Question

KIC, Inc., plans to issue $8 million of bonds with a coupon rate of 6 percent and 30 years to maturity. The current market interest rates on these bonds are 10 percent. In one year, the interest rate on the bonds will be either 10 percent or 4 percent with equal probability. Assume investors are risk-neutral.

  

a.	If the bonds are noncallable, what is the price of the bonds today? Assume a par value of $1,000 and semiannual payments. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

     

Price of the bonds

$ ___________

    

b.	If the bonds are callable one year from today at $1,040, will their price be greater or less than the price you computed in part a?
	Less than _____ or Greater than _______

Answer 1

Solution:

a.Given that Coupon payment, C = 6%/2*1000= $30, Number of periods, n = 30*2 = 60 and Face value, FV = 1000

Because the interest rate is unknown, calculate the expected interest rate. Because the rate will be 4 or 10% with equal probability, the average of those two scenarios (7%) should be used.

Price of bond = C (PVIFA @ i, n) + FV (PVIF @ i, n)

Price of bond = $30 (PVIFA @ 7%/2, 60) + 1000 (PVIF @ 7%/2, 60)

Price of bond = $30 [(1.035^60-1)/(0.035*1.035^60)] + 1000 (1/1.035^60)

Price of bond = $30 (24.9447) + 1000 (0.1269)

Price of bond = $875.28

b. The price of the bond will be greater than $875.28, if the bonds are callable one year from today at $1,040.