Question

Trevor Price bought 10-year bonds issued by Harvest Foods five years ago for $4,532.35. The bonds make semiannual coupon payments at a rate of 8.4 percent. If the current price of the bonds is $6,750, what is the yield that Trevor would earn by selling the bonds today? (Round intermediate calculations to 4 decimal places, e.g. 1.2514 and final answer to 2 decimal places, e.g. 15.25%.)

1000

Answer 1

Answer )

Bond investors are not obligated to take an issuer's bond and hold it until maturity. The return on a bond or asset over the period in which it was held is called the holding period return (HPR). There is an active secondary market for bonds. This means that someone could buy a 30-year bond that was issued 12 years ago, hold it for a five-year period, then sell it again. In such a circumstance, the bondholder doesn't care what the yield of the 12-year old bond will be until it matures 18 years later. If an investor holds the bond for five years, they only care what yield they will earn between years 12 and 17.

The bondholder ought to attempt to calculate the bond's five-year holding period return. This can be approximated by slightly modifying the YTM formula. The bondholder can substitute the sale price for the par value and change the term to equal the length of the holding period. The holding period return formula is as follows:

Holding Period Return= (I + EPV -IV)/ IV

where:
I=Income
EPV=End of Period Value
IV=Initial Value

Income from coupons in 5 years =​ 10 coupons are received in 5 years

assuming bonds issued at par

coupon amount = 8.4% of 4532.35 = 380.7174

Total coupon payment = 380.7174*10 = 3807.7140

therefor HPY = 3807.7140+6750-4532.35/4532.35 = 132.9294%

anualised return = (1+132.9294%)^1/5 = 18.43%

therefore yield hearned by selling the bond = 18.43%

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