Question

A federal treasury bill issued bonds with the following characteristics: Face value = $5,000 and coupon rate is 1.5% per quarter and payments are quarterly. This bond is bought in the bond market before maturation and there are only 22 payments remaining. The next payment is due in one month which you collect if you buy this bond now. How much would you be willing to pay for this bond today if the next interest payment is due today? As investor, you wish to earn 7% compounded daily. Assume for simplicity that there are 30 days a month and 90 days in a quarter.

Answer 1

The given face value is $5,000 The coupon rate is 1.5% quarterly. The payment made quarterly is 5,000x1.5%= $75 If the bond is purchased a month before the next due interest payment then, there are total 22 payment periods remaining before the bond matures. This means that there are total of 21 remaining period, if the interest payment is due today The required rate of return of the investor is 7% compounded daily The required rate of return is converted quarterly in order to discount the future cash flows which would in turn help in determining the current price of the bond. The required rate of return effective quarterly is 1+ -1 _ 90 7% 1+ -1 90 = 7.25% Next step is to calculate the price of the bond. Discounted Coupon Payments = Coupon Interest x Present Value Annuity Factor of 7.25% for 21 periods Discounted Coupon Payments=$75x10.62=$796.5 The face value of the bond is the amount which is required to be paid on the maturity and it will be discounted to determine the current price. 21 1 Discounted face value of the bond = $5,000 x| $1,150 _ 1.0725 investor is willing to pay requiring a return of The current price of the bond is the amount that 7% compounded daily. It will be summation of discounted coupon payments for the remaining period and discounted face value of the bond to be paid on maturity is 796.5+1150 $1946.5 an