Question

Sheridan Information Systems management is planning to issue 10-year bonds. The going market yield for such bonds is 8.450 percent. Assume that coupon payments will be made semiannually. Management is trying to decide between issuing an 8 percent coupon bond or a zero coupon bond. Sheridan needs to raise $1 million. What will be the price of an 8 percent coupon bond? (Round answer to 2 decimal places, e.g 15.25.) Bond value $ How many 8 percent coupon bonds would have to be issued? (Round answer to 0 decimal places, e.g 5,275.) Number of bonds issued What will be the price of a zero coupon bond? (Round answer to 2 decimal places, e.g 15.25.) Price of a zero coupon bond $ How many zero coupon bonds will have to be issued? (Round answer to 0 decimal places, e.g 5,275.) Number of bonds issued

Answer 1

(1)-Price of an 8 percent coupon bond

The Price of the Bond is the Present Value of the Coupon Payments plus the Present Value of the face Value

Face Value of the bond = $1,000

Semi-annual Coupon Amount = $40 [$1,000 x 8% x ½]

Semi-annual Yield to Maturity = 4.225% [8.45% x ½]

Maturity Period = 20 Years [10 Years x 2]

The Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $40[PVIFA 4.225%, 20 Years] + $1,000[PVIF 4.225%, 20 Years]

= [$40 x 13.32353] + [$1,000 x 0.43708]

= $532.94 + $437.08

= $970.02

“Bond Value = $970.02”

(2)-Number of 8 percent coupon bonds to be issued

Number of 8 percent coupon bonds to be issued = Amount raised / Bond Value

= $10,00,000 / $970.02

= 1,031 Bonds

“Number of bonds issued = 1,031 Bonds”

(3)-The price of a zero-coupon bond

Face Value = $100

Semi-annual Yield to Maturity (YTM) = 4.225% [8.45% x ½]

Maturity Period = 20 Years [10 Years x 2]

The Price of Zero-Coupon Bond = Face Value / (1 + YTM)ⁿ

= $1,000 / (1 + 0.04225)²⁰

= $1,000 / 2.28791

= $437.08

“Bond Value = $437.08”

(4)-Number of Zero-Coupon Bonds to be issued

Number of Zero-Coupon Bonds to be issued = Amount Raised / Bond Value

= $10,00,000 / $437.08

= 2,288 Bonds

“Number of bonds issued = 2,288 Bonds”

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)ⁿ} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.  

--The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.