You purchase a twenty year, 5% coupon bond with a yield of 5%. One year later you sell the bond at a yield of 4%. What is your rate-of-return?

18.13%

Explanation:

Assume Face value of bond = 1.000

Term = 20

Coupon rate = 5%

Yield rate = 5%

Coupon rate = Face value*Coupon rate = $1,000*5% = $50

Purchase price of bond = Face value = $1,000

After 1 year, Yield rate(YTM) = 4% and remaining term = 19 years

Sale price of bond = Coupon amount*PVIFA(YTM,n) + Maturity value*PVIF(YTM,n)

Sale price of bond = $50*PVIFA(4%, 19) + $1,000*PVIF(4%, 19)

Sale price of bond = $50*13.134 + $1,000*0.4746

Sale price of bond = $656.7 + $474.6

Sale price of bond = $1,131.30

Rate of return in 1 year = [Annual coupon amount + (Sale price-Purchase price) / Purchase price

Rate of return in 1 year = $50 + ($1,131.30-$1,000) / $1,000

Rate of return in 1 year = $181.3 / $1,000

Rate of return in 1 year = 0.1813

Rate of return in 1 year = 18.13%

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