Kevin Rogers is Interested in Buying a Five-Year Bond Answer Revealed
by Niranjani
Updated Oct 20, 2023
Kevin Rogers is interested in buying a five-year bond that pays a coupon of 10 percent on a semiannual basis. The current market rate for similar bonds is 8.8 percent. What should be the current price of this bond?
The correct answer is $1,047.71.
The present value of a bond can be calculated as the sum of two components: the present value of its coupon payments and the present value of its maturity value, both discounted at the current market rate. Let's break down the calculation for a bond with a face value of $1,000.
- Coupon Payment:
- The bond pays a coupon of 10% annually, which is $1,000 x 10% = $100 per year.
- Since payments are made semi-annually, each payment is $100 / 2 = $50.
- The bond has a total of 5 years, which is equivalent to 10 semi-annual periods.
- The market rate is 8.8% annually, or 4.4% semi-annually.
Using the present value formula for an ordinary annuity:
PV of Coupon Payment = $50 * [1 - 1 / (1 + 0.044)^10] / 0.044 PV of Coupon Payment ≈ $397.5884
- Maturity Value:
- The bond's face value is $1,000, and it matures in 10 years.
- The market rate remains at 4.4% semi-annually.
Using the present value formula for a single lump sum:
PV of Maturity = $1,000 / (1 + 0.044)^10 PV of Maturity ≈ $650.1222
Now, to find the total present value of the bond, we add the present values of the coupon payment and the maturity value:
Total PV = PV of Coupon Payment + PV of Maturity Total PV ≈ $397.5884 + $650.1222 ≈ $1,047.7106
So, the present value of the bond is approximately $1,047.71.
Kevin Rogers is interested in buying a five-year bond -FAQ
The answer is $1,047.71.