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 $86,000.

Step-by-step solution

Definition of bonds

A bond is a long-term liability that a company issues with borrowing a large amount of money.

Calculation of the present value of bonds

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

$\begin{array}{rcl}PresentValue& =& FutureValue\times PVfactorofi=7\%,n=20\\ & =& \$86,000\times 0.2584\\ & =& \$22,222.4\end{array}$

Present value of interest:

role="math" localid="1656254623899" $\begin{array}{rcl}PresentValue& =& Amountofcashflow\times AnnuityPVfactor\\ & =& \$6,020\times 10.59401\\ & =& \$63,776\end{array}$

Present Value of bonds

$\begin{array}{rcl}PresentValue& =& PresentValueofprincipal+PresentValueofinterest\\ & =& \$22,223+63,776\\ & =& \$86,000\end{array}$