Question

The Loughran Corporation has issued zero-coupon corporate bonds with a five-year maturity. Investors believe there is a 30% chance that Loughran will default on these bonds. If Loughran does default, investors expect to receive 25% of their promised payoff at maturity (e.g., $0.25 cents per dollar they are promised). If investors require a 7% expected return on their investment in these bonds, which of the following statements most accurately describes the price and YTM of these bonds?

a.	This bond is priced at $77.50 per $100 face value with a current YTM of 5.2%.
	b.	This bond is priced at $49.91 per $100 face value with a current YTM of 14.9%.
	c.	This bond is priced at $71.30 per $100 face value with a current YTM of 7.0%.
	d.	This bond is priced at $55.26 per $100 face value with a current YTM of 7.0%.
	e.	This bond is priced at $55.26 per $100 face value with a current YTM of 12.6%.

Answer 1

The promised payoff at end of the period is face value of zero coupon bond is $100.
We would calculate the expected price that would be received at maturity.
Expected maturity value	[100*(1-default rate)]+[100*default rate*Percentage received]
Expected maturity value	[100*(1-0.30)]+[100*30%*25%]
Expected maturity value	70+7.50
Expected maturity value	$77.50
Price of zero coupon bond	Expected maturity value*(1/(1+r^n))
r is the expected return and n is number of years
Price of zero coupon bond	77.50*(1/(1.07^5))
Price of zero coupon bond	77.50*0.712986
Price of zero coupon bond	$55.26
Thus, price of zero coupon bond per $100 is $55.26.
Calculation of current YTM
Current YTM	(Face value/Price)^(1/n) - 1
Current YTM	(100/55.26)^(1/5) - 1
Current YTM	12.6%
This bond is priced at $55.26 per $100 face value with a current YTM of 12.6%.
Thus, current statement is option (e)