2. You purchased a zero-coupon bond that has a face value of $1,000, five years

Question

2. You purchased a zero-coupon bond that has a face value of $1,000, five years to maturity, and a yield to maturity of 7.3%. It is one year later and similar bonds are offering a yield to maturity of 8.1%. You will sell the bond now. You have a tax rate of 40% on regular income and 15% on capital gains. Calculate the following for this bond o The purchase price of the bond (3 points) o The current price of the bond (3 points) o The imputed interest income (4 points) o The capital gain (or loss) on the bond (4 points) o The before-tax rate of return on this investment (4 points)

Explanation / Answer

Face Value $1,000.00 Coupon Payment $0.00 Period 5 YTM 7.30% Purchased Price (PV) $703.07 (a) PV(7.30%,5,0,-1000) Face Value $1,000.00 Coupon Payment $0.00 Period 4 YTM 8.10% Purchased Price (PV) $732.31 (b) PV(8.10%,4,0,-1000) c)Imputed Interest Income Change in price at original YTM = imputed interest income Face Value $1,000.00 Coupon Payment $0.00 Period 4 YTM 7.30% Purchased Price (PV) $754.40 PV(7.30%,4,0,-1000) Imputed Interest Income = $754.40 - $703.07 $51.32 (c) Capital gain(loss) =Change in price due to interest rate change = $732.31-754.40 -$22.09 (d) Rate of return %=($732.31-703.07)/$703.07 4.16% (e)

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