Question

Stark industries has just issued bonds with $1,000 par value, a $30 coupon paid semiannually (SA), and a 20-year maturity. This means the original issue yield was 6% (($30 * 2) / $1,000 = .06 or 6%). You buy one $1,000 Stark 20-yr 6% bond at issue. 3 years later, you call your broker and tell her to sell it (17 years until maturity). At this point, yields for Stark’s bonds and similar issues have dropped to 4%. What is the PV of the bond now? Did you time the buying of the bond well and make money? What is your capital gain on this trade?

Two years later after you have sold, the interest on comparable bonds (bonds with the same maturity and credit risk as the Stark Bond) increases from 4% all the way to 8%. What is the value of the Stark Industries bond from the question above at this point? In retrospect, are you happy with your decision to sell?

Answer 1

Price (PV) of the bond after three years of issue is calculated using the PV function of Excel at $1244.985917 per bond as shown below with cell values:

Clipboard Font Alignment fPV(D11/D5,D9, D10, D2,0) D12 A C Formula Cell Ref. 1 2 Face Value (FV) $1,000 Given 3 Coupon rate (R) 4 Interest frequency 6% Given Semiannual Given Number of coupon payments a year 5 2 6 Original term (T) 7 Priod expired (years) (t) 8 Time to maturity (no. of years) (N) Given 20 Given T-t D6-D7 17 9 Number of future coupon payments (t) N*t 10 Amount of coupon payment D5*D6 34 FV*R/2 $30 D1*D2/D4 11 Interest rate (YTM) 4% Given 12 Price (Present value) (1,244.985917) PV 13

The investor has timed the buying rightly and earned money.

Capital gain on this transaction per bond = Selling price-Buying price = $1244.985917-$1000 = $244.985917

Capital gain yield= (Difference in price/Buying price)*100 = (244.985917/1000)*100 = 24.4985917%

Value of the Bond after two of sale, with increase in yield to 8% is $827.079667 per bond. Detailed working in Excel as follows:

fiPV(D11/D5,D9, D10, D2,0) D12 A C Formula Cell Ref. 2 Face Value (FV) $1,000 Given 3 Coupon rate (R) 6% Given 4 Interest frequency 5 Number of coupon payments a year Semiannual Given 2 6 Original term (T) Given 20 7 Priod expired (years) (t) Given 5 Time to maturity (no. of years) (N) D6-D7 8 T-t 15 9 Number of future coupon payments (t) N*t D5* 30 10 Amount of coupon payment 11 Interest rate (YTM) FV*R/2 D1*D2/D4 $30 8% Given 12 Price (Present value) (827.079667) PV 13

In retrospect, the investor is happy of earlier decision 2 years ago to sell, as the price has decreased and the investor could have incurred loss if continued to hold.