To determine the price of Haswell Enterprises' bonds, we need to calculate the present value of the bond's cash flows, which include the semiannual coupon payments and the par value at maturity.
### Step-by-Step Solution:
1. Identify the bond parameters:
- Par value ([tex]\(FV\)[/tex]): [tex]$1000
- Coupon rate: \(6.25\%\)
- Maturity period: 10 years
- Going rate (\(rd\)): \(4.75\%\)
- Compounding periods per year: 2 (since it's semiannual)
2. Calculate the number of total periods:
\[
\text{Total periods} = \text{Maturity years} \times \text{Periods per year} = 10 \times 2 = 20
\]
3. Determine the semiannual coupon payment:
\[
\text{Coupon payment} = \text{Par value} \times \left(\frac{\text{Coupon rate}}{\text{Periods per year}}\right) = 1000 \times \left(\frac{6.25\%}{2}\right) = 1000 \times 0.03125 = 31.25
\]
Thus, the semiannual coupon payment is $[/tex]31.25.
4. Calculate the semiannual discount rate:
[tex]\[
\text{Discount rate per period} = \frac{\text{Going rate}}{\text{Periods per year}} = \frac{4.75\%}{2} = 0.02375
\][/tex]
5. Calculate the present value of the coupon payments:
The present value of an annuity formula is used here:
[tex]\[
PV_{\text{coupons}} = \text{Coupon payment} \times \left(1 - (1 + \text{Discount rate})^{-\text{Total periods}}\right) / \text{Discount rate}
\][/tex]
Substituting in the values:
[tex]\[
PV_{\text{coupons}} = 31.25 \times \left(1 - (1 + 0.02375)^{-20}\right) / 0.02375 = 492.96327268023634
\][/tex]
6. Calculate the present value of the par value:
[tex]\[
PV_{\text{par}} = \frac{\text{Par value}}{(1 + \text{Discount rate})^{\text{Total periods}}} = \frac{1000}{(1 + 0.02375)^{20}} = 625.3479127630204
\][/tex]
7. Calculate the total bond price:
[tex]\[
\text{Bond Price} = PV_{\text{coupons}} + PV_{\text{par}} = 492.96327268023634 + 625.3479127630204 = 1118.3111854432568
\][/tex]
Thus, the bond's price is approximately [tex]$1118.31. Therefore, the correct choice is:
\[ \boxed{3) \, $[/tex]1118.31$} \]
