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 $$45,000.$ Carlos will make $a25\%$ down payment and finance the rest $of$ the van with $an$ amortized loan over $5$ years $ata6\mathrm{.}5\%$ interest rate. Carlos predicts that $by$ catering approximately $8$ weddings a year $at$ about $$5,000$ per wedding, $he$ will increase his operating receipts $by$ $$40,000$ per year. However, his operating expenses such $as$ food, fuel, labor and insurance will increase $by$ approximately $$25,000$ per year. Carlos assumed a straight$-$line depreciation over $8$ years and the life $of$ the investment $is5$ 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 $is23\%.$

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

$a\mathrm{.}6\mathrm{.}5\%b\mathrm{.}6\mathrm{.}93\%$

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$b$

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

$a.$ $$45,000b.$ $$,37,500$

$c.$ $$38,000d.$$$33,750$

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$a$

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

$a.$$$7,000*b.$$$,5,625$

$c.$$$6,500d.$$$6,250$

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$b$

$(iv)$ What are the yearly after$-$tax net returns?

$a.$$$12,000b.$$$15,000$

$c.$$$9,240d.$$$11,550$

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$d$

$(v)$ What $is$ the after$-$tax terminal value?

$a.$$$26,981\mathrm{.}25b.$$$30,000$

$c.$$$27,412\mathrm{.}50d.$$$27,500\mathrm{.}50$

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$a$

$(vi)$ What $is$ the $NPV?$

$a.$$$27,061\mathrm{.}07b.$$$13,470\mathrm{.}83$

$c.$$$13,789\mathrm{.}98d.$$$26,928\mathrm{.}56$

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$a$

$(vii)$ 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.

$a.$ $$33,558b.$ $$34,263$

$c.$ $$27,506d.$ $$35,695$