De\'Andre purchased one of XXXL Shirt Company\'s bonds last year when the market

Question

De'Andre purchased one of XXXL Shirt Company's bonds last year when the market interest rate on similar-risk bonds was 6 percent. When he purchased the bond,                     it had 7 years remaining until maturity. The bond's coupon rate of interest (paid semi-annualy) is 5 percent, and its maturity value is $1000. Today, the                     market rate on similar risk bonds as the one De'Andre purchased one year ago is 4 percent. (A) If he were to sell the bond today, what return would De'Andre                     earn? (B) What portion of this return represents the capital gains, and what portion represents the current yield?                 

Explanation / Answer

Hi,

Please find the answer as follows:

Purchase Price of Bond:

Rate = 6%/2 = 3%

PMT = 1000*.05/2 = 25

FV = 1000

Nper = 7*2 = 14

PV = ?

Purchase Price = PV(rate,nper,pmt,fv) = PV(3%,14, 25,1000) = 943.52

Current Price of Bond:

Rate = 2%/2 = 2%

PMT = 1000*.05/2 = 25

FV = 1000

Nper = 6*2 = 12

PV = ?

Current Price = PV(rate,nper,pmt,fv) = PV(2%,12, 25,1000) = 1052.88

Part A:

Return = (Current Price - Purchase Price + Interest)/Purchase Price = (1052.88-943.52 + 1000*.05)/943.52 = 16.89%

Part B:

Capital Gain = (Current Price - Purchase Price)/Purchase Price = (1052.88-943.52)/943.52 = 11.59%

Part C:

Current Yield = Interest Payment/Market Price =(1000*.05)/943.52 = 5.299% or 5.30%

Thanks.

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