Carlos owns and operates a restaurant. To help expand his business, Carlos is considering the feasibility of offering a wedding catering service. To open this service, Carlos needs a van to deliver his food to the various weddings. After doing some research and price$-$checking, he has found a suitable new van online costing $$55,000.$ Carlos will make a $25\%$ down payment and finance the rest of the van with an amortized loan over $5$ years at a $6\mathrm{.}5\%$ interest rate. Carlos predicts that by catering approximately $8$ weddings a year at about $$3,500$ per wedding, he will increase his operating receipts by $$28,000$ per year. However, his operating expenses such as food, fuel, labor and insurance will increase by approximately $$18,000$ per year. Carlos assumed a straight$-$line depreciation over $8$ years and the life of the investment is $5$ years. The terminal value of the van is $$30,000$ after the $5$ years, and Carlos requires a pretax $9\%$ rate of return to capital. The marginal tax rate over the next $7$ years is $23\%.$

$($i$)$ What is the appropriate discount rate to calculate the NPV in this problem?

a$\mathrm{.}6\mathrm{.}5\%$

b$.6\mathrm{.}93\%$

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$($ii$)$ What is the initial cost for the service?

a$.$ $$55,000$

b$.$ $$,37,500$

c$.$ $$38,000$

d$.$ $$41,250$

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$($iii$)$ What is the yearly allowable depreciation using the straight$-$line method?

What are the yearly after tax net returns?

What is the after tax terminal value?

What is the NPV$?$

What is the maximum operating expense for food, fuel, labor and insurance that can be spent on this investment and still be a good investment.