Final answer:
The value of bonds changes with market interest rates; to find the value when rates change, use the present value formulas for annuities and lump sums. For ABC Health's bond with a 10% coupon, the annual interest amount is $500.
Step-by-step explanation:
To calculate the bond value, we use the present value formula for both the remaining coupon payments and the par value:
Present Value of Annuity (PVA) = C * [(1 - (1 + r)^-n) / r]
Present Value of the Par Value (PV) = F / (1 + r)^n
Where:
C is the annual coupon payment
F is the face or par value of the bond
r is the new required interest rate
n is the number of years to maturity
For a bond with a 10% coupon rate, the annual coupon payment (C) is $500 (10% of $5,000). If the new required interest rate after 3 years is 5.5% (r = 0.055) and there are 2 years to maturity (n = 2), the value of the bond is calculated as follows:
a) If the interest rate falls to 5.5%:
PVA = $500 * [(1 - (1 + 0.055)^-2) / 0.055]
PV = $5,000 / (1 + 0.055)^2
The sum of PVA and PV will give us the bond's value.
b) If the interest rate rises to 15%:
We use the same formula with r = 0.15:
PVA = $500 * [(1 - (1 + 0.15)^-2) / 0.15]
PV = $5,000 / (1 + 0.15)^2
Again, adding PVA and PV will provide the bond's value.
c) The annual amount of interest:
The bond's annual interest is $500, simply 10% of the $5,000 par value.