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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 i
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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

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