Question

Splash World is considering purchasing a water park in​ Atlanta, Georgia, for $ 1,870,000 . The new facility will generate annual net cash inflows of $ 472,000 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, and its stockholders demand an annual return of 12 ​% on investments of this nature.

Requirements

1. Compute the payback, the ARR, the NPV, the IRR, and the profitability index of this investment.
2. Recommend whether the company should invest in this project.

Answer 1

Answer:

1)

Payback period = Initial investment / Annul cash flow

Payback period = 1,880,000 / 480,000

Payback period = 3.92 years

2)

Accounting rate of return = Average cash flow / ( initial investment - book value) / 2

Accounting rate of return = 480,000 / ( 1,880,000 - 0)/2

Accounting rate of return = 0.5106 or 51.06%

3)

NPV = Present value of cash inflows - present value of cash outflows

NPV = 480,000 * 4.968 - 1,880,000

NPV = $504,640

4)

IRR is the rate of return that makes NPV equal to 0

NPV = Annuity * [ 1 - 1 / ( 1 + R)n] / R - initial investment

NPV = 480,000 * [ 1 - 1 / ( 1 + R)8] / R - 1,880,000

Using trial and error method, i.e, after using various values for R, let's try R as 19.32%

NPV = 480,000 * [ 1 - 1 / ( 1 + 0.1932)8] / 0.1932 - 1,880,000

NPV = 0

Therefore, IRR is 19.32%

Splash world should invest in the project as it has a positive NPV and and IRR greater than cost of capital