Madsen Motors's bonds have 18 years remaining to maturity. Interest is paid annually, they have a $1,000 par value, the coupon interest rate is 10%, and the yield to maturity is 13%. What is the bond's current market price

The bond's current market price is $794.80.

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.

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