Question

Haswell Enterprises' bonds have a 12-year maturity, an 8.2% coupon rate, and a par value of $1,000. The going interest rate (rd) is 8.1%. Assuming semiannual compounding, what is the bond's price?

Answer 1

The price of Haswell Enterprises' bonds, with a 12-year maturity, 8.2% coupon rate, and $1,000 par value, in a semiannual compounding scenario at a going interest rate
`(\(r_d\))` of 8.1%, is approximately $1,053.69.

Step-by-step explanation:

To calculate the bond's price, we can use the present value formula for a bond, taking into account its coupon payments and the par value. The formula is given by:

`\[ P = (C * (1 - (1 + r_d)^(-nt)))/(r_d) + (F)/((1 + r_d)^(nt)) \]`

Where:

- P is the bond price,

- C is the semiannual coupon payment,

-
`\( r_d \)` is the semiannual discount rate,

- n is the total number of compounding periods (twice the number of years to maturity),

- t is the number of years to maturity,

- F is the par value.

For Haswell Enterprises' bonds:

-
`\( C = (8.2\% * \$1,000)/(2) \)` (semiannual coupon payment),

-
`\( r_d = (8.1\%)/(2) \)` (semiannual discount rate),

-
`\( n = 2 * 12 \)` (semiannual compounding for 12 years),

- t = 12 years,

- F = $1,000 (par value).

Substituting these values into the formula, we find that the bond's price is approximately $1,053.69. This reflects the present value of both the future coupon payments and the par value, discounted at the semiannual discount rate.