Q30E_3 - Horngren'S Financial And Managerial Accounting

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%.

Step-by-Step Solution

Answer

The present value of the bonds is $77,557

Step 1: Definition of interest rate

A interest rate is the rate at which company pays the sum of money to the bondholder for using the money provided by them.

Step 2: Calculation of the present value of bonds

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

$\begin{array}{rcl}Presents Value& =& Future Value\times PV factor of i=8\%,n=20\\ & =& \$86,000\times 0.21455\\ & =& \$18,452\end{array}$

Present value of interest:

$\begin{array}{rcl}Presents Value& =& Amount of cashflow\times Annuity PV factor\\ & =& \$6,020\times 9.8181\\ & =& \$59,105\end{array}$

Present Value of bonds 

$\begin{array}{rcl}Presents Value& =& Present Value of principal+Present Valur of interest\\ & =& \$18,452+\$59,105\\ & =& \$77,557\end{array}$