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.

Q- 8.  What was the risk premium for this bond on October 15, 2020? [To 3 decimal places.]

Answer 1

As of Oct 15, 2020, the following cash flows are expected:

on Oct 15, 2021, i.e., t=1 $60

on Oct 15, 2022, i.e., t=2 $60

on Oct 15, 2023, i.e., t=3 $60

on Oct 15, 2024, i.e., t=4 $60

on Oct 15, 2025, i.e., t=5 $60

on Oct 15, 2026, i.e., t=6 $60

on Oct 15, 2026, i.e., t=6 $1000 (principal redemption)

The sum of the PVs of these using the formula CF/(1+r)^t = $975, since this is the price at which this bond is selling on Oct 15, 2020.

We can solve for r using solver in Excel as follows:

		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

We get r=6.5% and since the risk free interest rate is 4%, the risk premium on this bond is 6.5%-4% = 2.5%