Answer:
$327.08
Explanation:
The following steps are followed:
Step 1: Calculation of the present value of the coupon (PVC) of cash flows
To achieve this, the formula for calculating the PV of an ordinary annuity is employed as below:
PVC = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] …………………………………. (1)
Where;
PVC = Present value of the coupon (PVC) cash flow = ?
P = Semiannual coupon amount = $100 × (4.4% ÷ 2) = $2.2
0
r = Yield to maturity rate = 1.2% +5.3% annual = 6.5% annual = 6.5% ÷ 2 semiannually = 3.25% or 0.0325 semiannually
n = number of period = 20 years = 20 × 2 semiannual = 40 semiannual
Substituting the values into equation (1), we have:
PVC = 2.20 × [{1 - [1 ÷ (1+0.0325)]^40} ÷ 0.0325] = $48.86
Step 2: Calculation of the present value of the face value (PVFAV) of the bond
The following PV formula is used to calculated this:
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 described in step 1 above
Substituting the values into equation (2), we have:
PVFAV = $1,000 ÷ (1 + 0.0325)^40 = $278.23
Step 3: Calculation of the price of the firm's outstanding 20-year bonds
The price of a bond can be obtained by adding the PV of expected cash flows and PV of the face value of the bond as follows:
Price of bond = PVC + PVFAC …………………………… (3)
Since PVC = $48.86 and PVFAV = $278.23, we have:
Price of bond = $48.86 + $278.23 = $327.08
Therefore, the price of the firm's outstanding 20-year bonds with face value of $1000 is $327.08
.
