a company intends to raise finance through the issue of 15% $200 corporate bond redeemable in 15 years. what is the fair value of the bond to an investor with an expected rate of return of 18%?
To determine the fair value of a bond, we need to calculate the present value of the bond's future cash flows by discounting them back at the investor's expected rate of return. Here's how you can calculate the fair value of the bond:
1. Determine the future cash flows: In this case, the bond has a face value of $200 and pays an annual coupon rate of 15% on that face value for 15 years.
- Annual coupon payment = 15% of $200 = $30
- Number of periods (years) = 15
2. Calculate the discounted cash flows: Apply the investor's expected rate of return of 18% (0.18) as the discount rate.
- Discount Rate (expected rate of return) = 18% or 0.18
To calculate the present value of the annual coupon payments, you can use the formula for the present value of a growing annuity:
Present Value of Growing Annuity = Payment / (Discount Rate - Growth Rate)
Since the coupon rate is fixed, the growth rate is zero.
Present Value of Coupon Payments = $30 / (0.18 - 0) = $30 / 0.18 = $166.67
Present Value of Face Value = $200 / (1 + 0.18)^15 = $23.59
3. Sum up the present values: Add the present value of the coupon payments to the present value of the face value to get the fair value of the bond.
Fair Value of the Bond = Present Value of Coupon Payments + Present Value of Face Value
= $166.67 + $23.59
= $190.26
Therefore, the fair value of the bond to an investor with an expected rate of return of 18% is approximately $190.26.