# Capital Budgeting

Capital budgeting is a process that assess the convenience of carrying out an investment or not. If there are many profitable investments available, the capital budgeting tries to find out which one is more advisable.

There are different measurements to find out which investment is more profitable. When we are evaluating a private investment, the criteria of private profitability should be take into account. When we are evaluating a public investment, social benefits and costs should be taken into account. In both scenarios, we have to take other considerations into account, like the investment risk.

An investment will be beneficial for the investor if it’s able to generate added value for him. This happens when profits outweigh costs. Within costs, we have to take into consideration the opportunity costs of the investment, that will be given by the best alternative investment with similar risk.

We will describe some measures for capital budgeting. But first, we need to analyze some important elements of investment projects that are needed for capital budgeting:

## Initial investment

It is the expenditure that is made in the first period. For example, if we are assessing the purchase of a car to be used as a taxi, the initial investment will be the price of the car plus all expenses to make the car a taxi (painting, legal paperwork, etc.).

## Cash Flow

It’s a report that contains the flow of money into or out of a business. In the case of capital budgeting, we will use an expected cash flow, that contains estimations of future flows of money. For example, if the initial investment for the taxi was \$10.000 and it will produce a net income of \$1.000 during one year, at the end of which the taxi will be sold for \$5.000, the cash flow will be the following:

 - \$10,000.00 1 \$1,000.00 2 \$1,000.00 3 \$1,000.00 4 \$1,000.00 5 \$1,000.00 6 \$1,000.00 7 \$1,000.00 8 \$1,000.00 9 \$1,000.00 10 \$1,000.00 11 \$1,000.00 12 \$6,000.00

Because it’s a future cash flow, we are talking about estimations. An important part of capital budgeting has to do with making accurate estimations. Besides, there are ways to take into account the probability that the expected value will be different as the observed value one encounters in reality.

## Discount Rate

As mentioned earlier, capital budgeting takes the opportunity costs into consideration. The discount rate is usually the yield rate of the best alternative investment with similar risk.

## Measurements to find out the best investment alternatives

### Net Present Value

The Net Present Value (NPV) is the sum of the discounted cash flows.

Example: there is an investment project with only 2 periods, initial investment and sale of the investment. The initial investment is \$1000 and after 12 month, there will be a cash inflow of \$1210. The best possible alternative with similar risk is 1 year bond with an annual yield of 10%. The net present value of this investment is -\$1000 + \$1210/1.1 = \$100.

This means:
- The present value of the investment yield is \$100 higher than the best similar risk alternative.
- If we make the investment, our wealth will increase in \$100
- It is advisable to actually carry out the investment

A second example:

 - \$5,000.00 1 \$1,000.00 2 \$1,000.00 3 \$1,000.00 4 \$1,000.00 5 \$1,000.00 6 \$1,000.00 7 \$1,000.00 8 \$1,000.00 9 \$1,000.00 10 \$1,000.00 11 \$1,000.00 12 \$6,000.00

And the discount rate is 10%.

In this case, to calculate the NPV we can do:
NPV = -5000 + 1000/1.1 + 1000/1.12 + 1000/1.13 + … + 1000/1.111 + 1000/1.112

The NPV is \$3407, so it is advisable to carry out the investment.

Usually, the computation of the NPV is done by using a software like Microsoft Excel or Libreoffice Calc.

## Internal Rate of Return

The Internal Rate of Return (IRR) is the discount rate that makes the net present value of the cash flows equal to zero. There is no need to know the discount rate to calculate the IRR. Once we have the IRR calculated, it is compared with the discount rate. If the IRR is greater than the discount rate, it is advisable to carry out the investment, and vice versa.

Let’s go back to the example of an investment with only 2 cash flows: the initial investment is \$1000 and after one year there will be an inflow of money of \$1210. In this case, it’s very easy to calculate the IRR: The IRR is 21%, because -\$1000 + \$1210/1.21 = 0. To know if this investment is advisable, we compare 21% with the yield rate of the best alternative. If the yield rate of the best alternative is 10%, it is advisable to carry out the investment.

## Return over investment

The Return Over Investment (ROI) is the benefit resulting from an investment. It is calculated by subtracting the investment amount and losses from the cash inflows. It is a very simple measure. The percentage ROI is: net (benefit / investment) x 100.

Let’s go back to the example of an investment with just 2 cash flows. The initial investment is \$1000 and after one year, there is an inflow of \$1210. The ROI is \$1210 - \$1000 = \$210. The percentage ROI is 21%. In this simple example, and because the investment project has only 2 flows, the ROI is the same as the IRR. But usually this is not the case.

Another example:

 - \$5,000.00 1 \$1,000.00 2 \$1,000.00 3 \$1,000.00 4 \$1,000.00 5 \$1,000.00 6 \$1,000.00

In this example, the ROI is \$1000 and the percentage ROI is 20%.

### Discounted ROI

The ROI and the percentaje ROI are easy to understand and calculate, but they do not take the time into account. A project can generate 21% ROI in 1 year or 10 years, and the ROI will be the same.

To solve this issue, the discounted ROI can be calculated. The discounted ROI uses the discounted cash flows. The percentage discounted cash flow is a better measure than the percentage ROI.

## TL;DR

Capital budgeting is a key element to estimate the profitability of an investment project before execution. The main elements needed by capital budgeting are the estimated cash flows and the discount rate. There are several measures for capital budgeting, the most important are the IRR and the VPN. The ROI must be used with caution.