Case

AAA Health, Inc. $($NYSE: A$3$H$)$ is evaluating a new product, a vitamin C$/$fish oil blended energy

drink. As an assistant director of the capital budgeting division of AAA Health, you are

responsible for the evaluation of the proposed project. You collected the following information

about the project and the cost of capital. You should make an accept$/$reject recommendation to

the director of your division based on your evaluation.

Information about the Proposed Project

$$ Initial investment and depreciation: The new drink would be produced in an unused building

$($owned by AAA Health$),$ which is fully depreciated. The new equipment required for the

project would cost $$500,000,$ plus an additional $$50,000$ for shipping and installation. With

the new project, inventories would rise by $$60,000,$ and accounts payable would increase by

$$10,000.$ All of these costs would be incurred at t $=0.$ The machinery will be depreciated

under the Modified Accelerated Cost Recovery System $($MACRS$)$ as $3-$year property. The

depreciation rates are $33\%$ at t $=1,45\%$ at t $=2,15\%$ at t $=3,$ and $7\%$ at t $=4.$

$$ Project life and salvage value: AAA Health expects to run the project for four years. The

cash inflows are assumed to begin one year after the project is undertaken, or at t $=1,$ and to

continue to t $=4.$ At the end of the project$$s life $($t $=4),$ the equipment is expected to have a

salvage value of $$50,000.$ Also, the firm will recover the net working capital at the end of the

project life.

$$ Sales and operating costs: Unit sales are expected to total $50,000$ bottles per year, and the

expected sale price is $$10$ per bottle. Cash operating expenses for the project $($total operating

costs excluding depreciation$)$ are expected to amount to $40$ percent of sales revenue.

$$ Tax rate: AAA$$s marginal tax rate is $30$ percent.

Information for the Cost of Capital Estimation

$$ AAA Health has outstanding bonds with a $6\%$ annual coupon rate, $10$ years remaining until

maturity, and a face value of $$1,000.$ The bonds make semiannual coupon payments and

currently are trading in the market at a price of $$864\mathrm{.}10.$

$$ A$3$H can issue preferred stock with an offering price of $$25\mathrm{.}00$ per share, an annual per$-$share

dividend of $$2\mathrm{.}40.$ Flotation costs are equal to $4\mathrm{.}0\%$ of the gross proceeds.

$$ Ten$-$year Treasury bond yield $=5\mathrm{.}52\%$; the market risk premium $=5\%$; the beta of A$3$H $=$

$1\mathrm{.}6.$

$$ Target weight of capital: $40$ percent debt, $10$ percent preferred stock, and $50$ percent common

equity.

$$ A$3$H can undertake a new project without issuing new shares of common stock if the

required initial investment does not exceed $$600,000.$ If the initial investment is greater than

$$600,000,$ the firm should sell new common stock.

FIN $565($Financial Management$)$: Project, $1$

Instructions: Please read carefully and work accordingly.

$1.$ Use the appropriate methods covered in the Lectures of Modules $7,8,$ and $9$ of this class. Do

not use different approaches found in other sources, including the Internet.

$2.$ Show all work including setting up necessary equations with the proper inputs identified. If

you show only the final results, you will get a score of zero without exception.

$3.$ The project should be done with Microsoft Word or Excel. Do not use Apple Pages. I will

not consider any jpeg files $($or jpg files$)$ of pictures of handwritten papers and PDF files as

acceptable submissions. When you type formulas and$/$or equations in MS Word, please use

the equation editing function $($Insert $>$ Equation$).$ You can use an Excel spreadsheet to show

your work. As long as I can click on the cells and see your inputs, you will be fine.

$4.$ Use four decimal places for your calculations. Show your answers by rounding the

calculation results to the nearest whole number if answers are in dollars. For example, if your

calculation results in $$100\mathrm{.}1265,$ show your answer as $$100.$ If you need to show your

answers as a percent, take four decimal places from your calculation, converting them into a

percent. For example, if your calculation results in $0\mathrm{.}4567,$ show $45\mathrm{.}67\%,$ not $46\%.$ To set

your Texas Instrument BA II PLUS calculator at $4$ decimal places, press $[2$ND$]$ FORMAT $4$

$[$ENTER$].$

$5.$ Do NOT show financial calculator keys. If you show financial calculator keys with your

results instead of showing equations with the proper inputs plugged in$,$ you will receive a

score of zero.

Part III. Capital Budgeting Techniques $(2\mathrm{.}5$ points each: $2$ points for part a; $0\mathrm{.}5$ points for

part b$)$

Assume there is no constraints for the capital budget.

$16.$ Traditional payback period

a$.$ Calculate the traditional $($regular$)$ payback period for the project.

b$.$ If the firm is using only the regular payback method to make its capital budgeting

decision and the target cutoff period is $2$ years, should this firm undertake this project?

Why?

$17.$ Discounted payback period

a$.$ Calculate the discounted payback period for the project.

b$.$ If the firm is using only the discounted payb