Question

Mason Co. issued $460,000 of five-year, 12% bonds with interest payable semiannually, at a market (effective) interest rate of 10%. Determine the present value of the bonds payable, using the present value tables in Exhibit 4 and Exhibit 5. Round to the nearest dollar.

Answer 1

The following is the calculation of present value of bonds:

Present value of bonds = (interest payment ) *(relevant present value of annuity factor) + (face value )*(present value factor)

here,

semi annual interest payment = $460,000 * 12% *6/12 =>$27,600.

relevant present value of annuity factor = [1 - (1+r)^(-n)]/r

here,

r = effective interest rate = 10% per annum

=> 5% for semi annual period.=>0.05.

n = number of periods = 5 years * 2 semi annual period each year =>10 semi annual periods.

=>[1 - (1+0.05)^(-10)]/0.05.

=>[1-0.61391325]/0.05

=>0.3860868/0.05

=>7.72173...(to 5 decimals).

here,

face value = $460,000

present value factor

=>1/ (1+r)^n

=>1 /(1+0.05)^10

=>0.61391...(to 5 decimals)

now,

present value of bonds payable = ($27,600)*(7.72173) +($460,000)*(0.61391)

=>$213,119.748 + $282,398.6

=>$495,518...(rounded to nearest dollar)