Zero coupon Bonds: Calculate price, interest, after tax return, yield to maturity

#1 You purchased a zero-coupon bond that has a face value of $1,000, five years to maturity and a yield to maturity of 7.3%. It is one year later and similar bonds are offering a yield to maturity of 8.1%. You will sell the bond now. You have a tax rate of 40% on regular income and 15% on capital gains. Calculate the following for this bond.

* the purchase price of the bond
* the current price of the bond
* the imputed interest income
* the capital gain (or loss) on the bond
* the before-tax rate of return on this investment
* the after-tax rate of return on this investment

#2 You have purchased a bond for $973.02. The bond has a coupon rate of 6.4%, pays interest annually, has a face value of $1,000, 4 years to maturity, and a yield to maturity of 7.2%. The bond's duration is 3.6481 years. You expect that interest rates will fall by .3% later today.

* Use the modified duration to find the approximate percentage change in the bond's price. Find the new price of the bond from this calculation.
* Use your calculator to do the regular present value calculations to find the bond's new price at its new yield to maturity.
* What is the amount of the difference between the two answers?
Why are your answers different? Explain the reason in words and illustrate it graphically.