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First Union Bank Corporation is evaluating two capital investment proposals for a driveup ATM kiosk, each requiring an investment of \(\$ 300,000\) and each with an eight-year life and expected total net cash flows of \(\$ 480,000\). Location 1 is expected to provide equal annual net cash flows of \(\$ 60,000\), and Location 2 is expected to have the following unequal annual net cash flows: \(\begin{array}{lrrr}\text { Year 1 } & \$ 90,000 & \text { Year 5 } & \$ 45,000 \\ \text { Year 2 } & 80,000 & \text { Year 6 } & 45,000 \\ \text { Year 3 } & 65,000 & \text { Year 7 } & 45,000 \\ \text { Year 4 } & 65,000 & \text { Year 8 } & 45,000\end{array}\) Determine the cash payback period for both proposals.

Step by step solution

01

Understanding the Payback Period

The payback period is the time it takes for an investment to generate an amount of money equal to the cost of the investment. For both locations, we need to calculate how long it will take to recover the initial investment of \(\$ 300,000\).

02

Calculate Payback Period for Location 1

For Location 1, the annual net cash flow is equal to \(\\( 60,000\). Since the cash flows are consistent each year, the payback period can be calculated by dividing the initial investment by the annual cash flow:\[\text{Payback Period} = \frac{\\) 300,000}{\$ 60,000} = 5 \text{ years}\]

03

Calculate Cumulative Cash Flows for Location 2

For Location 2, the cash flows are not uniform. Calculate the cumulative cash flow each year until the initial investment \(\\( 300,000\) is recovered. The sequence is as follows:- Year 1: \(\\) 90,000\)- Year 2: \(\\( 90,000 + \\) 80,000 = \\( 170,000\)- Year 3: \(\\) 170,000 + \\( 65,000 = \\) 235,000\)- Year 4: \(\\( 235,000 + \\) 65,000 = \$ 300,000\)

04

Determine Payback Period for Location 2

For Location 2, the cumulative cash flow reaches \(\$ 300,000\) by the end of Year 4. Therefore, the payback period for Location 2 is 4 years.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Cash Payback Period

The cash payback period is a simple way to evaluate how long it takes for an investment to generate enough cash to recover the initial outlay. It doesn't take into account the time value of money, but it's useful for getting a quick estimate of the time required to recoup the investment.
For example, if First Union Bank Corporation invests \\(300,000 in a project, the cash payback period tells us how many years it will take to get back that \\)300,000 from the project's cash flows.

• Location 1, with steady annual cash flows, will recover the initial investment in 5 years.
• Location 2, with varying annual cash flows, will take 4 years to reach payback.

This makes Location 2 more attractive for quicker payback, even if it's not necessarily a superior investment without further analysis.

Capital Investment Proposals

Capital investment proposals involve large financial commitments expected to bring returns over time. Businesses use proposed projects, like First Union Bank's ATM kiosk locations, to choose the best capital allocation.
When evaluating these proposals, factors like potential return, risk, and cash payback period come into play.

• A shorter cash payback period, as seen with Location 2, often makes the project less risky as funds are returned sooner.
• However, it should be combined with other measures like net present value (NPV) for a comprehensive assessment.

An effective proposal will identify whether an investment aligns with a company's strategic goals, cash flow needs, and financial health.

Cumulative Cash Flow

Cumulative cash flow keeps track of the total cash flow over time from an investment. It's useful to see when an investment has fully paid back its initial cost. Cumulative cash flow is crucial for projects like Location 2, where yearly cash flows vary.
Let's track how cumulative cash flow worked for Location 2:

• Year 1 generated \\(90,000, the base cumulative flow for that year.
• Year 2 added \\)80,000 to make the cumulative flow \\(170,000.
• Year 3 saw a further increase of \\)65,000, totaling \\(235,000.
• Finally, in Year 4, it reached \\)300,000, completing the recovery.

Understanding cumulative cash flow aids in assessing where a project stands at any given time in relation to payback.

Net Cash Flows

Net cash flows represent the financial inflow from a project after accounting for outflows. For First Union Bank's ATM locations, each year's net cash flow indicates profitability after initial investment-related costs are considered.
This calculation highlights how each project year contributes to the total \\((480,000\ total expected net cash flow for both locations. While some years generate higher cash flows than others, it's the sum of these individual yearly net cash flows that matters most.

• Location 1 shows consistent annual net cash inflows of \\)60,000.
• Location 2 has variable amounts, with early high flows and smaller amounts later on.

Evaluating net cash flows helps determine if a capital investment proposal is likely to meet projected financial goals and assurances.