Present value is a formula that estimates the current value of a given amount of cash flow generated in a future date, considering that the value of money decreases as time passes. It is a concept widely employed in financial analysis to determine how much a future stream of cash would be worth today.
What is the Present Value of an Investment?
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Present value estimations are present in almost any modern valuation techniques, considering that the underlying concept of the time value of money has been accepted by the investment community as a cornerstone of financial analysis. Valuation methods such as the Discounted Cash Flow Model and the Net Present Value method employ formulas that incorporate the calculation of the present value of future income, which makes it one of the most widely applied concepts in finance.
The calculation of present value includes an element known as the discount rate, which is the minimum rate of return expected by the investor or given by the market, or it could also be the opportunity cost of investing in the project being evaluated rather than other projects. Additionally, the value of the cash flows will be smaller as the time period in which they are generated is farther from present. This means that a cash flow generated in time period number 2 will have a higher present value than a cash flow produced in time period number 5.
Present Value Formula
The formula to calculate the present value of any amount:
PV = CF / (1+r)n
Present Value Equation Components
CF = Cash Flow in currency
r = Discount rate, in decimals
n = Time period in which the cash flow occurs
This basic formula is incorporated in the Discounted Cash Flow Model, which formula is basically a combination of present value calculations for each cash flow that the company produces, commonly annually, forecasted for the next 5 to 10 years.
Alternatively, the same logic is employed in the Net Present Value formula, with the only variation that it includes the cost of the project under evaluation and then the cash flows are added to that cost. If the result is equal or higher than 0 it means the project is a profitable one to undertake.
Present Value Calculation Example
Lunar Technologies is a company that produces sensors and parts for airplanes. They are a highly sophisticated business in a niche where they have next to no competition and this has allowed them to produced millions of dollars in profits for years.
Currently, an airplane manufacturer has the intention to take over the company to incorporate it to its business as an exclusive supplier, to cut their competitor’s capacity to incorporate this technology to their airplanes, which will give them an extra competitive advantage.
In order to make an offer, the airplane manufacturer, AirTour, employed a financial advisory firm to estimate the value of the business. To do so, they employed the Discounted Cash Flow Model by using the following information:
FCF2018: $58,900,000
Weighted Average Cost of Capital: 11.6%
Expected Growth of FCF for the next 5 years: 2.3% per year
Time horizon of the model: 5 years.
By employing the DCF Formula, the firm can estimate the present value of the cash flows generated during the next 10 years, and the formula will look as the following:
PV = $65,732,400 / (1+0.116)1 + $73,357,358 / (1+0.116)2 + $81,866,811 / (1+0.116)3 + $91,363,362 / (1+0.116)4 + $101,961,512 / (1+0.116)5
PV = $249,339,357
According to this analysis, AirTour should pay a maximum of $250,000,000 for the company today. If the company decides to pay a premium over that it will only be due to the strategic value it has on its operations.
Present Value Analysis
Present value calculation present one main challenge and that is to determine the appropriate discount rate. For corporations, the discount rate can be estimated as the weighted average cost of capital, which combines the cost of each funding source that is part of the business’ financial structure according to the weight each has on the total available funds, this includes equity and debt. For individual investors though, the discount rate should be their cost of capital, or the average return of other similar investment opportunities.
In any case, the longest the time horizon of the investment the higher the effect of the discount rate. For this reason, when it comes to estimating the present value of future cash flow streams, estimating the end result at different discount rate levels is highly recommended to understand how susceptible the model is to variations in the minimum expected rate of return.
Discount rates are also extremely associated to interest rates. This is because the baseline for estimating the minimum expected rate of return is the return on a risk-free asset. In the U.S., T-bills, which are a government-issued debt instrument, are often seen as the risk free asset for reference. If the yield on T-bills increases, usually the discount rate for all players in the market will rise, as they will expect a higher premium to be paid on any investment that includes an additional level of risk compared to the T-bill.
The higher the discount rate, the lower the present value of a future cash flow will be, and vice-versa. This is the reason why projects, companies and investment opportunities that are significantly risky will be valued at a lower multiple of their earnings than those that carry a lower risk.
Present Value Uses, Cautions, Pitfalls
An important element to take into account is how long the time horizon for the investment is. For the purpose of corporate finance, estimating cash flows for a period longer than 10 years is a long shot. Nobody knows how a business will lookg like in ten years and pretending that you can is unrealistic. Additionally, after ten years, the contribution of any additional cash flow generated by the business to the overall value estimated through the first 10 years is considerably low.
For this reason, the time horizon of a present value calculation, for the purpose of a Discounted Cash Flow model such as the one presented above, should be done for a period of time equal or lower than 10 years.