Several years ago, Castles in the Sand Inc. issued bonds at face value of $1,000

Question

Several years ago, Castles in the Sand Inc. issued bonds at face value of $1,000 at a yield to maturity of 5.6%. 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 13%. What is the price of the bond now? (Assume semiannual coupon payments.) (Do not round intermediate calculations. Round your answer to 2 decimal places.)

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 82% of face value at maturity. If they buy the bond today, what yield to maturity do they expect to receive? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Explanation / Answer

a. The price of the bond is calculated by PV formula in excel as in =PV(rate,nper,pmt,fv) where rate = 0.13/2, nper = 5*2 = 10, pmt = 5.6% of 1000 = 56 and 56/2 = 28 semi annual, and FV =1000

So price =pv(0.065, 10,28,1000) = $734.01

b. Now the YTM is calculated as =rate(nper,pmt,pv,fv) where FV = 82% of 1000 = 820

So semi annual YTM =rate(10,28,-734.01,860) = 5.169%

Annual Yield = 5.169*2 = 10.34%

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