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?

Solutions

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 1 year ago

Next > < Previous

Related Solutions

Consider a coupon bond that has a face value of $1,000, a coupon rate of 4%,...

Consider a coupon bond that has a face value of $1,000, a coupon rate of 4%, and five years to maturity. What is the price of the bond if the yield to maturity on similar bonds is 6%? What should its price be the following year if the yield to maturity on similar bonds falls to 5%? Would this change in yields be a good thing or not if you purchased the bond one year earlier at the price you...

A corporate bond has a face value of $10,000, a coupon rate of interest of 8.25%...

A corporate bond has a face value of $10,000, a coupon rate of interest of 8.25% per annum, payable semi-annually, and six and a half years remaining to maturity. The market interest rate for bonds of similar risk and maturity is currently 9.5% per annum, what is the present value of the bond?

Consider a 4-year, 5% annual coupon bond with a face value of $10,000, which was issued...

Consider a 4-year, 5% annual coupon bond with a face value of $10,000, which was issued three years ago. The bond just paid the coupon. Therefore, this bond has one year to maturity, and the next payment of the face and coupon will be made in exactly one year, after which the bond will cease to exist. If the bond defaults before next year, it will pay total of $8,000 in one year. The effective 1-year risk-free rate is 3.55%....

A. Bond A has the following features: Face value = $1,000, Coupon Rate = 4%, Maturity...

A. Bond A has the following features: Face value = $1,000, Coupon Rate = 4%, Maturity = 6 years, Yearly coupons The market interest rate is 4.05% If interest rates remain at 4.05%, what will the price of bond A be in year 1? B.Bond B has the following features: Face value = $1,000, Coupon Rate = 4%, Maturity = 4 years, Yearly coupons The market interest rate is 5.04% If interest rates remain at 5.04%, what is...

A mortgage bond with face value of $10,000 has a bond interest rate of 8% per...

A mortgage bond with face value of $10,000 has a bond interest rate of 8% per year payable quarterly. What is the amount of the bond interest (I) or interest payment every quarter?

Question 1:: Consider a corporate bond with the face value of $1,000, the coupon rate of...

Question 1:: Consider a corporate bond with the face value of $1,000, the coupon rate of 8% per annum, paying coupons semi-annually and the remaining term to maturity of 6 years. The current required yield-to-maturity of this bond is 6% per annum. Suppose an investor buys one bond and holds it for two years. At the end of year 2, required yield-to-maturity is expected to rise from 6% to 8% per annum. Find the investor's annual rate of return over...

Consider a 3 year bond with a face value is $1,000 and a 10% coupon rate...

Consider a 3 year bond with a face value is $1,000 and a 10% coupon rate a) If the current interest rate is 2%, what should be the price of the bond? b) If you could purchase the bond for $1,100, is the yield you are getting higher or lower than 2%? How can you tell? c) Assume you purchase the bond for $1,100 and hold if for one year. You collect one coupon payment and then sell the bond...

A bond has years to maturity, a coupon rate of 6.7% , and a face value...

A bond has years to maturity, a coupon rate of 6.7% , and a face value of $1000. The yield to maturity is 14%. Assume annual compounding. What is the current price of the bond, the coupon yield, and the capital gain yield? Also, what will be the price of the bond when it has 4 years to maturity (one year from today) and what is the percentage increase/decrease in price during the year? (Note: use negative signs to indicate...

A corporate bond has a face value of $1,000 and a coupon rate of 5%. The...

A corporate bond has a face value of $1,000 and a coupon rate of 5%. The bond matures in 15 years and has a current market price of $950. If the corporation sells more bonds it will incur flotation costs of $25 per bond. If the corporate tax rate is 35%, what is the after-tax cost of debt capital? please show all steps in the calculation.

Bond A has a face value of $5,000, a coupon rate of 2%, and a maturity...

Bond A has a face value of $5,000, a coupon rate of 2%, and a maturity date of five years. Bond B has a face value of $4,000, a coupon rate of 10%, and a maturity date of 10 years. Bond C has a face value of $4,500, a coupon rate of 3%, and a maturity date of four years. If these bonds are being sold for $6,300 each, which should you buy? Assume that the prevailing interest rate is...

Subjects