$11$ Sandhill Company is considering a capital investment of $$189,000$ in additional productive facilities. The new machinery is expected to have a useful life of $5$ years with no salvage value. Depreciation is by the straight$-$line method. During the life of the investment, annual net income and net annual cash flows are expected to be $$11,529$ and $$54,000,$ respectively. Sandhill has a $12\%$ cost of capital rate, which is the required rate of return on the investment.

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$($a$)$

Compute the cash payback period. $($Round answer to $1$ decimal place, e$.$g$.10\mathrm{.}5.)$

Cash payback period

years

Compute the annual rate of return on the proposed capital expenditure. $($Round answer to $2$ decimal places, e$.$g$.10\mathrm{.}52\%.)$

Annual rate of return

$\%$

$($b$)$

Using the discounted cash flow technique, compute the net present value. $($If the net present value is negative, use either a negative sign preceding the number e$.$g$.-45$ or parentheses e$.$g$.(45).$ Round answer for present value to $0$ decimal places, e$.$g$.125.$ For calculation purposes, use $5$ decimal places as displayed in the factor table provided.$)$

Net present value