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Homework answers / question archive / Suppose that you bought a 20-year, 6

Suppose that you bought a 20-year, 6

Finance

Suppose that you bought a 20-year, 6.5% annual coupon bond with face (par) value of $1,000, last year at yield to maturity 9.75%. What is your total rate of return if after holding it for one year, you sell it at current yield 9.19%?

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Step: 1. Finding Beginning Value of the Bond

a.) We have been given:

Face Value of The bond = $1000

Yield to maturity (r) = 9.75%

Number of years to maturity (n) = 20 years

Coupon Rate = 6.5%

Coupon Amount = $65

b.) Market price of the Bond =

\Rightarrow  65 \times PVAF(9.75%, 20) + 1000 \times PVIF (9.75%, 20)

Side Note:- i) PVAF = [1-1/(1+0.0975)20]/0.0975

= 8.66088087464

ii) PVIF = 1/(1+0.0975)20

= 0.15556411463   

\Rightarrow 65 \times 8.66088087464 + 1000 \times 0.15556411463

\Rightarrow 562.95725685 + 155.56411463

\Rightarrow 718.5214

\Rightarrow $718.52

Step: 2. Finding Ending Value of the Bond=

a.) We have been given:

Face Value of The bond = $1000

Yield to maturity (r) = 9.19%

Number of years to maturity (n) = 19 years

Coupon Rate = 6.5%

Coupon Amount = $65

b.) Market price of the Bond =

\Rightarrow  65 \times PVAF(9.19%, 19) + 1000 \times PVIF (9.19%, 19)

Side Note:- i) PVAF = [1-1/(1+0.0919)19]/0.0919

= 8.83395823384

ii) PVIF = 1/(1+0.0919)19

= 0.18815923819   

\Rightarrow 65 \times 8.83395823384 + 1000 \times 0.18815923819

\Rightarrow 574.2073 + 188.1592

\Rightarrow 762.3665

\Rightarrow $762.37

Step: 3. Rate of Return on bond =

Return = [Ending Value / Beginning Value] - 1

= [762.37 / 718.52] - 1

= 0.061028

= 6.10%

Therefore answer is 6.10%.

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