Question

A newly issued 10-year maturity, 5% coupon bond making annual coupon payments is sold to the public at a price of $740. The bond will not be sold at the end of the year. The bond is treated as an original-issue discount bond.

a. Calculate the constant yield price. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. What will be an investor's taxable income from the bond over the coming year? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

a.

N=10 (10 - year maturity)

PMT= 50 (5% of 1000(which is the face value of the bond)

PV= $740

FV= $1000

Putting all the value in the financial calculator

we get yield to maturity as 9.06%

or using this formula and putting the values and using a bit of hit and trial we can find the value of YTM

PV= PMT/(1+r)+PMT/(1+r)^2+..............(PMT+FV)/(1+r)^10

b. Using the constant yield method, we can compute the price in one year( when maturity falls to 9 years)

Putting I/Y= 9.06%

and N=9

and all other values remaining the same we get PV= $757.18

which is an increase of 757.18 - 740 =$17.18

Now the total taxable income will be 50+17.1= $67.18