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

(1) Price of bond

t: time to maturity = 12 years

Coupon = 7% (paid quarterly)

y: yield to maturity = 15%

n (semi-annuall) = 4 (quarterly)

FV: Face value = 1000

Substituting the above values in the equation we get, Price of bond = $587.07

2) The company is sure to pay the coupons, but the principal returned (ie face value) is probabilistic in nature

So in the above equation, we will change the value of FV & find the price of bond

Probability	Face value	Price of bond
30%	0	$400.17
40%	50%*1000 = 500	$493.62
30%	80%*1000 = 800	$549.69

Expected value received at maturity = 30%*0+40%*500+30%*800 = $440

3) Expected price of bond = 30%*400.17+40%*493.62+30%*549.69 = $482.406

Price of bond = $587.07

Face value = $440

yield = ?

Everything else remaining constant, we put these values in the above equation & find y

y = 11.34% (adjusted yield)