eEgg is considering the purchase of a new distributed network computer system to help handle its warehouse inventories. The system costs $$40,000$ to purchase and install and $$27,000$ 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 $$48,000$ per year. The firm$$s cost of capital $($discount rate$)$ is $9\%.$

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 $28\%$ 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 $28\%$ 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.