A. Several years ago, Castles in the Sand, Inc., issued bonds at face value at a

Question

A. Several years ago, Castles in the Sand, Inc., issued bonds at face value at a yield to maturity of 5.8%. Now, with 5 years left until the maturity of the bonds, the company has run into hard times and the yield to maturity on the bonds has increased to 15%. What is the price of the bond? (in dollars)

B. Suppose that investors believe that Castles can make good on the promised coupon payments, but that the company will go bankrupt when the bond matures and the principal comes due. The expectation is that investors will receive only 85% of face value at maturity. If they buy the bond today, what yield to maturity do they expect to receive? (in percentage %)

Explanation / Answer

1.

Old YTM = 5.8%

New YTM = 15%

Years left = 5

Face value = $1000 (supposed)

So, bond price = Present value of coupon payment in 5 years + P.V. of face value of the bond

Here Coupon payment = 5.8%*1000 = $58

     bond price = 58*(1-1/1.15^5)/.15 +   1000/1.15^5 = 194.425 + 497.176 = $691.6

2.

If payment of face value = $850 ( as stated in the problem )

New , YTM = R

then 691.6 = 58*(1-1/(1+R)^5)/R   +   850/(1+R)^5 -------------------------------(1)

By trial and error method

at R = 11%

P.V. of all payments = 718.794 ( as per ------(1))

at R = 12%

P.V. of all payments = 691.38

Now, as per the formula of interpolation

YTM = 11% + (12%-11%) * (691.6 - 691.38)/(718 - 691.38)   = 11.98% = 11.98% approx

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