Question

In: Finance

Consider a bond that has a $10,000 face value and a coupon rate of 4%. Show...

Consider a bond that has a $10,000 face value and a coupon rate of 4%.

Show the expression to find the price and find the price in each of the following cases:

1. The bond has one year to maturity and the interest rate is 3%.

2. The bond has one year to maturity and the interest rate is 5%.

3. The bond has two years to maturity and the interest rate is 3%.

4. The bond has two years to maturity and the interest rate is 5%.

5. Compute the percentage change in the price for the one-year bond as the interest rate rises from 3% to 5%.

6. Compute the percentage change in the price for the two-year bond as the interest rate rises from 3% to 5%.

7. Are your results consistent with the fact that a change in the interest rate reduces the price by a larger percentage for long term bonds than for short term bonds?

Expert Solution

Face Value = $10,000

Annual Coupon Rate = 4%
Annual Coupon = 4% * $10,000
Annual Coupon = $400

Answer 1.

Annual Interest Rate = 3%
Time to Maturity = 1 year

Price of Bond = $400 * PVIF(3%, 1) + $10,000 * PVIF(3%, 1)
Price of Bond = $400 / 1.03 + $10,000 / 1.03
Price of Bond = $10,097.09

Answer 2.

Annual Interest Rate = 5%
Time to Maturity = 1 year

Price of Bond = $400 * PVIF(5%, 1) + $10,000 * PVIF(5%, 1)
Price of Bond = $400 / 1.05 + $10,000 / 1.05
Price of Bond = $9,904.76

Answer 3.

Annual Interest Rate = 3%
Time to Maturity = 2 years

Price of Bond = $400 * PVIFA(3%, 2) + $10,000 * PVIF(3%, 2)
Price of Bond = $400 * (1 - (1/1.03)^2) / 1.03 + $10,000 / 1.03^2
Price of Bond = $10,191.35

Answer 4.

Annual Interest Rate = 5%
Time to Maturity = 2 years

Price of Bond = $400 * PVIFA(5%, 2) + $10,000 * PVIF(5%, 2)
Price of Bond = $400 * (1 - (1/1.05)^2) / 1.05 + $10,000 / 1.05^2
Price of Bond = $9,814.06

jeff jeffy answered 2 years ago

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