Questions: Westco Company issued 17-year bonds one year ago at a coupon rate of 6.3 percent. The bonds make semiannual payments and have a par value of 1,000. If the YTM on these bonds is 5.5 percent, what is the current price of the bond in dollars? Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16. Current bond price

Solution Steps

To find the current price of the bond, we need to calculate the present value of its future cash flows, which include the semiannual coupon payments and the par value at maturity. The coupon payment can be calculated using the coupon rate and the par value. The present value of these cash flows is determined using the yield to maturity (YTM) as the discount rate. Since the bond makes semiannual payments, we need to adjust the YTM and the number of periods accordingly.

The semiannual coupon payment \( C \) can be calculated using the formula: \[ C = \frac{r \cdot P}{m} \] where:

• \( r = 0.063 \) (annual coupon rate),
• \( P = 1000 \) (par value),
• \( m = 2 \) (number of payments per year).

Substituting the values: \[ C = \frac{0.063 \cdot 1000}{2} = 31.5 \]

The total number of remaining periods \( n \) is given by: \[ n = (17 - 1) \cdot 2 = 32 \]

The semiannual yield to maturity \( y \) is calculated as: \[ y = \frac{YTM}{m} = \frac{0.055}{2} = 0.0275 \]

The present value of the coupon payments \( PV_C \) is calculated using the formula: \[ PV_C = \sum_{t=1}^{n} \frac{C}{(1 + y)^t} \] Substituting the values: \[ PV_C = \sum_{t=1}^{32} \frac{31.5}{(1 + 0.0275)^t} \approx 664.6603 \]

The present value of the par value \( PV_P \) is calculated as: \[ PV_P = \frac{P}{(1 + y)^n} = \frac{1000}{(1 + 0.0275)^{32}} \approx 419.7410 \]

The current price of the bond \( P_b \) is the sum of the present values of the coupon payments and the par value: \[ P_b = PV_C + PV_P \approx 664.6603 + 419.7410 \approx 1084.4013 \]

Final Answer