$15.$ A new project is expected to have an $8-$year economic life. The project will have an initial cost of

$$100,000.$ Installation and shipping charges for the equipment are estimated at $$10,000.$ The

equipment will be depreciated as a $7-$year asset under MACRS rules. A working capital investment of

$$15,000$ is required to undertake the project. The revenues from the project in year $1$ are expected to

be $$60,000.$ These are expected to increase at a compound annual rate of $6$ percent. Operating costs

exclusive of depreciation are $$15,000.$ These costs are expected to increase at an $8$ percent compound

annual rate. The firm$$s marginal tax rate is $40$ percent. The expected salvage value of the equipment at

the end of year $8$ is $$20,000.$

a$.$ Compute the project$$s net investment.

b$.$ Compute the annual net cash flows for the project.

c$.$ If the firm$$s cost of capital is $19$ percent, should the project be undertaken?

d$.$ The managers of the firm have also decided to evaluate this project using the certainty equivalent

approach. They have established the following certainty equivalent factors for the cash flows forecasted

in each year:

Year $\backslash$alpha

$01\mathrm{.}00$

$10\mathrm{.}95$

$20\mathrm{.}90$

$30\mathrm{.}80$

$40\mathrm{.}60$

$50\mathrm{.}50$

$60\mathrm{.}45$

$70\mathrm{.}40$

$80\mathrm{.}35$

The risk$-$free rate is $8$ percent. Compute the certainty equivalent NPV for this project