# X Company has an opportunity to accept a special order that will result in an immediate profit of...

## Question:

X Company has an opportunity to accept a special order that will result in an immediate profit of $79,000. The marketing manager believes that if X Company accepts the order, the company will lose regular customers. Specifically, she believes the effect will be lost profits of$9,500 in each of the next 4 years. Assuming a discount rate of 5%, what is the net present value of accepting the special order?

## Opportunity Costs

Opportunity costs are potential benefits which differ by choosing one option over another, such as forgone income. An opportunity cost does not necessarily represent an actual outflow of cash but is considered as a differential cost in scenario analysis.

In this example, the following will be considered the cash flows of the company:

Year Cash Flows
0 79,000
1 (9,500)
2 (9,500)
3 (9,500)

To determine the net present value (NPV), which computes the net difference of the present value of all cash inflows and outflows, we will use the following formula:

{eq}NPV = C_0 + \frac{C_1}{(1+r)^{1}} +\frac{C_2}{(1+r)^{2}}+...+\frac{C_n}{(1+r)^{n}} \\ where \\ C_0 = Cash\ flow\ at\ period\ 0 \\ C_1\ to\ C_n = Cash\ flows\ after\ period\ 0 \\ r = Discount\ rate \\ n = No.\ of\ periods {/eq}

Using the cash flows above, we compute for the NPV at a discount rate of 5%:

{eq}\begin{align*} NPV &= 79,000 - \frac{9,500}{(1+5\%)^{1}} - \frac{9,500}{(1+5\%)^{2}}-\frac{9,500}{(1+5\%)^{3}} \\&= 79,000 - 9,048 - 8,617 - 8,206 \\& = 53,129 \end{align*} {/eq}

We determine the NPV for the special order to be \$53,129.