GMAT Focus EditionQuantitative ReasoningMedium
A financial analyst is evaluating a bond that pays an annual coupon of $50. The bond has a face value of $1000 and matures in 5 years. If the current market interest rate for similar bonds is 6%, what is the approximate present value of the bond's future cash flows?
- A$979.08
- B$1000.00
- C$957.88
- D$1023.56
Show answer & explanationAnswer & explanation
Correct answer: C. $957.88
To find the present value (PV) of the bond, we need to discount both the annual coupon payments and the face value at maturity back to the present using the market interest rate. The sum of these PVs gives the bond's present value.
Why the other options are wrong
- A. This value would be obtained if the interest rate was slightly lower or if the face value was discounted incorrectly.
- B. This would be the value if the market interest rate was equal to the coupon rate (par value), which is not the case here.
- D. This value would be obtained if the interest rate was significantly lower, leading to a higher present value.
Present Value of a Bond
The present value of a bond is the sum of the present values of its future coupon payments and its face value at maturity, discounted at the market interest rate.
- Bonds are valued by discounting future cash flows.
- Cash flows include periodic coupon payments and the face value at maturity.
- The discount rate used is the market interest rate (yield to maturity) for similar bonds.
Memory trick: Bonds' worth is found by bringing future money back home.