Question

Star Light & Power has junk bonds with an 8% coupon rate, 20 years to maturity, and pays semi-annual coupons. You purchase the junk bonds at the market price of 82.50% of par.

Suppose that you believe that Star Light & Power’s junk bonds will receive a ratings upgrade to investment grade due to increasing financial strength in Star Light & Power’s balance sheet. If the average investment grade bond has a yield to maturity of 5% and Star Light & Power’s does receive the ratings upgrade, what is your expected profit?

Answer 1

Given that the bond has a coupon rate of 8% paid semi-annually, with time to maturity 20 years and market price at which it is bought is 82.50%. Considering the face value FV of the bond is $100.
Market price P = 82.50%*100 = $82.50
Coupon paid semi-annually = 8%*100 / 2 = $4
Number of period to maturity N = 20*2 = 40 ( since semi-annual payment is done)

Now, since the YTM is expected to be 5% after upgrading the bond, semiannual YTM r = 2.5% the new price of the bond would be calculated as follows:

Price = C*PVIFA(r%,N) + FV*PVIF(r%,N)
Using formula
C * ({1 − [1 / (1 + r )^N ]} / r ) + [FV / (1 + r )^N]
4*({1-[1/(1+ .025) ⁴⁰ ]} / 0.025) + [100/(1+0.025)⁴⁰
4*({1- 0.37243}/0.025} + [100/2.68506]
4*25.10278 + 37.24306
100.4111 + 37.24306
137.6542

The new price would be now $137.6542

Expected profit = 137.6542 - 87.50
= $50.15

Expected rate of profit = 50.15/87.50

= 57.32%

Expected profit would be $50.15 with expected rate of profit being 57.32%