The figure for the par value of bond is wrong. The correct figure is $1000. The complete question is,
Bond X is a premium bond making semiannual payments. The bond has a coupon rate of 9.3 percent, a YTM of 7.3 percent, and has 18 years to maturity. Bond Y is a discount bond making semiannual payments. This bond has a coupon rate of 7.3 percent, a YTM of 9.3 percent, and also has 18 years to maturity. Assume the interest rates remain unchanged and both bonds have a par value of $1,000.
What are the prices of these bonds today?
Answer:
a)
The current price of Bond X is $1198.60
b)
The current price of Bond Y is $826.82
Explanation:
The bond's price is calculated as the sum of the present value of the annuity of interest payments by the bond and the present value of the face value of the bond that will be received at maturity. The discount rate used to calculate the present values is the market interest rate or YTM.
As both the bonds are semiannual bonds, we will use the semi annual coupon payment, the semi annual percentage of YTM and the number of semi annual periods outstanding.
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<u>For Bond X</u>
Semi annual coupon payment = 1000 * 0.093 * 6/12 = $46.5
Number of semiannual periods till maturity = 18 * 2 = 36 periods
Semi annual YTM rate = 7.3% / 2 = 3.65%
Price of bond = 46.5 * [ (1 - (1+0.0365)^-36) / 0.0365 ] + 1000 / (1+0.0365)^36
Price of bond = $1198.6002 rounded off to $1198.60
<u>For Bond Y</u>
Semi annual coupon payment = 1000 * 0.073 * 6/12 = $36.5
Number of semiannual periods till maturity = 18 * 2 = 36 periods
Semi annual YTM rate = 9.3% / 2 = 4.65%
Price of bond = 36.5 * [ (1 - (1+0.0465)^-36) / 0.0465 ] + 1000 / (1+0.0465)^36
Price of bond = $826.819 rounded off to $826.82
