Chapter 11, Problem 1ST

To determine

Calculate the change in NPV.

Explanation of Solution

Present worth (PW) of an investment can be calculated by using the following formula:

$\text{PW}=10,450\left(2\text{X}-\text{Y}\right)-7,890$        (1)

Substitute the respective values in Equation (1) to obtain the present worth of the investment.

$\begin{array}{c}\text{PW}=10,450\left(2\times 20-10\right)-7,890\\ =10,450\left(30\right)-7,890\\ =313,500-7,890\\ =305,610\end{array}$

Hence, the present worth of the investment is $305,610.

Substitute the respective values in Equation (1) to obtain the present worth of investment at new price.

$\begin{array}{c}\text{PW}=10,450\left(2\times 22-10\right)-7,890\\ =10,450\left(34\right)-7,890\\ =355,300-7,890\\ =347,410\end{array}$

Hence, the present worth of the investment at new price is $$347,410$.

Change in present worth as 10 percent increase in sales price is calculated as follows:

$\begin{array}{c}\text{Change}=\frac{P{W}_{new}}{P{W}_{old}}-1\\ =\frac{347,410}{305,610}-1\\ =0.1368\end{array}$

The present worth increased by13.68%.  Thus, option ‘c’ is correct.