# Project Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Cash Flow Cash Flow Cash Flow Cash Flow Cash...

## Question:

{eq}\begin{array}{|c|c|c|c|c|c|c|} \hline & \text{Year 0} & {Year 1} & {Year 2} & {Year 3} & {Year 4} & {Year 5} \\ \hline \text{Cash Flow A} & -11,000 & 6,000 & 6,000 & 6,000 & 6,000 & 6,000 \\ \hline \text{Cash Flow B} & -11,000 & 7,000 & 7,000 & 7,000 & 7,000 & 7,000 \\ \hline \text{Cash Flow C} & -12,000 & 12,000 & 2,000 & 20 \\ \hline \end{array} {/eq}

A) The cash flows for three projects are shown above. The cost of capital is 11%. The net present value (NPV) of project A is?

B) If an investor decided to take projects with a payback period of 2 years or less, which of these would he take?

1) investment A

2) investment B

3) investment C

4) None of these investments

## Calculating Net Present Value:

The Net Present Value (NPV) calculation is an extension of the concept of the Time Value of Money (TVM). The TVM states that a dollar today has more value than a dollar at some point in the future. The concept of NPV extends this and looks at one or more project's forecasted cash inflows and cash outflows over a period of time to determine which project is the one that should be invested in. Each cash inflow and cash outflow is discounted using the standard present value calculation at the given cost of capital. These discounted cash flows are then summed and used to determine which project has the higher NPV. The highest positive NPV is the project that should be invested in. A positive NPV means the project is going to add value to the company, while a negative NPV means it's going to decrease the company's overall value.

The following is the present value equation:

{eq}PV = FV / (1+r)^n {/eq}

where PV = Present Value; FV = Future Value; r = Cost of Capital; n = Time.

Net Present Value Equation:

{eq}NPV = -C_{0} + C_{1} / (1+r) + C_{2} / (1+r)^2 + C_{3} / (1+r)^3 + ... + C_{r} /(1+r)^r \\ where \ -C_{0} \ is \ the \ initial \ cash \ investment \ ; \ C_{1} ... \ C_{n} \ are \ the \ cash \ inflows \ each \ period \ ; \ and \ r \ is \ the \ cost \ of \ capital. {/eq}

The payback period is the amount of time it takes for a project to make back all of the money the company has invested in the project. The key point about the payback period is that it does NOT take into account the Time Value of Money. This limits its usefulness from a financial perspective, but the payback period is easy for a non-finance person to understand and thus, it's used quite a bit in the real world.

Here's the payback period equation:

{eq}Payback = C_{0} + \sum CI \\ until \ the \ Payback \ = 0 \\ where \ C_{0} \ is \ the \ initial \ investment \ (cash \ outflow) \ in \ Time \ 0 \ and \ CI \ is \ the \ sum \ of \ the \ cash \ inflows \ per \ period. {/eq}

We set up a table and calculate the net cash flows until the net cash flow is positive. Once we know this, we can calculate the payback period.

To solve Part A, we first need to calculate the present value of each of the cash flows for Project A. We're given the cost of capital for this...

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