problem i cant seem to solve

Question

A corporate bond was issued a few years ago at face value of $1,000 with a YTM of 7% and quarterly paid coupons. Now with 12 years left until the maturity, the company has run into hard times and the yield to maturity has increased to 15%.

1) What is the bond price now?

2) Suppose the company defer the loss to future and will make good on the promised coupon payments. However, the deferred loss will finally drive the company out of business at the maturity of this bond. It's estimated that investors will lose all the face value with a probabilty of 30%, receive 50% of the face value with a probability of 40%, and 80% of the face value with 30% probability. What is the expected value investors will receive at maturity?

3) Given the calculated expected value received at maturity, how should investors adjust their estimate of the YTM?

Answer 1

Very Interesting Question Monica and lots of Fun. A bond with 7% coupon paid quarterly has coupons of $17.5.

With 12 years to go we have 48 payment periods. The price of the bond is the annuity value of the coupons plus the PV of the principal.. Use the Annuity Formula to value the coupon stream and discount the face value at a 15% rate to come up with the price of the bond.

I assume your professor wants you to continue to discount the coupoun stream at 15% and simply adjust the expected redemption value of the principal. The expected value of the face is (0*.3 +.5*.4 +.3*.8) = 48% of Face. So discount 480 dollars back to PV at 15% and add that to the annuity value of the coupon stream to come up with the new bond price.

If you have any questions please feel free to reach out. I have been discounting cash flows longer than Tom Brady has been throwing footballs.