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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