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?

Please can you do manually.

thank you

Answer 1

Whenever the bond is issued, it is issued at a price which provides yields equal to the yields of similar issues in the market. Thus the bonds on issue always sells at par. Thus the purchase price of the bond should be $1000.

Now after 3 years, the bond will pay a coupon of $30 semiannually, for 17 years, and a lumpsum of $1000 at the time of maturity. The market yield = 4%

The present value of any security is the present value of the cash flows from the security, discounted at the market yield.

Thus PV of bond = PV of $1000 discounted at at 4% + PV of annuity of $30 semiannual paying bond at 4%.

The formula will be = +

Where FV = $1000 , r=0.04, n=17. Keep in mind that the coupon payments are semiannual thus for the calculation of the PV of the coupon payments take C= 60/2 = 30, r=(0.04/2) = 0.02 , and n = 17*2 = 34

Substituting the value in the formula, we will get = +  

After solving this you will get = $513.373 + 734.96

Thus PV of the bond = $1248.33 (You will get wrong answer (around $1243.31) if you put the same value for r=4%, n=17 and C=60 to find the PV of annuity, remember that the coupon is being paid semiannually and thus C=30,n=34, r=2% for calculating the PV of the annuity)

Thus the time of buying the bond was right and there is a possibility of making money if sold right now.

The capital gain on this trade = Selling price - Purchase Price = $1248.33 - $1000 = $248.33