You are considering a capital budgeting proposal to make 'glow$-$in$-$the$-$dark' pacifiers for

anxious first$-$time parents. You estimate that the equipment to make the pacifiers would cost

you $$50,000($which you can depreciate straight line over the lifetime of the project, which is

$10$ years$)$ and that you can sell $15,000$ units a year at $$2$ a unit. The cost of making each

pacifier would be $$0\mathrm{.}80,$ and the tax rate you would face would be $40\%.$ You also estimate

that you will need to maintain an inventory at $25\%$ of revenues for the period of the project

and that you can salvage $80\%$ of this working capital at the termination of the project.

Finally, you will be setting up the equipment in your garage, which means you will have to

pay $$2000$ a year to have your car garaged at a nearby private facility $($assume that you can

deduct this cost for tax purposes$).$ To estimate the discount rate for this project, you find that

there are comparable firms being traded on the financial markets with the following betas:

Company Debt$-$Equity ratio Tax rate Beta

Nuk$-$Nuk $0\mathrm{.}500\mathrm{.}401\mathrm{.}3$

Gerber $1\mathrm{.}000\mathrm{.}501\mathrm{.}5$

You expect to finance this project entirely with equity, and the current T$.$Bond rate is $11\mathrm{.}5\%.$

$($a$)$ What is the appropriate discount rate to use for this project?

$($b$)$ What is the after$-$tax operating cashflow each year for the lifetime of the project?

$($c$)$ What is the NPV of this project?