Question

Today (T=0), an investor purchased a nine year bond with an 8.0% coupon for $9,680. The bond has a face value of $10,000. In six months (T=0.5) interest rates have increased by 1.0% and the investor decides to sell the bond immediately after receiving the first coupon payment. What is the investor’s total gain (loss) on the bond? HINT: Total Gain (Loss) = Price Change in Bond + Coupon

Answer 1

Coupon = 8%*1000 = 80
Coupon semiannual = 80/2 = 40
For YTM using Financial Calculator we get
N = 18; PMT = 40; FV = 10000; PV = -9680; CPT I/Y
YTM half Yearly = 4.26%

Rate = 4.26%*2 = 8.52%

New YTM = 8.52%+1 = 9.52%
New Price of bond = PV of Coupons for 17 months + PV of Par Value = 40*(1-(1+9.52%)^-17/9.52% + 1000/(1+9.52%)¹⁷ = 9127.60

Profit = 9127.60 + 40 - 9680 = -513

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