Final answer:
To determine the value of a $1,000 bond with a 10% coupon rate and 3 years to maturity at a 12% interest rate, discount the future coupon payments and the face value to the present at the market rate. The calculated present value of the bond is approximately $951.96.
Step-by-step explanation:
The question refers to the valuation of a bond using the present value concept. A bond's price is the present value of its future cash flows, which include interest payments (coupons) and the repayment of the principal (face value) at maturity. Given a $1,000 bond with a 10% coupon rate, annual payments, and 3 years to maturity, the appropriate method to value the bond at a 12% market interest rate is to discount each cash flow at the given market rate.
The annual coupon payment will be $1,000 * 10% = $100 per year. Each of these payments, as well as the repayment of the principal amount at the end of year 3, must be discounted back to the present at the 12% interest rate. Thus, the present value of the bond can be calculated using the formula for the present value of an annuity for the coupon payments, plus the present value of a lump sum for the principal amount.
The present value of a bond formula is:
PV = C * [(1 - (1 + r)^(-n)) / r] + FV / (1 + r)^n
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- C is the annual coupon payment ($100)
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- r is the market interest rate (12% or 0.12)
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- n is the number of years to maturity (3)
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- FV is the face value of the bond ($1,000)
Calculating each part:
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- The present value of the coupon payments is $100 * [(1 - (1 + 0.12)^(-3)) / 0.12]
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- The present value of the face value is $1,000 / (1 + 0.12)^3
After calculating, the present value of the bond is approximately $951.96.