Answer:
$906.18
Explanation:
Step 1: Calculation of the present value of the coupon (PVC) cash flow
The formula for calculating the PV of an ordinary annuity is used as follows:
PVC = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] …………………………………. (1)
Where;
PVC = Present value of the coupon (PVC) payment =?
P = Quarterly coupon amount = $1,000 × (10%/4) = $25
r = interest rate = 12% annual = 12% ÷ 4 quarterly = 3% or 0.03 quarterly
n = number of period = 5 years = 7 × 4 quarters = 28 quarters
Substitute the values into equation (1) to have:
PVC = 25 × [{1 - [1 ÷ (1+0.03)]^28} ÷ 0.03] = $469.10
Step 2: Calculation of the present value of the face value (PVFAV) of the bond
The simple PV formula is used as follows:
PVFAV = FAV ÷ (1 + r)^n ……………………………………. (2)
Where;
PVFAC = Present value of the face value of the bond = ?
FAC = Face value of the bond = $1,000
r and n are as already given in step 1 above
Substituting these values into equation (2), we have:
PVFAV = FAV ÷ (1 + 0.03)^28 = $437.08
Step 3: Calculation of the market price of the bond
Market price of the bond = PVC + PVFAC …………………………… (3)
From step 1, PVC is $469.10, and PVFAC is $437.08 from Step 2. We can them substitute for them in equation (3) and have:
Market price of the bond = $469.10 + $437.08 = $906.18
Conclusion
Therefore, she should pay $906.18 for the bond.
