Question

Water City is considering purchasing a water park in Omaha, Nebraska, for \(1,920,000. The new facility will generate annual net cash inflows of \)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.

Short answer

1. Different figures of capital budgeting methods:

Payback period: 4.07 years

ARR: 24.58%

NPV: 425,840

IRR: 18.08%

Profitability index: 1.22

1. The business entity must invest in the project.

Step-by-step solution

Definition of Internal Rate of Return

The metric used in capital budgeting to determine the project’s profitability is the internal rate of return. IRR is calculated using the same formula as used for NPV. Under calculation of IRR net present value is considered as 0.

Calculation of payback, ARR, NPV, IRR and Profitability Index

a) Payback period:

$\begin{array}{c}\mathrm{Payback}\mathrm{period}=\frac{\mathrm{Initial}\mathrm{investment}}{\mathrm{Net}\mathrm{cash}\mathrm{inflows}}\\ =\frac{\mathrm{\$}1,920,000}{\mathrm{\$}472,000}\\ =4.07\mathrm{years}\end{array}$

b) ARR:

$\begin{array}{c}\mathrm{ARR}=\frac{\mathrm{Average}\mathrm{annual}\mathrm{revenue}}{\mathrm{Initial}\mathrm{investment}}\times 100\\ =\frac{\mathrm{\$}472,000}{\mathrm{\$}1,920,000}\times 100\\ =24.58\mathrm{\%}\end{array}$

c) NPV:

Time	Particular	Net cash inflow	Ordinary annuity PV factor	PV factor	Present value
1-8years	PV of annuity	$472,000	4.97	-	$2,345,840
8 years	Residual value	$0	-		$0
Total PV of net cash flow					$2,345,840
0	Initial investment				($1,920,000)
Net present value of the project					$425,840

d) IRR:

$\begin{array}{c}\mathrm{NPV}=\sum _{\mathrm{t}=0}^{}\frac{{\mathrm{C}}_{\mathrm{t}}}{{\left(1+\mathrm{IRR}\right)}^{\mathrm{t}}}\\ 0=\left(\begin{array}{l}\frac{-1,920,000}{{\left(1+\mathrm{IRR}\right)}^0}+\frac{\mathrm{\$}472,000}{{\left(1+\mathrm{IRR}\right)}^1}+\frac{\mathrm{\$}472,000}{{\left(1+\mathrm{IRR}\right)}^2}+\\ \frac{\mathrm{\$}472,000}{{\left(1+\mathrm{IRR}\right)}^3}+\frac{\mathrm{\$}472,000}{{\left(1+\mathrm{IRR}\right)}^4}+\frac{\mathrm{\$}472,000}{{\left(1+\mathrm{IRR}\right)}^5}+\\ \frac{\mathrm{\$}472,000}{{\left(1+\mathrm{IRR}\right)}^7}+\frac{\mathrm{\$}472,000}{{\left(1+\mathrm{IRR}\right)}^6}+\frac{\mathrm{\$}472,000}{{\left(1+\mathrm{IRR}\right)}^7}+\frac{\mathrm{\$}472,000}{{\left(1+\mathrm{IRR}\right)}^8}\end{array}\right)\\ \mathrm{IRR}=18.08\mathrm{\%}\end{array}$

e) Profitability index:

$\begin{array}{c}\mathrm{Profitability}\mathrm{index}=\frac{\mathrm{Present}\mathrm{value}\mathrm{of}\mathrm{net}\mathrm{cashflows}}{\mathrm{Initial}\mathrm{investment}}\\ =\frac{\mathrm{\$}2,345,840}{\mathrm{\$}1,920,000}\\ =1.22\end{array}$

Investment decision

The business entity must invest in the project because the project is performing well according to the answers given by each capital budgeting method.

1. Payback period is 4.06 years only.
2. Accounting rate of return is 24.58%.
3. NPV is positive.
4. IRR is more than the minimum required rate of return.
5. Profitability index is more than 1.