Question

a. Several years ago, Castles in the Sand Inc. issued bonds at face value of $1,000 at a yield to maturity of 7%. Now, with 8 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 price of the bond now? (Assume semiannual coupon payments.) (Do not round Intermediate calculations. Round your answer to 2 decimal places.) Bond price 5 641,01 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 80% of face value af 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.) Yield to maturity 1287

Answer 1

1. This Bond was issued at par therefore the coupon rate is equal to initial yield to maturity of 7%

Now we have following formula for calculation of bond’s Price

Bond price P0 = C* [1- 1/ (1+YTM) ^n] /YTM + M / (1+YTM) ^n

Where,

M = value at maturity, or par value = $1000

P0 = the current market price of bond =?

C = coupon payment = 7% of $1000 = $70 but semiannual coupon, therefore C = $70/2 = $35

Years remaining prior to maturity = 8 years; therefore number of payments n = 8 *2 = 16

YTM = current interest rate, or yield to maturity = 15% or 15%/2 = 7.5% semiannual

Now we have,

Bond price P0 = $35 * [1 – 1 / (1+7.5%) ^16] /7.5% + 1000 / (1+7.5%) ^16

= $319.95 + $314.39

= $634.34

Therefore Bond Price is $634.34

2. We have following formula for calculation of bond’s yield to maturity (YTM) in the given situation

Bond price P0 = C* [1- 1/ (1+YTM) ^n] /YTM + M / (1+YTM) ^n

Where,

P0 = the current market price of bond = $634.34

Face value or Par value of the bond = $1000

M = value at maturity = 80% of Face value = 80% * $ 1000 = $800

C = coupon payment = 7% of $1000 = $70 but semiannual coupon, therefore C = $70/2 = $35

n = number of payments (time remaining to maturity) = 8 years; therefore number of payments n = 8 *2 = 16

YTM = interest rate, or yield to maturity =?

Now we have,

$634.34 = $35 * [1 – 1 / (1+YTM) ^16] /YTM+ $800/ (1+YTM) ^16

By trial and error method we can calculate the value of YTM = 6.49% semiannual

Or annual YMT = 2 *6.49% = 12.99% per year

[Or you can use excel function for YTM calculation in following manner

“= Rate(N,PMT,PV,FV)”

“Rate(16,-35,634.34,-800)” = 6.49%]

Therefore yield to maturity of the bond is 12.99%