds’ yields represent the averages of the expected one-year interest rates for the remaining
lives of the bonds, the one-year interest rates for Year 6 and Year 7 can be computed as follows:
5-11 Because the bonds’ yields represent the averages of the expected one-year interest rates for the remaining
lives of the bonds, the one-year interest rates for Year 3 and Year 4 can be computed as follows:
5-12 rRF = r* + IPn = 3% + IPn, where IPn is the average annual inflation rate over n years.
5-13 rRF = r* + IPn = 2% + IPn, where IPn is the average annual inflation rate over n years.
IPn = Avg. inflation = (Infl1 + Infl2 + … + Infln)/n
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
Chapter 5 CFIN5
We know that Infl1 = Infl2 = 1.5%. Therefore, IP1 = IP2 = 1.5%
We also know that inflation is constant after Year 2. Thus, we can set up this table:
Year r* Inflation Average inflation = IPn rRF = r* + IPt
1 2% 1.5% 1.5%/1 = 1.5% 3.5%
2 2 1.5 (1.5% + 1.5)/2 = 1.5 3.5
5-14 We know the following:
Year One-Year Rate
2017 2.2%
2018 1.8
2019 2.9
a. Yield on a two-year bond = (2.2% + 1.8%)/2 = 2.0%
b. Yield on a three-year bond = (2.2% + 1.8% + 2.9%)/3 = 2.3%
5-15 We know the following:
Year One-Year Inflation Rate
2017 2.1%
a. IP1 = (2.1%)/1 = 2.1%; thus, rRF = 2.0% + 2.1% = 4.1%
b. IP2 = (2.1% + 1.5%)/2 = 1.8%; thus, rRF = 2.0% + 1.8% = 3.8%
c. IP3 = (2.1% + 1.5% + 0.9%)/3 = 1.5%; thus, rRF = 2.0% + 1.5% = 3.5%
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
Chapter 5 CFIN5
Alternative Solution:
Year r* One-Year Inflation Rate rRF
2017 2.0% 2.1% 4.1%
2018 2.0 1.5 3.5
2019 2.0 0.9 2.9
a. One-year bond yield = 4.1%
5-16 We know the following:
Yield on a four-year bond = 2.5%; thus, the sum of the returns for the four-year period must equal
Year One-Yearl Rate
2021 4.5%
2022 2.3
5-17 Other than their yields, the only difference among the bonds is their terms to maturity. As a result, the
difference in the yields of these bonds must be the result of their MRPs. The nine-month bond does not
have an MRP, which means rRF = 2.3%. Thus,
5-18 rRF = 3.2%
a. Because the only difference between Company F’s three-year bond and its seven-year bond is
the term to maturity, the difference in the yields of these two bonds must be the result of their
MRPs. Thus,
b. Because there is no liquidity premium associated with Company F’s bonds, we know the following
exists:
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
Chapter 5 CFIN5
Thus, DRP = 5.0% – (3.2% + 0.6%) = 1.2%
Alternative Solution:
5-19 rRF = 3.2%
a. Because the only difference between Bond T and Bond Q is their terms to maturity, the
difference in the yields of these two bonds must be the result of their MRPs. Thus,
b. Because there is no liquidity premium associated with the two bonds, we know the following
exists:
Yield on Bond T (a five-year bond) = 5.3% = rRF + MRP + DRP
5-20 Based on the information that is given, we know the following relationships exist:
Bond yield = rRF + LP + DRP + MRP
= 2.4% + 0.3% + 0.0% + DRP
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
