Step $1$

Let's break down the calculation step by step.

Given information:

Explanation:

Initial investment $=$ $$130\mathrm{.}0$M

Salvage value $=$ $$17\mathrm{.}424$M

Change in working capital $=-$$$46\mathrm{.}62$M

Annual after$-$tax operating cash flows $($ATOCF$)$: $$30\mathrm{.}0$M for the first three years and $$15\mathrm{.}0$M afterwards

We want to find the minimum initial real unit price for DEVICE such that the project will be acceptable. The NPV equation is:

NPV $=130+30/(1+0\mathrm{.}0581)^1+30/(1+0\mathrm{.}0581)^2+30/(1+0\mathrm{.}0581)^3+15/(1+0\mathrm{.}0581)^4+17\mathrm{.}424/(1+0\mathrm{.}0581)^546\mathrm{.}62/(1+0\mathrm{.}0581)^5$

Explanation:

Where:

$0\mathrm{.}0581$ is the real discount rate calculated as $6\%/(1+3\mathrm{.}2\%)$

The first five terms on the right side of the equation represent the present value of the after$-$tax operating cash flows for each year

The next term represents the present value of the salvage value

The last term represents the present value of the change in working capital

Step $2$

Setting NPV to zero and solving for the unit price, we get:

$130=28\mathrm{.}37+26\mathrm{.}74+25\mathrm{.}15+11\mathrm{.}72+10\mathrm{.}867\mathrm{.}59+$ Sales Volume $\backslash$times Unit Price $\backslash$times $0\mathrm{.}295$

$130=95\mathrm{.}25+$Sales Volume $\backslash$times Unit Price$\backslash$times $0\mathrm{.}295$

$34\mathrm{.}75=$ Sales Volume $\backslash$times Unit Price$\backslash$times $0\mathrm{.}295$

Unit Price$=34\mathrm{.}75/$ Sales Volume$\backslash$times $0\mathrm{.}295$

Substitute the sales volume value of $5\mathrm{.}0$M units for the first year:

Unit Price$=34\mathrm{.}75/5\mathrm{.}0$M$\backslash$times $0\mathrm{.}295$

Unit Price$=34\mathrm{.}75/1\mathrm{.}475$M

Unit Price $$ $$0\mathrm{.}0235$ per unit

Explanation:

Therefore, the minimum initial real unit price for DEVICE such that the project will be acceptable is approximately $$0\mathrm{.}0235$ per unit.

Answer

To find the minimum initial real unit price for DEVICE, we used the Net Present Value $($NPV$)$ method.

The NPV equation considers the initial investment, salvage value, change in working capital, and the present value of after$-$tax operating cash flows.

We set NPV to zero and solved for the unit price, which resulted in approximately $$0\mathrm{.}0235$ per unit.

This means that the project will be acceptable if the initial real unit price for DEVICE is at least $$0\mathrm{.}0235.$