Question

On December 31, 2018, when the market interest rate is 12%, Benson Realty issues $600,000 of 9.25%, 10-year bonds payable. The bonds pay interest semiannually. Determine the present value of the bonds at issuance. (Round all currency amounts to the nearest whole dollar.) (Click the icon to view Present Value of $1 table.) (Click the icon to view Present Value of Ordinary Annuity of $1 table.) (Click the icon to view Future Value of $1 table.) (Click the icon to view Future Value of Ordinary Annuity of $1 table.) The present value of the bonds at issuance amounts to $

Answer 1

The Present Value of the Bond at Issuance

The issue (sale) price of the bond is the Present Value of the Coupon Payments plus the Present Value of the face Value

Par Value of the bond = $600,000

Semi-annual coupon amount = $27,750 [$600,000 x 9.25% x ½]

Semi-annual Yield to Maturity of the Bond = 6.00% [12.00% x ½]

Maturity Period = 20 Years [10 Years x 2]

Therefore, the Issue Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $27,750[PVIFA 6.00%, 20 Years] + $600,000[PVIF 6.00%, 20 Years]

= [$27,750 x 11.470] + [$600,000 x 0.312]

= $318,293 + $187,200

= $505,493

“Hence the Present Value of the Bond at Issuance will be $505,493”

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.