Question

Determining the present value of bonds payable

Interest rates determine the present value of future amounts. (Round to the nearest

dollar.)

Requirements

1. Determine the present value of 10-year bonds payable with face value of $86,000

and stated interest rate of 14%, paid semiannually. The market rate of interest is

14% at issuance.

2. Same bonds payable as in Requirement 1, but the market interest rate is 16%.

3. Same bonds payable as in Requirement 1, but the market interest rate is 12%.

Short answer

The present value of the bonds is $95,864

Step-by-step solution

Definition Face value

Face value is the stated amount of the bond. Face value also known as the par value as this value is the value mentioned on the bond.

Calculation of the present value of bonds

In this, we take n= 20 and i=7%

$\begin{array}{rcl}PresentValue& =& FutureValue\times PVfactorofi=6\%,n=20\\ & =& \$86,000\times 0.31180\\ & =& \$26,815\end{array}$

Present value of interest:

$\begin{array}{rcl}PresentValue& =& Amountofcashflow\times AnnuityPVfactor\\ & =& \$6,020\times 11.4699\\ & =& \$69,049\end{array}$

Present Value of bonds

$\begin{array}{rcl}PresentValue& =& PresentValueofprincipal+PresentValueofinterest\\ & =& \$26,815+\$69,049\\ & =& \$95,864\end{array}$