JLB Corporation is attempting to determine whether to lease or purchase research equipment. The firm is in the $21\%$ tax bracket, and its after$-$tax cost of debt is currently $8\%.$ The terms of the lease and of the purchase are as follows:

LEASE$$Annual end$-$of$-$year lease payments of $$25,200$ are required over the three$-$year life of the lease. All maintenance costs will be paid by the lessor; insurance and other costs will be borne by the lessee. The lessee will exercise its option to purchase the asset for $$5,000$ at termination of the lease.

PURCHASE$$The equipment costs $$60,000$ and can be financed with a $14\%$ loan requiring annual end$-$of$-$year payments of $$25,844$ for three years. JLB will depreciate the equipment under MACRS using a three$-$year recovery period. $($See Table $4\mathrm{.}2$ for the applicable depreciation percentages.$)$ JLB will pay $$1,800$ per year for a service contract that covers all maintenance costs; insurance and other costs will be borne by the JLB$,$ who plans to keep the equipment and use it beyond its three$-$year recovery period.

Rounded Depreciation Percentages by Recovery Year Using MACRS for First Four Property Classes

Percentage by recovery year $2$

Recovery year $3$ years $5$ years $7$ years $10$ years

$133\%20\%14\%10\%$

$245322518$

$315191814$

$47121212$

$51299$

$6598$

$797$

$846$

$96$

$106$

$114$

Totals $100\%100\%100\%100\%$

a$.$ Calculate the after$-$tax cash outflows associated with each alternative.

b$.$ Calculate the present value of each stream, using the after$-$tax cost of debt.

c$.$ Which alternative$$lease or purchase$$would you recommend? Why?

Please show your work and all formulas$/$equations$.$ Thank you!