The bonds of company A, carry a 10% annual coupon, have a 100,000 face value, and mature in 4years. Bonds of equivalent risk yield 7%. What is the market price of Company A.
To calculate the market price of the bonds of Company A, you need to determine the present value of the bond's future cash flows. In this case, the cash flows are the 10% annual coupon payments and the face value at maturity.
To calculate the present value of the coupon payments, you can use the formula for the present value of an ordinary annuity:
PV = C * [1 - (1 + r)^(-n)] / r
Where:
PV = Present value of the annuity
C = Cash flow per period (coupon payment)
r = Discount rate (yield rate)
n = Number of periods (number of years)
In this case, the cash flow per period (coupon payment) is $10,000 (10% of $100,000), the discount rate (yield rate) is 7%, and the number of periods (number of years) is 4. Plugging these values into the formula, we get:
PV_coupon = $10,000 * [1 - (1 + 0.07)^(-4)] / 0.07
≈ $34,067.75
To calculate the present value of the face value at maturity, you can use the formula for the present value of a single payment:
PV = F / (1 + r)^n
Where:
PV = Present value of the single payment
F = Future value of the payment (face value)
r = Discount rate (yield rate)
n = Number of periods (number of years)
In this case, the future value of the payment (face value) is $100,000, the discount rate (yield rate) is 7%, and the number of periods (number of years) is 4. Plugging these values into the formula, we get:
PV_faceValue = $100,000 / (1 + 0.07)^4
≈ $74,974.18
Finally, to calculate the market price of Company A, you need to sum the present values of the coupon payments and the face value at maturity:
Market price = PV_coupon + PV_faceValue
= $34,067.75 + $74,974.18
≈ $109,041.93
Therefore, the market price of Company A is approximately $109,041.93.