978-1305661653 Chapter 5 Solutions Manual

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

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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

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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%

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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

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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%

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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:

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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

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