Question

River Wild is considering purchasing a water park in Oakland, California​, for $1,950,000.The new facility will generate annual net cash inflows of $495,000 for eight years. Engineers estimate that the facility will remain useful for eight years and have no residual value. The company uses​ straight-line depreciation. Its owners want payback in less than five years and an ARR of 10​% or more. Management uses a 14% hurdle rate on investments of this nature.

Requirements

1.Compute the payback​ period, the​ ARR, the​ NPV, and the approximate IRR of this investment.​ (If you use the tables to compute the​ IRR, answer with the closest interest rate shown in the​ tables.)

2.Recommend whether the company should invest in this projec

urchasing a water park in Oakland, California, for $1,950,000. The new facility will generate annual net cash inflows of $495,000 for eight years. Engineers estimate that the facility will remain useful for eight years and e company uses straight-line depreciation. Its owners want paybad ew the present value annuity table.) 5 (Click the icon to view Reference ew the future value annuity table.) (Click the icon to view Present Value of $1 Periods the payback period, the ARR, the NPV, and the approximate IRR Round the payback period to years. 6 7 8 2% 0.980 0.961 0.942 0.924 0.906 0.888 0.871 0.853 0.837 0.820 0.804 0.788 0.773 0.758 0.743 9 1% 0.990 0.980 0.971 0.961 0.951 0.942 0.933 0.923 .914 0.905 0.896 0.887 0.879 0.870 0.861 0.820 0.780 0.742 0.672 0 3% 0.971 0.943 0.915 0.888 0.863 0.837 0.813 0.789 0.766 0.744 0.722 0.701 0.681 0.661 0.642 0.554 0.478 0.412 0.307 4% 0.962 0.925 0.889 0.855 0.822 0.790 0.760 0.731 0.703 0.676 0.650 0.625 0.601 0.577 0.555 0.456 0.375 0.308 0.208 5% 6% 8% 10% 0.952 0.943 0.926 0.909 0.907 0.890 0.857 0.826 0.864 0.840 0.794 0.751 0.823 | 0.792 0.735 | 0.683 0.784 0.747 0.681 0.621 0.746 0.705 0.630 0.564 0.711 0.665 0.583 0.513 | 0.677 0.627 0.540 0.467 0.6450.592 0.500 0.424 0.614 0.558 0.463 0.386 0.585 0.527 0.429 0.350 0.557 0.497 0.397 0.319 0.530 0.469 0.368 0.290 0.505 0.442 0.340 0.263 0.481 0.417 0.315 0.239 0.377 0.3120.215 0.149 0.295 0.233 0.146 | 0.092 0.231 0.174 0.099 0.057 0.1420.097 0.046 0.022 12% 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404 0.361 0.322 0.287 0.257 0.229 | 0.205 | 0.183 0.104 0.059 0.033 0.011 14% 16% 18% 20% 0.877 0.862 0.847 0.833 0.769 0.743 0.7430.718 0.7180.694 0.675 0.641 0.609 | 0.579 0.592 0.552 0.516 0.482 0.519 0.476 0.437 0.402 | 0.456 | 0.410 0.370 0.335 0.400 0.354 0.314 0.279 0.351 0.305 0.266 0.233 0.308 0.263 0.225 0.194 | 0.270 0.227 0.191 0.162 0.237 0.195 0.162 | 0.135 0.208 0.168 0.137 0.112 0.182 0.145 0.116 0.093 0.160 0.125 0.099 0.078 0.140 0.108 0.084 0.065 0.073 0.051 0.037 0.026 0.038 0.024 0.0160.010 0.020 0.0120.007 0.004 0.005 0.003 0.001 0.001 0.673 0.610 0.552 0.453 Print Done edit fields and then click Check Answer.
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Answer 1

Solution 1:

Payback period = Initial investment / Annual cash inflows = $1,950,000 / $495,000 = 3.94 years

Annual depreciation = $1,950,000 / 8 = $243,750

Annual net income = Annual cash inflows - Depreciation = $495,000 - $243,750 = $251,250

Average investment = (Cost + Residual value) / 2 = ($1,950,000 + 0)/2 = $975,000

ARR = Annual net income / Average investment = $251,250 / $975,000 = 25.77%

Computation of NPV
Particulars	Period	Amount	PV factor at 14%	Present Value
Cash outflows:
Initial investment	0	$1,950,000.00	1	$1,950,000
Present Value of Cash outflows (A)				$1,950,000
Cash Inflows
Annual cash inflows	1-8	$495,000.00	4.639	$2,296,305
Present Value of Cash Inflows (B)				$2,296,305
Net Present Value (NPV) (B-A)				$346,305

Cumulative PV factor at IRR = Initial investment / Annual cash inflows = $1,950,000 / $495,000 = 3.939

Refer PV factor table, this factor falls at nearest to IRR = 19%

Solution 2:

Company should invest in this project as all criteria are met.