eEgg is considering the purchase of a new distributed network computer system to help handle its warehouse inventories. The system costs $$50,000$ to purchase and install and $$36,000$ to operate each year. The system is estimated to be useful for $4$ years. Management expects the new system to reduce the cost of managing inventories by $$62,500$ per year. The firm$$s cost of capital $($discount rate$)$ is $7\%.$

Required:

$1.$ What is the net present value $($NPV$)$ of the proposed investment under each of the following independent situations? $($Use the appropriate present value factors from Appendix C$,$ TABLE $1$ and Appendix C$,$ TABLE $2.)$

$1$a$.$ The firm is not yet profitable and therefore pays no income taxes.

$1$b$.$ The firm is in the $29\%$ income tax bracket and uses straight$-$line $($SLN$)$ depreciation with no salvage value. Assume MACRS rules do not apply.

$1$c$.$ The firm is in the $29\%$ income tax bracket and uses double$-$declining$-$balance $($DDB$)$ depreciation with no salvage value. Given a four$-$year life, the DDB depreciation rate is $50\%($i$.$e$.,2\backslash$times $25\%).$ In year four, record depreciation expense as the net book value $($NBV$)$ of the asset at the start of the year.

$2.$ What is the internal rate of return $($IRR$)$ of the proposed investment for situations in requirement $1,$ parts $($a$)$ through $($c$)?$ Use the IRR builit$-$in function in Excel to compute the IRR.

The firm is not yet profitable and therefore pays no income taxes. $($Round your answer to nearest whole dollar amount.$)$

Net present value

The firm is in the $29\%$ income tax bracket and uses straight$-$line $($SLN$)$ depreciation with no salvage value. Assume MACRS rules do not apply. $($Round your answer to nearest whole dollar amount.$)$

Net present value

The firm is in the $29\%$ income tax bracket and uses double$-$declining$-$balance $($DDB$)$ depreciation with no salvage value. Given a four$-$year life, the DDB depreciation rate is $50\%($i$.$e$.,2\backslash$times $25\%).$ In year four, record depreciation expense as the net book value $($NBV$)$ of the asset at the start of the year. $($Negative amounts should be indicated by a minus sign. Round discount factor to $3$ decimal places and other answers to the nearest whole dollar amount.$)$

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Year Pre$-$Tax Cash Inflows DDB Depreciation Expense Taxable Income Income Taxes After$-$tax Net Cash Inflow Discount Factor Present Values

$0$

$1$

$2$

$3$

$4$

Net present value $($NPV$)=$ $$0$

What is the internal rate of return $($IRR$)$ of the proposed investment for situations in requirement $1,$ parts $($a$)$ through $($c$)?$ Use the IRR builit$-$in function in Excel to compute the IRR. $($Round "Estimated IRR" to $1$ decimal place.$)$

Estimated IRR

a$.\%$

b$.\%$

c$.\%$