Question

2. A bond pays a coupon of $100. If the current market interest rate is 15%, then the bond will sell at a ... If the market interest rate is 9%, then the bond will sell at a A) discount; discount B) premium; premium - C) discount; premium D) premium; discount S T T L 11. 5 / 1.. ...

Answer 1

Solution: Coupon amount = $100

Let, Par Value be $1000

Coupon Rate = Coupon/Par Value = 100/1000 = 10%

Case 1) The market interest rate = 15% = YTM of bond

Since YTM of the bond is greater than the coupon rate, hence, the bond will be trading at a discount.

Case 2) The market interest rate = 9% = YTM of bond

Since YTM of the bond is less than the coupon rate, hence, the bond will be trading at a premium.

Hence, option C is correct.

The above conditions can be explained below:

Let, Coupon rate = 10%, Par Value = $1000

Coupon Amount = 10%*1000 = $100

Let number of years (N) be 5

Case 1) Yield to Maturity (YTM) = 15%

The cash flows are as follows:

Year	Cash Flows
t=1	$                100
t=2	$                100
t=3	$                100
t=4	$                100
t=5	$            1,100
YTM	15%
Current bond price	=NPV(rate, cash flows)
	$                832

Hence, when YTM>Coupon rate, the bond trades at a discount

Case 2) Yield to Maturity (YTM) = 8%
The cash flows are as follows:

Year	Cash Flows
t=1	$                100
t=2	$                100
t=3	$                100
t=4	$                100
t=5	$            1,100
YTM	8%
Current bond price	=NPV(rate, cash flows)
	$            1,080

Hence, when YTM<Coupon rate, the bond trades at a premium