If you’ve ever bought a lottery ticket, you may know the advertised jackpot is set up to be paid to a winner in equal annual installments over a long period. What you may not notice, in fine print under the big amount, is the smaller amount the winner could have upfront, without waiting for future installments. That amount is known as the cash option, or the cash present value of the advertised jackpot.
How does the lottery determine the value of the cash option? It calculates what each annual payment is worth today, based on an assumed rate of interest and the number of years until each annual payment would be made. This is a process called discounting future values, or discounting cash flows.
What is discounted cash flow?
Discounted cash flow is a method of calculating the current value of something—a company’s stock, a rental property, or another income-producing asset—based on how much money the asset is expected to generate in the future.
The discounting of future cash flows is based around a key concept in modern finance: the time value of money. This means money grows in value over time because it can be invested to earn interest. So, $100 today is worth more than $100 a year from now—at a 5% annual interest rate, for example, $100 now will increase to $105 in one year. In future years, the amount will grow even faster because of what’s known as compounding, which can be thought of as interest earned on interest.
Here’s an example of compounding based on $100 earning 5% annual interest for three years. The interest rate is expressed as a decimal .05 with the constant 1, or 1.05:
$100 x 1.05 x 1.05 x 1.05 = $115.76 compounded value
You could think of discounting as the reverse of compounding. While compounding starts with money now and calculates how it grows over time through reinvestment of principal and interest, discounting does the opposite: it projects a sum of money in the future and progressively reduces it by the same compounding process to a current value today—the discount value.
Imagine someone who was going to receive $100 three years from now. If the assumed annual interest rate is 5%, the calculation works this way:
$100 ÷ 1.05 ÷1.05 ÷ 1.05 = $86.38 discounted value
So $100 three years from now is worth $86.38 today.
Here’s another way to think of discounted cash flows. How many small investors have thought to themselves, “I want to have $1 million in 10 years. How much money do I need now, assuming I can earn 5% annually, so it grows to $1 million?”
Discounting $1 million by the 5% rate compounded for 10 years, or 1.05 to the 10th power, or exponent, computes to 1.62889 and the calculation would be:
$1,000,000 ÷ 1.62889 = $613,915 discounted cash flow
So a small investor could start with $613,915 and let it grow at 5% annual interest compounded for 10 years, to reach $1 million.
How is discounted cash flow used?
贴现现金弗洛的主要目的w is to determine a theoretical value or price for an asset, such as an appropriate stock price for a company. Comparing the discounted cash flows a business generates against the stock price can help an investor assess whether the company is undervalued or overvalued.
For example, if discounting a company’s expected cash flows results in a theoretical per-share valuation of $125, and the shares are trading at $110, an investor might conclude the company is undervalued and a bargain to buy.
Other uses for discounted cash flows include determining a fair price for income-generating property such as rental apartments or office buildings, or valuing bonds or loans that might be traded. Discounted cash flow can also be used in cost-benefit analysis of proposed business projects or investments.
How does discounted cash flow work?
The discounting process starts with a series of estimated cash flows in future periods, usually years. Then a discount rate is assumed. For stocks, the discount rate is typically a company’s weighted average cost of capital, or the rate of return shareholders seek. The average cost of capital is determined by a company’s mix of debt and equity, and the proportionate interest rates that must be paid for each.
Each cash flow is reduced by the discount rate to the power (or exponent) of the time period. For instance, the second period’s cash flow would be reduced by the discount rate squared, the third period’s flow reduced by the discount rate cubed, and so on.
After each period’s cash flow is discounted, they are added up. For stocks, a lump-sum total for estimated cash flow in later years is included, called the terminal value. The total of all these discounted cash flows can serve as a theoretical share or asset price.
The terminal value usually accounts for most of the total discounted cash flows, and it can vary, depending on the estimated terminal-value length—the estimate of a company’s lifespan beyond the initial discounting years. For instance, one financial analyst may estimate a 10-year lifespan for terminal value, while another may use 20 years.
Many financial analysts and fund managers take a further step in the discounting process. They use a higher growth rate for the company in its early years, followed by a lower rate for the terminal-value years. This makes the discountedcash flow analysismore sophisticated, but also more complex and potentially tricky, because it uses two different rates.
What is the discounted cash flow formula?
The basic formula for discounting cash flows, or DFC, looks like this:
DCF = CF + CF2 + CF3 + CF4 + CF5 + CF(n)
(1 + r) (1 + r) ² (1 + r)³ (1 + r)⁴ (1 + r)⁵ (1 + r)ⁿ
DCF = sum of the discounted periodic cash flows and terminal value cash flow
CF = cash flow (or net income or free cash flow) each for period, usually a year = discount rate
An example with numbers, a DFC model might look like this. Company X, currently trading at $375 a share, has the following projected cash flows per share:
Year 1 Year 2 Year 3 Year 4 Year 5 Years 6–15
$20 $40 $60 $80 $100 $400
Assumption: 7% discount rate
Terminal value: 10 years after years 1 through 5
贴现现金流7% the power of each year, while years 6 to 15 (the terminal value) discounted at 7% to the 10th power would be:
Year 1 Year 2 Year 3 Year 4 Year 5 Years 6–15
$18.69 $34.94 $48.98 $61.04 $71.30 $203.34
The sum of the discounted annual cash flows is $438.29 a share. An investor might conclude that Company X seems undervalued, because its $375 stock price is less than the discounted cash flows.
Benefits and limitations of discounted cash flow
Discounted cash flow analysis can benefit business managers and investors in several ways:
- It tries to establish the intrinsic value of a stock, asset or project, independent of the market value or price. A valuation based on discounted cash flows might, for example, save a business owner from investing in an expansion that won’t pay off.
- It accounts for major expectations and assumptions, such as a company’s expected growth rate, and the discount rate, as well as the company’s lifespan.
- It can also be used to determine the internal rate of return on an investment or business project, and for cost-benefit analysis by investment banks of proposed mergers and acquisitions.
- Discounted cash flows are used in scenario analysis and sensitivity analysis, sometimes called what-if analysis. For example, investors might raise the discount rate by a percentage point to see how a company’s theoretical value changes.
At the same time, discounting cash flows has some drawbacks, including:
- It relies on assumptions and expectations, and the calculation of discounted cash flows is very sensitive to changes in those assumptions and expectations, making valuations prone to error.
- Because discounted cash flow examines a stock or business project in isolation, ignoring comparable companies or projects, there is no basis for relative valuation—no sizing up of Company X against its competitors. Analysts and fund managers often use discounted cash flow analysis together with relative-value comparisons to make investment decisions.
Discounted cash flow FAQ
How do you calculate discounted cash flow?
Discounted cash flow is calculated by summing up each projected cash flow, which is reduced to a present value by the discount rate to the power, or exponent, of the number of periods ahead for the cash flow. Most calculations and analyses use years as the time periods.
What is an example of discounted cash flow?
Everyday examples include lottery jackpots that provide a cash option, as well as US savings bonds, and zero-coupon bonds sold by companies and government agencies. For example, think of a lottery with a jackpot of $100 million that pays the winner $4 million a year for 25 years. But what happens if a winner chooses the cash option? The lottery might use an appropriate discount rate of 3%, for example, and the lump sum would be $47.8 million today.
Are NPV and DCF the same?
They’re similar, but they’re not the same. Net present value (NPV) uses the same discounting process. But after the discounted cash flow is calculated, the stock price or current asset value is subtracted. The difference is net present value. Positive NPV could indicate that a stock is worth buying at the current price, or that investing in a business project makes financial sense.