Suppose the current, zero-coupon, yield curve for risks free bonds is as follows. Maturity years 1...

Suppose the current, zero-coupon, yield curve for risks free bonds is as follows.

Maturity years 1 YTM 5.00%, Maturity Years 2 YTM 5.50%, Maturity years 3 YTM 5.75%, Maturity Years 4 YTM 5.95%, Maturity years 5 6.05%. Please be detailed with answers

A. what is the price per $ 100 face value of a 2 year, zero coupon risk free bond? The price is (round to the nearest cent)

B. What is the price per $100.00 face value of a 4-year, zero coupon, risk free bond? The price is (round to the nearest cent)

C. What is the risk free interest rate for a 5-year maturity? The risk free rate is (round to two decimal places)

Solutions

Expert Solution

The concept is simple, we can think of time value of money equation which is: Future value=Present value*(1+interest rate)^Number of years
In case of bonds, the future value is the amount paid at maturity. The future value amount is the face value (assuming the bond is held till maturity).
Interest rate in case of bonds is the yield to maturity.
So, the equation of the time value of money becomes: Face value=(Present value of the bond)*(1+yield to maturity)^Number of years
=>Present value of the bond=(Face value)/(1+yield to maturity)^Number of years

Answer A:
Face value=$100
Number of years=2
Risk free rate of interest or the yield to maturity for 2 years period is 5.5%
So, current price of the bond=$100/(1+5.5%)^2=$100/(1.055)^2=$89.84524157 or $89.85 (Rounded to the nearest cent)

Answer B:
Face value=$100
Number of years=4
Yield to maturity for 4 years period=5.95%
So, current price of the bond=$100/(1+5.95%)^4=$100/(1.0595)^4=$79.35899436 or $79.36 (Rounded to the nearest cent)

Answer C:
Risk free rate of interest for a 5-year maturity=6.05%
On zero coupon bonds, no coupon payments are made. Zero coupon bonds are sold at a discount to the face value. However, on maturity an investor gets a fixed amount equal to the face value of the bond. Suppose a zero coupon bond is issued at $990 and face value is $1000, then the capital gains will be $10. Here, the annual rate of return (or the interest rate) is the risk free rate. For bonds, interest rate refers to yield to maturity. The risk free rate in this case (for 5 year maturity) is the yield to maturity for 5 year period. So, the risk free interest rate for a 5-year maturity is 6.05%

jeff jeffy answered 1 month ago

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