A $1,000 bond has a coupon rate of 10 percent and matures after 8 years. Interes

Question

A $1,000 bond has a coupon rate of 10 percent and matures after 8 years. Interest rates are currently 7%.

a) What will the price of this bond be if the interest is paid annually?
b) What will the price be if investors expect that the bond will be called with no call pennalty after two years?
c) What will the price be if the investors expect that the bond will be called after two years and there will be a call penalty of one year's interest?
d) Why are your answers different for questions a, b and c?

Please show your calculations

Explanation / Answer

a) What is the current price of the bond if the comparable rate of interest is 8 percent?

Since coupon rate is equal to the current yield of the bond, the price will be equal to face value = $1000

b) What is the current price of the bond if the comparable rate of interest is 10 percent?

PMT= 80 (8%* 1000)

I= 10%

N= 10 years

FV= 1000

PV= 877.11 (from financial calculator or excel)

c) What are the current yields given the prices determined in parts (a) and (b)?

Current yield = coupon amount/current price of bond

For part a, current yield will be 8% calculated from coupon value (80) divided by current price of the bond (1000).

For part b, current yield will be 9.12% calculated by 80 divided by 877.11.

d) Prices in a and b are different because the rate of interest used for discounting the cash flows of the bond are different. Higher the rate of interest, lower the price of the bond.

Current yield is calculated by coupon value divided by current price of the bond. Current price is determined by current interest rates. Since current interest rates are different, current prices are different and hence current yields are different.

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