Capital Budgeting

<h3>Net Present Value (NPV) Function</h3>
The NPV function calculates the present value of a series of cash flows at equal time intervals. The function is represented as follows:

= NPV(rate,value1,value2,...)

Here, rate is the discount rate for one period, and values are the cash flows. Any payments are entered with a negative sign, and income is entered as positive.

Note that even though the function is named Net Present Value (NPV), it doesn’t really calculate the net present value. This is because it does not take into consideration the initial investment at time 0.

To calculate the net present value, you will need to subtract the initial investment from the result you get from the NPV function.

Lets take an example to demonstrate this function. Assume that you started a business with an initial investment of $10,000 and received the following income for the next five years.

<img class="aligncenter size-full wp-image-934" title="Net Present Value Cash Flows" src="https://financetrain.com/wp-content/uploads/2010/09/NPV1.gif" alt="" width="277" height="221" />

To calculate the net present value, we will apply the NPV function as follows:

<img class="aligncenter size-full wp-image-935" title="Net Present Value Calculation" src="https://financetrain.com/wp-content/uploads/2010/09/NPV2.gif" alt="" width="300" height="256" />

This is the present value of all the future cash flows.

The net present value will be:

Net Present Value = 11,338.77 – 10,000

= $1,338.77
<h3>Internal Rate of Return (IRR) Function</h3>
IRR is based on NPV. It as a special case of NPV, where the rate of return calculated is the interest rate corresponding to a 0 (zero) net present value.

IRR function is represented as follows:

<TextFormula>= IRR(values,guess)</TextFormula>
<TextFormula>= IRR(values,guess)</TextFormula>
This function accounts for the inflows and the outflows, including the initial investment at time 0.

Using the same example above, the IRR calculation is shown below:

<img class="aligncenter size-full wp-image-936" title="Internal Rate of Return - IRR" src="https://financetrain.com/wp-content/uploads/2010/09/NPV3.gif" alt="" width="316" height="308" />

The IRR of 14.974% means that at this rate the net present value will be zero.
<h3>Other Related Functions</h3>
<strong>MIRR:</strong> MIRR calculates the modified internal rate of return for a series of periodic cash flows, considering both cost of investment and interest on reinvestment of cash.

Syntax: MIRR(values,finance_rate,investment_rate)

<strong>XNPV:</strong> This function calculates the net present value for a series of cash flows that are not equally spaced in time.

Syntax: XNPV(rate,values,dates)

<strong>XIRR: </strong>This function calculates the internal rate of return for a series of cash flows that are not equally spaced in time.

Syntax: XIRR(values,dates,guess)

Download the <a href="https://financetrain.com/wp-content/uploads/NPV_IRR.xls">NPV IRR.xls</a> to view these example calculations.

Calculating Net Present Value (NPV) and Internal Rate of Return (IRR) in Excel

This video explains the concept of net present value (NPV) and shows how it is calculated.

<iframe src="http://www.youtube.com/embed/enpBDVo3kZ0" frameborder="0" width="600" height="437"></iframe>

Net Present Value of a Project

A company, from time to time, will have to make investments in a variety of capital projects. Whether it is the need to purchase new machinery, expanding the production facility, or even buying new transport, all these projects require firms to make high investment now. In all these projects, the cash flow or the benefit is expected to be received for several years.

A company at any time may have many capital projects in foresight. It is the responsibility of the finance manager to evaluate these projects through the capital budgeting process which involves evaluating each project for its profitability, eliminating the ones that are not profitable, and prioritizing the profitable ones based on the company’s available resources and requirements. The finance manager needs to follow a consistent process and exercise caution while making capital budgeting decisions, as they involves huge cost, and can significantly impact the shareholder value.

The capital budgeting process involves four steps:

<strong>Step 1: Capital Project Ideas </strong>

The first step is to get or generate project ideas. These ideas can be put forth by the management, employees, or even outsiders.

<strong>Step 2: Evaluate Each Project proposal for Profitability</strong>

The finance manager needs to accept or reject each capital project proposal based on its profitability. To do so, a cash flow forecast will be created and the project will be evaluated using <a title="Net Present Value of a Project" href="https://financetrain.com/net-present-value-of-a-project/">NPV/IRR</a>.

<strong>Step 3: Prioritize Profitable Projects Based on the Firm-wide Project</strong>

Once the profitable projects have been identified, the finance manager needs to prioritize these projects based on the firm-wide capital budget, requirements and strategy. Sometime a project may be profitable but can wait for some time compared to another project which is critical for the firm’s strategy. For example, while choosing between buying new machinery vs. replacing an existing technology with a new one, the finance manager needs to evaluate the pros and cons of both, timings of future cash flows, etc., before prioritizing them.

<strong>Step 4: Feedback and Evaluation</strong>

Once the capital budgeting decisions have been made, they need to be constantly monitored and evaluated for their performance. The finance department needs to check whether the actual cash flow matches the forecasted cash flow or not, and if not, they need to identify the reasons for the mismatch. They also need to look for any systematic errors committed in the forecasting process and provide feedback so that the forecasting processes can be improved.
<h2>Types of Capital Budgeting Projects</h2>
Capital budgeting projects can fall under the following categories:
<ul>
	<li>Replacement projects for business maintenance</li>
	<li>Replacement projects to reduce cost (replacing outdated technology with new leaner one)</li>
	<li>Expansion projects</li>
	<li>New product development</li>
	<li>Mandatory projects as required by government agencies, such as for safety or environment.</li>
	<li>Other projects (such as R&amp;D)</li>
</ul>

The Capital Budgeting Process

Even though the capital budgeting decisions can be very complex with lots of underlying assumptions and variations, most decisions have the following basic principles underlying them.

<strong>1. Decisions are based on cash flow not accounting income</strong>

The capital budgeting decisions are based on the cash flow forecasts instead of relying on the accounting income. These are the incremental cash flows, that is, the additional cash flow that will occur if the project is undertaken compared to if the project is not undertaken.

While estimating these cash flows certain costs such as the <strong>sunk cost</strong> will be ignored. This is because sunk cost is the cost that is already incurred whether the project is undertaken or not. Similarly any intangible costs and benefits are ignored.

The investment analysis should also account for any <strong>externalities</strong>. An externality refers to the effect of the project/investment on other things than the project itself. A common externality is <strong>cannibalization</strong>, where a new project reduces the cash flow of another project. This is a negative externality. A project can also have a positive externality where a new project has positive effect on the revenue from another project.

<strong>2. Timing of cash flow</strong>

Another important aspect of the analysis is to estimate the timing of cash flow as accurately as possible. As the capital budgeting analysis uses the concept of time value of money, the time at which the cash flow occurs significantly impacts the present value of the project. The earlier the cash flow occurs the more valuable it is.

<strong>3. Opportunity cost should be considered</strong>

The project analysis should include opportunity costs. Opportunity cost is the cash flow that the company loses because of undertaking the new project.

<strong>4. Cash flow should be adjusted for taxes</strong>

After-tax cash flow should be used for capital budgeting analysis.

<strong>5. Financing Costs Should be Ignored</strong>

Financing costs should not be included in the cash flow. Analysts will take the after-tax operating cash flows and will discount them using the required rate of return to arrive at the net present value. The financing costs are already reflected in the required rate of return and the cash flow should not be adjusted for the same, irrespective of whether the project is financed using equity, debt or a combination of both.

A project may have conventional or unconventional cash flow pattern. In case of a conventional cash flow pattern, there is an initial outflow of cash followed by one or more cash inflows. In case of unconventional cash flows, there could be a series of cash inflows and outflows at different times.

Principles of Capital Budgeting

The cash flow analysis for making capital decisions can become more complex because of the interaction between different projects. The finance manager will have to work with these complexities while evaluating and selecting projects

<strong>Independent Vs. Mutually Exclusive Projects</strong>

The projects being analyzed by a company may be completely independent of each other or mutually exclusive. When two projects are independent, it means that there cash flows are independent of each other, and so is their profitability. A company may decide to undertake both the projects if they are both profitable.

When two projects are mutually exclusive, it means that the firm wants to undertake only one of these two projects, not both. For example, while deciding between two delivery trucks that have different costs and output, the firm will have to choose one truck between the two.

<strong>Project Sequencing</strong>

Sometimes projects can only be executed in a sequence. For example, if three projects A, B and C can be executed in a sequence, then project B can be executed only after project A has been executed. Once the project A has been executed, it creates the opportunity for project B to be executed. The firm will also see if project A has been profitable before going ahead with project B.

<strong>Unlimited Funds Vs. Capital Rationing</strong>

The company may have unlimited access to capital in which case it can execute all profitable projects simultaneously. However, in reality firms will have constraints on how much funds they have to invest. If there are more capital projects then the funds available, the firm will have to exercise capital rationing and prioritize the projects and first execute those that have the highest impact on shareholder’s value.

Mutually Exclusive Projects, Project Sequencing, and Capital Rationing

The payback period of a project is defined as the number of years it takes for the project to recover its original investment.

Let’s take a simple example to understand how payback period is calculated. Assume that a company invests $5,000 in a project, which generates the following cash flow in the next 5 years.
<table width="134" border="0" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td><strong>Year</strong></td>
<td><strong>Cash Flow</strong></td>
</tr>
<tr>
<td>
0
</td>
<td>
$-5,000.00
</td>
</tr>
<tr>
<td>
1
</td>
<td>
$2,000.00
</td>
</tr>
<tr>
<td>
2
</td>
<td>
$2,000.00
</td>
</tr>
<tr>
<td>
3
</td>
<td>
$2,000.00
</td>
</tr>
<tr>
<td>
4
</td>
<td>
$1,000.00
</td>
</tr>
<tr>
<td>
5
</td>
<td>
$1,000.00
</td>
</tr>
</tbody>
</table>
The payback period will be equal to the time period when the firm has generated back its $5,000 investment.

In year 1, the firm generates $2000. In year 2, it generates $2,000. By the end of the year 2, the cumulative cash inflow is $4,000. In year 3, it generates $2,000. At the end of year 3, the cumulative cash flow is $6,000, which is more than our initial investment. That means the payback period is somewhere between year 2 and year 3.

By the end of year 2, we have recovered $4,000. The unrecovered amount is $1,000. In year 3, the total cash flow is $2,000.

With this information, the payback period can be calculated as follows.

Payback period = 2 years + $1,000/$2000 = 2.5 years

The payback period is a measure of the firm’s liquidity. Generally, the shorter the payback period is, the better it is for the firm. However, the method has some drawbacks. For example, it does not consider time value of money, or the cash flows after the payback period. Because of these drawbacks, the payback period method cannot be used as a measure of profitability.

This method is generally used along with another method such as NPV or IRR while making capital investment decisions.

How to Calculate Payback Period

We learned that one of the drawbacks of payback period is that it does not consider time value of money. An alternative is to use the discounted payback period.

The discounted payback period is the number of years it takes to recover the initial investment in terms of the present value of the cash flows. The present value of each cash flow is calculated and then added to arrive at the discounted payback period.

Let’s take the same example with the cash flows for 5 years. Assuming that the firm has a cost of capital of 10%, the discounted cash flows are presented in the third column. Column 4 shows the cumulative discounted cash flows.
<table>
<tbody>
<tr>
<td><strong>Year</strong></td>
<td><strong>Cash Flow</strong></td>
<td><strong>Discounted Cash Flows</strong></td>
<td><strong>Cumulative Discounted Cash Flows</strong></td>
</tr>
<tr>
<td>0</td>
<td>-5000.00</td>
<td></td>
<td></td>
</tr>
<tr>
<td>1</td>
<td>2000.00</td>
<td>1818.18</td>
<td>1818.18</td>
</tr>
<tr>
<td>2</td>
<td>2,000.00</td>
<td>1652.89</td>
<td>3471.07</td>
</tr>
<tr>
<td>3</td>
<td>2,000.00</td>
<td>1502.63</td>
<td>4973.70</td>
</tr>
<tr>
<td>4</td>
<td>1,000.00</td>
<td>683.01</td>
<td>5656.72</td>
</tr>
<tr>
<td>5</td>
<td>1,000.00</td>
<td>620.92</td>
<td>6277.64</td>
</tr>
</tbody>
</table>
As you can see, the project generates a total of $4973.70 in 3 years. By the end of four years, the total cash inflow is $5656.72. This means that the discounted payback period is between 3 and 4 years.

The discounted payback period can be calculated as follows:

Discounted Payback Period = 3 + (5000-4973.70)/683.01 = 3.04 years

Note that the discounted payback period is more than the simple payback period. This is because the cash flows have been discounted.

However, this method is still not considered a good measure of profitability because it doesn’t consider the cash flows that occur after the payback period.

How to Calculate Discounted Payback Period

The profitability index, also known as the profit investment ratio, is calculated as the ratio of the present value of the future cash flows and the initial investment in the project.

[latex]Profitability\ Index = \frac{PV\ of\ Future\ Cash\ Flows}{Initial\ Investment}[/latex]

Since <a href="https://financetrain.com/net-present-value-of-a-project/" title="Net Present Value of a Project">NPV</a> is the difference between the present value of future cash flows and initial investment, the profitability index can also be expressed in terms of NPV as follows:

[latex]Profitability\ Index = 1 + \frac{NPV}{Initial\ Investment}[/latex]

The firms use PI to decide whether to accept or reject a project.

PI &gt; 1, Accept the project

PI &lt; 1, Reject the project

Let's taken an example to understand how profitability index is calculated. Assume that a company invests $5,000 in a project, which generates the following cash flow in the next 5 years. The firm has a cost of capital of 10%. Column 3 presents the discounted cash flows.
<table>
<tbody>
<tr>
<td><strong>Year</strong></td>
<td><strong>Cash Flow</strong></td>
<td><strong>Discounted Cash Flows</strong></td>
</tr>
<tr>
<td>
0
</td>
<td>
-5000.00
</td>
<td></td>
</tr>
<tr>
<td>
1
</td>
<td>
2000.00
</td>
<td>
1818.18
</td>
</tr>
<tr>
<td>
2
</td>
<td>
2,000.00
</td>
<td>
1652.89
</td>
</tr>
<tr>
<td>
3
</td>
<td>
2,000.00
</td>
<td>
1502.63
</td>
</tr>
<tr>
<td>
4
</td>
<td>
1,000.00
</td>
<td>
683.01
</td>
</tr>
<tr>
<td>
5
</td>
<td>
1,000.00
</td>
<td>
620.92
</td>
</tr>
</tbody>
</table>
The total PV of future cash flows = 6277.64

Initial Investment = $5000

PI = 6277.64/5000 = 1.25

Since PI &gt; 1, the project can be accepted.

The profitability index is a useful tool for <a href="https://financetrain.com/mutually-exclusive-projects-project-sequencing-and-capital-rationing/" title="Mutually Exclusive Projects, Project Sequencing, and Capital Rationing">capital rationing</a>, as the projects can be ranked based on their PI.

Calculating Profitability Index of a Project

When you are analyzing a single conventional project, both <a title="Calculating Net Present Value (NPV) and Internal Rate of Return (IRR) in Excel" href="https://financetrain.com/net-present-value-npv-internal-rate-of-return-irr-excel/">NPV and IRR</a> will provide you the same indicator about whether to accept the project or not. However, when comparing two projects, the NPV and IRR may provide conflicting results. It may be so that one project has higher NPV while the other has a higher IRR. This difference could occur because of the different cash flow patterns in the two projects.

The following example illustrates this point.
<table>
<tbody>
<tr>
<td></td>
<td><strong>Project A</strong></td>
<td><strong>Project B</strong></td>
</tr>
<tr>
<td>Year 0</td>
<td>-5000</td>
<td>-5000</td>
</tr>
<tr>
<td>Year 1</td>
<td>2000</td>
<td>0</td>
</tr>
<tr>
<td>Year 2</td>
<td>2000</td>
<td>0</td>
</tr>
<tr>
<td>Year 3</td>
<td>2000</td>
<td>0</td>
</tr>
<tr>
<td>Year 4</td>
<td>2000</td>
<td>0</td>
</tr>
<tr>
<td>Year 5</td>
<td>2000</td>
<td>15000</td>
</tr>
<tr>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td><strong>NPV</strong></td>
<td><strong>$2,581.57</strong></td>
<td><strong>$4,313.82</strong></td>
</tr>
<tr>
<td><strong>IRR</strong></td>
<td><strong>29%</strong></td>
<td><strong>25%</strong></td>
</tr>
</tbody>
</table>
The above example assumes a discount rate of 10%. As you can see, Project A has higher IRR, while Project B has higher NPV.

If these two projects were independent, it wouldn’t matter much because the firm can accept both the projects. However, in case of mutually exclusive projects, the firm needs to decide one of the two projects to invest in.

When facing such a situation, the project with a higher NPV should be chosen because there is an inherent reinvestment assumption. In our calculation, there is an assumption that the cash flows will be reinvested at the same discount rate at which they are discounted. In the NPV calculation, the implicit assumption for reinvestment rate is 10%. In IRR, the implicit reinvestment rate assumption is of 29% or 25%. The reinvestment rate of 29% or 25% in IRR is quite unrealistic compared to NPV. This makes the NPV results superior to the IRR results. In this example, project B should be chosen.

The above example illustrated the conflicting results of NPV and IRR due to differing cash flow patterns. The conflicting results can also occur because of the size and investment of the projects. A small project may have low NPV but higher IRR.
<table width="195" border="0" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td></td>
<td><strong>Project A</strong></td>
<td><strong>Project B</strong></td>
</tr>
<tr>
<td>Year 0</td>
<td>-5000</td>
<td>-20000</td>
</tr>
<tr>
<td>Year 1</td>
<td>2000</td>
<td>7000</td>
</tr>
<tr>
<td>Year 2</td>
<td>2000</td>
<td>7000</td>
</tr>
<tr>
<td>Year 3</td>
<td>2000</td>
<td>7000</td>
</tr>
<tr>
<td>Year 4</td>
<td>2000</td>
<td>7000</td>
</tr>
<tr>
<td>Year 5</td>
<td>2000</td>
<td>7000</td>
</tr>
<tr>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td><strong>NPV</strong></td>
<td><strong>$2,581.57</strong></td>
<td><strong>$6,535.51</strong></td>
</tr>
<tr>
<td><strong>IRR</strong></td>
<td><strong>29%</strong></td>
<td><strong>22%</strong></td>
</tr>
</tbody>
</table>
In this case, Project A has lower NPV compared to Project B but has higher IRR. Again, if these were mutually exclusive projects, we should choose the one with higher NPV, that is, project B.

Conflict Between NPV and IRR

This quiz is a part of the CFA Level 1 reading 'Capital Budgeting'. 

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