Chapter 13, Problem 3P

To determine

To calculate: the minimum EUAC for the machine and its economic life

Answer to Problem 3P

Minimum EUAC is 7016.99 or 7017 and the economic life is 6 years

Explanation of Solution

First cost of machine = $\$24,000$

Market value declines = $20\%$

Firm’s MARR = $12\%$

Market value = $24,000-20\%=19,200$

There is increase of $\$900$ each year

Assume the machine is kept for n years.

  $\begin{array}{c}\text{EUAC }\left(n=1\right)=(24000+0\left(P/A,12\%,1\right)-19,200\left(P/F,12\%1\right)\left(A/P,12\%,1\right)\\ =\$7,680\end{array}$

  $\begin{array}{c}\text{EUAC }\left(n=2\right)=(24000+900\left(P/A,12\%,2\right)-15,360\left(P/F,12\%2\right)\left(A/P,12\%,2\right)\\ =\$7,380\end{array}$

  $\begin{array}{c}\text{EUAC }\left(n=3\right)=(24000+1,800\left(P/A,12\%,3\right)-12,288\left(P/F,12\%3\right)\left(A/P,12\%,3\right)\\ =\$7,182.99\end{array}$

  $\begin{array}{c}\text{EUAC }\left(n=4\right)=(24000+2,700\left(P/A,12\%,4\right)-9830.4\left(P/F,12\%4\right)\left(A/P,12\%,4\right)\\ =\$7,067.74\end{array}$

  $\begin{array}{c}\text{EUAC }\left(n=5\right)=(24000+3,600\left(P/A,12\%,5\right)-7,864.32\left(P/F,12\%5\right)\left(A/P,12\%,5\right)\\ =\$7,017.05\end{array}$

  $\begin{array}{c}\text{EUAC }\left(n=6\right)=(24000+4,500\left(P/A,12\%,6\right)-6,291.46\left(P/F,12\%6\right)\left(A/P,12\%,6\right)\\ =\$7,016.99\end{array}$

  $\begin{array}{c}\text{EUAC }\left(n=7\right)=(24000+5,400\left(P/A,12\%,7\right)-5,033.17\left(P/F,12\%7\right)\left(A/P,12\%,7\right)\\ =\$7,056.27\end{array}$

  $\begin{array}{c}\text{EUAC }\left(n=8\right)=(24000+6,300\left(P/A,12\%,8\right)-4,026.53\left(P/F,12\%8\right)\left(A/P,12\%,8\right)\\ =\$7,125.73\end{array}$

Minimum EUAC is 7016.99 or 7017 and the economic life is 6 years.

Economics Concept Introduction

Introduction: Equivalent Universal Annual Cost is considered the cost, which is used on assets’ operating, owing and maintaining the asset over the life of an asset. EAC is used by the company for budgeting decision of capital, as it helps in comparing the lifespan of all the assets available in the company.