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 6.2%. Now, with 6 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 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 90% 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.)

Several years ago, Castles in the Sand Inc. issued bonds at face value of $1,000 at a yield to maturity of 6.2%. Now, with 6 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 now? (Assume semiannual coupon payments.) (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Explanation / Answer

(a) Bond price = Present value (PV) of all future cash flows from bond

= PV of coupon interests + PV of redemption price

Semi-annual coupon = $1000 x 6.2% x (6/12) = $31

Number of periods till maturity = 6 x 2 = 12

Semi-annual YTM = 15% / 2 = 7.5%

So, Price ($) = 31 x PVIFA(7.5%, 12) + 1000 x PVIF(15%, 6)

= 31 x 7.7353 + 1000 x 0.4323275 = 239.7943 + 432.3275

= 672.12 (rounded off)

(b)

If C: Semi-annual coupon payment = $31,

F: Face value = $1000,

N: Periods till maturity = 12,

P = Bond price = $1000 x 0.9 = $900,

Then using approximation formula,

Yield to maturity = [C + (F - P) / N] / [(F + P) / 2]

= [31 + (1000 - 900) / 12] / [(1000 + 900) / 2]

= [31 + 8.33] / [1900 / 2]

= 39.33 / 950

= 0.0414, or 4.14%

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