The current term-structure of spot interest rates for safe zero-coupon bonds is as follows:
Maturity, in years
Interest rate(r)
1 8%
2 10%
3 11%
4 12%
5 13%
There is a safe bond B which has 4 years before maturity and pays a coupon
of 12% at regular annual intervals and a face value of $100 at maturity.
(a) What will be the current price of bond B?
Where is the answer
To calculate the current price of bond B, we need to determine the present value of its expected cash flows. The coupon payments and the face value represent the cash flows. Here's how you can calculate it:
Step 1: Calculate the present value of each cash flow.
- Coupon Payments: Bond B has a 12% coupon rate with a face value of $100. Since the coupon payments are made annually for 4 years, we have 4 coupon payments of $12 each. We need to discount each payment at the corresponding spot interest rate to calculate the present value of the coupon payments.
- Face Value: The face value of $100 will be received at maturity, which is in 4 years. Therefore, we need to discount the face value at the corresponding spot interest rate.
Step 2: Sum up the present values calculated in Step 1 to get the current price of bond B.
Let's go ahead and calculate it:
Coupon Payments:
- Present Value of the 1st coupon payment: $12 / (1+0.08)^1 = $11.11
- Present Value of the 2nd coupon payment: $12 / (1+0.10)^2 = $9.92
- Present Value of the 3rd coupon payment: $12 / (1+0.11)^3 = $9.05
- Present Value of the 4th coupon payment: $12 / (1+0.12)^4 = $8.15
Face Value:
- Present Value of the face value: $100 / (1+0.12)^4 = $68.06
Current Price of Bond B:
- Sum of the present values of coupon payments and face value:
$11.11 + $9.92 + $9.05 + $8.15 + $68.06 = $106.29
Therefore, the current price of bond B is $106.29.