Question

Issued 1000 bonds at contract rate of 8% for 10 years. The yield rate is 10 %.The bonds mature annually on January. What is the total issuance price.

Answer 1

Assumed Face Value of the bonds = $1,000

Annual Coupon Interest = Par Value $1,000 * Contract Rate 8% = $80

Period to maturity = 10

Yield Rate (R) = 10%

Issue Price of the bonds = Coupon Interest x PVIFA (10%, 10) + Par Value x PVIF (10%, 10)

= (80*6.14457) + (1000*0.61446)

= 491.57 + 385.44

= 877

Issue price of the bonds = $877

Note -- Calculation of Present Value Factor (Rounded to 5 decimal places)

PVIFA (R, n) = Present Value interest factor for ordinary annuity at R% for n periods = (1 – 1/(1+R)ⁿ) / R

PVIFA (10%,10) = (1 – 1/(1+0.10)¹⁰) / 0.10 = 6.14457

PVIF (R, n) = Present Value interest factor for ‘n’ period at ‘R’% = 1/(1+R)ⁿ

PVIF (10%, 10) = 1/(1+0.10)¹⁰ = 0.38554