Assume Venture Healthcare sold bonds that have a ten-year maturity, a 12 percent coupon rate with
annual payments, and a $1,000 par value.
a. Suppose that two years after the bonds were issued, the required interest rate fell to 7 percent.
What would be the bond's value?
b. Suppose that two years after the bonds were issued, the required interest rate rose to 13 percent.
What would be the bond's value?
c. What would be the value of the bonds three years after issue in each scenario above, assuming that
interest rates stayed steady at either 7 percent or 13 percent?
To calculate the bond's value, we need to use the present value formula, which discounts the future cash flows (coupon payments and the principal payment) to their present value.
The formula to calculate the present value of a bond is as follows:
Bond Value = C * (1 - (1 / (1 + r)^n)) / r + (M / (1 + r)^n)
Where:
- C is the coupon payment received each year (Coupon Rate * Par Value)
- r is the required interest rate
- n is the number of years remaining until maturity
- M is the par value of the bond
Now let's calculate the values for each scenario:
a. Bond value when the interest rate falls to 7 percent after two years:
In this case, the remaining maturity is 8 years (10 - 2).
- C = 0.12 * $1,000 = $120
- r = 0.07 (7%)
- n = 8
- M = $1,000
Plug these values into the formula:
Bond Value = $120 * (1 - (1 / (1 + 0.07)^8)) / 0.07 + ($1,000 / (1 + 0.07)^8)
Bond Value ≈ $1,348.70
b. Bond value when the interest rate rises to 13 percent after two years:
In this case, the remaining maturity is 8 years (10 - 2).
- C = 0.12 * $1,000 = $120
- r = 0.13 (13%)
- n = 8
- M = $1,000
Plug these values into the formula:
Bond Value = $120 * (1 - (1 / (1 + 0.13)^8)) / 0.13 + ($1,000 / (1 + 0.13)^8)
Bond Value ≈ $839.34
c. Bond value three years after issuance with steady interest rates:
For both scenarios, the remaining maturity is 7 years (10 - 3).
For an interest rate of 7%:
- C = 0.12 * $1,000 = $120
- r = 0.07 (7%)
- n = 7
- M = $1,000
Bond Value = $120 * (1 - (1 / (1 + 0.07)^7)) / 0.07 + ($1,000 / (1 + 0.07)^7)
Bond Value ≈ $1,225.06
For an interest rate of 13%:
- C = 0.12 * $1,000 = $120
- r = 0.13 (13%)
- n = 7
- M = $1,000
Bond Value = $120 * (1 - (1 / (1 + 0.13)^7)) / 0.13 + ($1,000 / (1 + 0.13)^7)
Bond Value ≈ $828.93
Keep in mind that these calculations assume annual coupon payments and interest rates.