Answer:
The bond's current market price is $794.80.
Step-by-step explanation:
This can be calculated using the following steps:
Step 1: Calculation of present value (PV) of coupon payments
This can be calculated using 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 = Annual coupon amount = $1,000 × 10% = $100
r = Yield to maturity rate = 13%, or 0.13
n = number of years to maturity = 18
Substitute the values into equation (1) to have:
PVC = $100 * [{1 - [1 ÷ (1 + 0.13)]^18} ÷ 0.13]
PVC = $100 * 6.83990529002993
PVC = 683.990529002993
Step 2: Calculation of the present value of the face value (PVFAV) of the bond
To calculate the PV of this single amount, we use the following simple PV formula:
PVFAV = FAV ÷ (1 + r)^n ……………………………………. (2)
Where;
PVFAC = Present value of the face value of the bond = ?
FAV = Face value of the bond = $1,000
r = Yield to maturity rate = 13%, or 0.13, i.e. as already given in Step 1.
n = number of years to maturity = 18, i.e. as already given in Step 1.
Substitute the values into equation (2) to have:
PVFAV = $1,000 / (1 + 0.13)^18
PVFAV = $1,000 / 9.02426796516826
PVFAV = 110.812312296109
Step 3: Calculation of the market price of a $1,000 face value bond
The current market price of a bond is is the addition of the present value of the annual coupon payments and present value of the face value of the bond. Mathematically, this can be given as follows:
Market price of the bond = PVC + PVFAC …………………………… (3)
Substituting the values in steps 1 and 2 into equation (3), we have:
Bond's current market price = 683.990529002993 + 110.812312296109 = $794.80
Therefore, the bond's current market price is $794.80.