$2.$ The partnership of Michele and Mark is considering the following long$-$term capital investment proposal. Relevant data on the project is listed below. Salvage value is expected to be zero for the project. Depreciation is computed by the straight$-$line method. The company$$s rate of return is the company$$s cost of capital, which $12\%.$

Brown

Capital Investment $$200,000\mathrm{.}00$

Annual Net Income:

Year $1$ $$25,000\mathrm{.}00$

Year $2$ $$16,000\mathrm{.}00$

Year $3$ $$13,000\mathrm{.}00$

Year $4$ $$10,000\mathrm{.}00$

Year $5$ $$8,000\mathrm{.}00$

Total $$72,000\mathrm{.}00$

Required:

a$.$ Compute the cash payback period for the project. $($round to two decimal places$)$

Cost of Capital $12\%$

Initial Investment $$200,000$

Useful Life $5$ Years

Depreciation per Year $$40,000($$$200,000/5)$

Year Net Income Depreciation Net Cash Flow Discount Factor Present Value of Cash Flows

$1$ $$25,000$ $$40,000$ $$65,0000\mathrm{.}89286$ $$58,035\mathrm{.}90$

$2$ $$16,000$ $$40,000$ $$56,0000\mathrm{.}79719$ $$44,642\mathrm{.}64$

$3$ $$13,000$ $$40,000$ $$53,0000\mathrm{.}71178$ $$37,724\mathrm{.}34$

$4$ $$10,000$ $$40,000$ $$50,0000\mathrm{.}63552$ $$31,776\mathrm{.}00$

$5$ $ $8,000$ $$40,000$ $$48,0000\mathrm{.}56743$ $$27,236\mathrm{.}64$

$$199,415\mathrm{.}52$

Year Net Cash Flow Cumulative

$1$ $$65,000$ $$65,000$

$2$ $$56,000$ $$121,000$

$3$ $$53,000$ $$174,000$

$4$ $$50,000$ $$224,000$

$5$ $$48,000$ $$272,000$

Initial Investment $$200,000$

Cumulative Balance Year $3$ $$174,000$

Total $ $26,000$

Total from Previous Calculation $ $26,000$

Net Cash Flow Year $4$ $ $50,000$

Divide to get fraction $0\mathrm{.}52$

Answer for Cash Back Period is $3\mathrm{.}52$ years.

b$.$ Compute the net present value for the project $($round to the nearest dollar$)$

Total from Chart in a $$199,415\mathrm{.}52$

Initial Investment $$200,000\mathrm{.}00$

Net Present Value $($$ $584\mathrm{.}48)$

c$.$ Compute the annual rate of return for the project.

d$.$ Compute the profitability index for the project.