Question

On October 15, 2016, Koala, Inc. issued a 10 year bond (with a typical $1000 face value) that had an annual coupon value of $60. [We are assuming that the 2020 coupon has just been redeemed.]

• Initially, the bond was sold for the premium price of $1,025.

• On October 15, 2020, this bond was selling for only $975.

• The market rate of interest for a riskless corporate bond, of this maturity, was 4.5% on October 15, 2016, which reflects market expectations about future rates of inflation.

• The market rate of interest for a riskless corporate bond, of this maturity, was 4.0% on October 15, 2020, which reflects market expectations about future rates of inflation.

Question-  What was the risk premium for this bond on October 15, 2016? [To 3 decimal places.]

Answer 1

We need to first find the rate of interest at which the cash flows from this bond as of Oct 15, 2020, need to be discounted to reach the PV of $975, which is the market price.

The cash flows are:

6 coupons of $60 each from Oct 15, 2021 to Oct 15, 2026

1 principal payment of $1000 on Oct 15, 2026

When we solve for r in the PV calculation which is the sum of individual CF's PV = CF/(1+r)^time, we get r = 6.5%. Since the risk free rate of interest is 4%, the risk premium on this bond is 2.5%, i.e., 6.5%-4%

		6.5%
Time	CF	PV = CF/(1+r%)^Time
1	60	56.34
2	60	52.90
3	60	49.67
4	60	46.64
5	60	43.79
6	1060	726.45
	Total	975.79