Answer:
The market price of the $1,000 face value bond is $961.12.
Explanation:
This can be calculated as follows:
Step 1: Calculation of the present value of the coupon (PVC) cash payments flow
To calculate this, we use the formula for calculating the PV of an ordinary annuity as follows:
PVC = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] …………………………………. (1)
Where;
PVC = Present value of the coupon (PVC) payment = ?
P = Semiannual coupon amount = $1,000 × (9.0%/2) = $45
r = Yield to maturity rate = 9.78% annual = 9.78% ÷ 2 semiannually = 4.87% or 0.0487 semiannually
n = number of period = 7 years = 7 × 2 semiannul = 14 semiannual
Substitute the values into equation (1) to have:
PVC = 45 × [{1 - [1 ÷ (1+0.0487)]^14} ÷ 0.0487] = $448.59
Step 2: Calculation of the present value of the face value (PVFAV) of the bond
Since this is just a single amount, not a flow, we use the simple PV formula 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 given in step 1 above
Substitute the values into equation (2) to have:
PVFAV = FAV ÷ (1 + 0.0487)^14 = $512.53
Step 3: Calculation of the market price of a $1,000 face value bond
The market price of a bond is the addition of the PV of expected cash flows and PV of the face value of the bond. For this question, the market price of a $1,000 face value bond can be calculated as follows:
Market price of the bond = PVC + PVFAC …………………………… (3)
Substituting the values already obtained in steps 1 and 2 above into equation (3), we have:
Market price of the bond = $448.59 + $512.53 = $961.12
Therefore, the market price of the $1,000 face value bond is $961.12.
