Wine and Roses, Inc., offers a bond with a coupon of 9.0 percent with semiannual payments and a yield to maturity of 9.78 percent. The bonds mature in 7 years. What is the market price of a $1,000 face value bond?

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.

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