Average Rate of Return, Cash Payback Period, Net Present Value Method for a Service Company

Spanish Peaks Railroad Inc. is considering acquiring equipment at a cost of $$208,000.$ The equipment has an estimated life of $10$ years and no residual value. It is expected to provide yearly net cash flows of $$52,000.$ The company's minimum desired rate of return for net present value analysis is $10\%.$

Present Value of an Annuity of $$1$ at Compound Interest

Year $6\%10\%12\%15\%20\%$

$10\mathrm{.}9430\mathrm{.}9090\mathrm{.}8930\mathrm{.}8700\mathrm{.}833$

$21\mathrm{.}8331\mathrm{.}7361\mathrm{.}6901\mathrm{.}6261\mathrm{.}528$

$32\mathrm{.}6732\mathrm{.}4872\mathrm{.}4022\mathrm{.}2832\mathrm{.}106$

$43\mathrm{.}4653\mathrm{.}1703\mathrm{.}0372\mathrm{.}8552\mathrm{.}589$

$54\mathrm{.}2123\mathrm{.}7913\mathrm{.}6053\mathrm{.}3532\mathrm{.}991$

$64\mathrm{.}9174\mathrm{.}3554\mathrm{.}1113\mathrm{.}7853\mathrm{.}326$

$75\mathrm{.}5824\mathrm{.}8684\mathrm{.}5644\mathrm{.}1603\mathrm{.}605$

$86\mathrm{.}2105\mathrm{.}3354\mathrm{.}9684\mathrm{.}4873\mathrm{.}837$

$96\mathrm{.}8025\mathrm{.}7595\mathrm{.}3284\mathrm{.}7724\mathrm{.}031$

$107\mathrm{.}3606\mathrm{.}1455\mathrm{.}6505\mathrm{.}0194\mathrm{.}192$

Compute the following:

a$.$ The average rate of return, giving effect to straight$-$line depreciation on the investment. If required, round your answer to one decimal place.

fill in the blank $1$

$\%$

b$.$ The cash payback period.

years

c$.$ The net present value. Use the above table of the present value of an annuity of $$1.$ Round to the nearest dollar. If required, use a minus sign to indicate negative net present value for current grading purpose.

Present value of annual net cash flows $fill in the blank $3$

Amount to be invested $fill in the blank $4$

Net present value $fill in the blank $5$