Question

Peter wants to buy a 3-year, AA-rated, $1000 par

value, zero-coupon bond being sold by Stark

Industries. The yield to maturity on the bonds

is estimated to be 8% and bond is semiannual

bond.

A) How much would he have to pay for it?

B) How much will he be taxed on the

investment after 2 year, if his marginal tax rate

is 20%?

Answer 1

Answer to A,

Price of the ond = $790.314525730146, rounded to 2 decimal places is $790.31

Price of Zero Coupon Bond is the present value of Lump sum repayment. = A/(1+i)ⁿ, "A" is the face value or repayment amount = $1,000.

Alternative method is there. annual yield is 8% PA, bond is semi annual. So semi-annual yield will be 8%/2 = 4% is "i". number of semi annual period will be 3 X 2 = 6 which is "n", then the Bond Price = $1,000 / (1.04⁶),

Bond Price = $790.314525730146.

Answer to Question B,

Zero-coupon investors must report a prorated portion of interest each year as income, even though it has not been paid or Received. Zeros are issued at a discount and mature at par value, and the amount of interest will be taxed.

Annual effective yield will be 1.04²)-1 = 0.0816 or 8.16%, Taxable amount of the bond at the end of year 1 will be

Purchase Price X Annual effective yield.

= $790.31 X 8.16% ,

= 64.4892960, rounded to 2 decimal places = $64.49,

At the end of year 2 , the amount on which the annual yeild to be applied will be the purchse price + interest taxed till begining of the current year.

= $790.31 + $64.49 = $854.80.

Current year interest = 854.80 X 8.16% = $69.7516225536, rounded to 2 decimal places $69.75.