Question

Suppose you purchase a 8-year, 6% semi-annual coupon bond for 89.153. Immediately after you purchase the bond, the yield for equivalently risk bonds decreases by 100 basis points. However, instead of holding the bond until maturity, you plan to hold the bond for 3 years and then sell it. All coupons will be reinvested at the prevailing yield on equivalently risky bonds. What will be your return on this investment in this scenario? Round your answer to three decimal places.

Answer 1

To find the YTM at the time of purchase, we need to put the following values in the financial calculator:

N = 8*2 = 16;

PV = -89.153;

PMT = (6%/2)*100 = 3;

FV = 100;

Press CPT, then I/Y, which gives us 3.93

So, Periodic Rate = 3.93%

YTM = Periodic Rate * No. of compounding periods in a year

= 3.93% * 2 = 7.85%

YTM after 3 years = 7.85% - 1% = 6.85%

Bond's Market Value after 3 years = PV of Coupon Payment + PV of Maturity Value

= [Periodic Coupon Payment * {(1 - (1 + r)^-n) / r}] + [Face Value / (1 + r)^n]

= [{(6%/2)*$100} * {(1 - (1 + 0.0685/2)^-(5*2)) / (0.0685/2)}] + [$100 / {1 + (0.0685/2)}^(5*2)]

= [$3 * {0.2860 / 0.0342}] + [$100 / 1.4005]

= [$3 * 8.3478] + $71.40

= $25.04 + $71.40 = $96.445

Return on the investment = [(P3 + C1 +C2 + C3) / P0] - 1

= [($96.445 + $6 + $6 + $6) / $89.153] - 1

= [$114.445 / $89.153] - 1

= 1.2837 - 1 = 0.2837, or 28.37%