Question

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Tidal Wave is considering purchasing a water park in San Diego comma California​, for $ 1 950 000. The new facility will generate annual net cash inflows of $ 500 000 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.

Requirement 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.) ​(Round the payback period to one decimal​ place.)

The payback period is

years.

​(Round the percentage to the nearest tenth​ percent.)

The ARR (accounting rate of return) is

%.

​(Round your answer to the nearest whole​ dollar.)

Net present value $

The IRR​ (internal rate of​ return) is between

▼

16% and 18%

20% and 22%

22% and 24%

18% and 20%

.

Requirement 2. Recommend whether the company should invest in this project.

​Recommendation:

▼

Do not invest in the new facility.

Invest in the new facility.

Answer 1

Payback Period = Initial Investment / Annual Net cash inflow

                                = $19,50,000 / $5,00,000

                                = 3.9 i.e. 3 year & 11 months approx.

ARR = Net Operating income / Initial Investment

        = $2,56,250 / $19,50,000

        = 13.14%

(W.N. = Net Operating Income = Annual net cash inflow – Depreciation

                                                          = $5,00,000 - $2,43,750

                                                          = $2,56,250

          Depreciation = Cost of Asset – Salvage value / Useful Life

                                     = $19,50,000 – 0 / 8

                                     = $2,43,750 )

NPV = Present Value of cash inflow – Present Value of cash Outflow

         = $23,19,432 - $19,50,000

         = $3,69,432

W.N.:

Present Value of cash inflow = Annual Net Income * Annuity Factor for “n” years

                                                        = $5,00,000 * (1/r)*(1-1/(1+r)^n) - where r = required rate, n = year

                                                        = $5,00,000 * [ (1/14%)*(1-1/{(1+14%)^8)} ]

                                                        = $23,19,432

IRR

Since the NPV is positive at 14% rate, Return from project is more than 14%

Let Find NPV at 18%

NPV = Present Value of cash inflow – Present Value of cash Outflow

         = $20,38,783 - $19,50,000

         = $88,783

Still NPV is positive rate of return from project is more than 18%

Let Find NPV at 20%

NPV = Present Value of cash inflow – Present Value of cash Outflow

         = $19,18,579 - $19,50,000

         = ($31,421)

Here NPV is negative therefore return is less than 20%

So IRR is between 18-20%

it can be find by following formula

Final Answer :

Payback period = 3.9 i.e. 3 year & 11 months approx.

ARR = 13.14%

NPV = $3,69,432

IRR = 19.48%

Since Payback period is less than 5 years, ARR is more than 10% & NPV at 14% rate is positive, Company should do invest in new facility.

(IRR can be find using excel also)

Note:

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