Q14SE - Horngren'S Financial And Managerial Accounting

Question

Determining the present value of bond at issuance

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 semi annually.

Determine the present value of the bonds at issuance.

Step-by-Step Solution

Answer

 The present value of the bond as issuance is $505,493

Step 1: Definition of cash flow

The cash flow the inflow and outflow of the cash and other items which are equivalent to the cash during a period.

Step 2: Present value of the bonds at issuance

Present value of principal:

 

$\begin{array}{c}\text{Present \hspace{0.17em}Value=\hspace{0.17em}Future\hspace{0.17em} Value×\hspace{0.17em}PV \hspace{0.17em}factor\hspace{0.17em} of \hspace{0.17em}i=6\%,\hspace{0.17em}n=20}\\ \text{ =\$600,000×\hspace{0.17em}}0.312\\ \text{ =\$187,200\hspace{0.17em}}\end{array}$

Present value of interest:

$\begin{array}{c}\text{Present\hspace{0.17em}Value=\hspace{0.17em}Amount\hspace{0.17em}of\hspace{0.17em}each\hspace{0.17em}cash\hspace{0.17em}flow\hspace{0.17em}\hspace{0.17em}×\hspace{0.17em}Annuity\hspace{0.17em}\hspace{0.17em}PV\hspace{0.17em}factor\hspace{0.17em}of\hspace{0.17em}i=6\%,\hspace{0.17em}n=20}\\ \text{ =\$27,750×\hspace{0.17em}}11.470\\ \text{ =\$318,293\hspace{0.17em}}\end{array}$

Present value at issuance:

$\begin{array}{c}\text{Present\hspace{0.17em}Value=\hspace{0.17em}Present\hspace{0.17em}\hspace{0.17em}Value\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}Principal+\hspace{0.17em}Present\hspace{0.17em}\hspace{0.17em}Value\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}Interest}\\ \text{ =\hspace{0.17em}\$187,200+\hspace{0.17em}\$318,293}\\ \text{ =\hspace{0.17em}\$505,493}\end{array}$