# Capitalized cash flow

Capitalizing a cash flow consists of calculating the value that an amount of money will have today at a future date. It is the opposite of discounting or updating.

Bringing an amount of money to a future value implies applying one of the following two formulas:

Future value = present value * (1 + i) ^ No. years, when interest is reinvested

Future value = present value * (1 + i * No. years), when interest is not reinvested

Where:

• Present value → It is the initial investment.
• I → It is the interest rate or profitability.

The capitalization responds to "how much will a euro today be worth tomorrow" or "how much money will I have in x time if today I invest a certain amount at a certain interest rate".

## Components of capitalized cash flow

Money has a different value over time. Thus, we all value more than 100 euros today than 100 euros next month due to the following reasons:

• Inflation: It reduces our purchasing power.
• Economic, political or social factors: Such as the scarcity of resources, supply and demand or world crisis, which can lead to the loss of the value of money.
• Opportunity cost: Receiving money tomorrow instead of today means losing the return on your investment. We can receive the money within a month, but it will be worth that, 100 euros, while if we received it last month and invested it, those 100 euros would be worth more money, depending on the interest rate that we would have achieved.

Precisely for this reason, it would not be very intuitive to compare the value of 100 euros today and the value that those 100 euros would have a year from now. Both the update or discount and the capitalization of a cash flow serve to take a reference point of the value of money over time and to be able to make equivalent comparisons.

Applied to the business sphere, before undertaking any project it is essential to analyze its economic viability through the prism of cash flow or treasury. That is, from the point of view of the hard cash that the project will generate or absorb.

The cash flow is independent of the concepts of the profit and loss account of the company or project. At the end of the day, cash flow is based on receipts and payments, which are actual transfers or movements of money. While the profit and loss account deals with income and expenses, representing rights or obligations, respectively.

To do this, the analyst must estimate the outflows and inflows of money throughout the project through financial projections and, again, choose a point in time to value it.

## Example of capitalized cash flow calculation

We have two capitalization formulas that we will use depending on whether the flows or profits generated are reinvested in the initial capital or not. Reinvesting or capitalizing interest means that these are added to the initial investment and, therefore, each year we have a greater capital.

Formula of simple capitalization: We use it when the generated flows are not reinvested in the initial capital:

VF = VP * (1 + i * No. years).

Formula of compound capitalization: We use it when the flows generated are reinvested in the initial capital. The reinvestment or capitalization of the interests means that we are reinvesting the benefits that we are obtaining, that is, adding them to the initial capital. With which the future profitability of the investment is applied to an increasing amount of money. In other words, there is a “snowball” effect that will generate more money and will allow us to benefit from the ability to exponentially multiply the initial capital:

VF = VP * (1 + i) ^ No. years.

So that:

Example 1, simple compounding: Suppose that, today, we have 1,000 currency units that we will not need for the next year. So we decided to make them profitable by investing in a listed company, whose price is stable and barely varies, which is going to pay us an annual dividend of 8%.

Assuming that the price has not changed and that, therefore, it is the same as a year ago, how much money will we have obtained after one year?

We apply the formula of simple capitalization:

VF = 1000 * (1+ 0.08 * 1 year) = 1,080 monetary units.

After one year we would get CU1,080, of which 80 comes from the dividend.

But, how much money would we get if we decided to keep the investment for 4 years?

FV = 1,000 * (1 + 0.08 * 4 years) = 1,320 mu

We would have 1,320 um.

Example 2, compound capitalization: Now, suppose that we are looking for an investment that, instead of distributing the interest / benefits generated annually, we want it to reinvest. Suppose we find, for example, an investment fund that invests in equities and reinvests the dividends paid by companies, with which we can obtain an average return of 8% in 4 years.

How much money will we have by then?

Applying the compound interest formula:

Future value = 1,000 * (1 + 0.06) ^ 4 = 1,360.49 um

As we can see, other conditions being equal (8% profitability for 4 years with the same initial capital and ignoring the increase or decrease in the share price and the fund's participation), we earn 40.49 euros more if we capitalize the interests.

This means that, if we believe in the growth possibilities of the project, it will be preferable to reinvest the generated profits, to increase our future wealth.

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