A euro today is worth more than what a euro will be worth ten years from now. How much will a euro be worth in ten years? The discounted cash flow method (in English "Discounted Cash Flow" or DCF) is used precisely to discount the cash flows expected in the future.
Steps
Step 1. Determine the discount rate
The discount rate can be estimated using the "Capital Asset Pricing Model" (CAPM). This has a formula: risk-free gross return + beta * (market-predicted risk premium). For equities, the risk premium is around 5 percent. Since financial markets determine the value of most stocks over an average 10-year period, the risk-free gross yield corresponds to the 10-year yield on T-bills, which was around 2 percent in 2012. So if the 3M company has a beta of 0.86 (which means that its stock has 86% of the volatility of a medium-risk investment, i.e. the general financial market), the discount rate we can take for 3M is 2% + 0, 86 (5%) i.e. 6, 3%.
Step 2. Determine the type of cash flow to discount
- A "simple cash flow" is a single cash flow over a specified future time period. For example, 1,000 euros over 10 years.
- An "annuity" is a steady flow of cash that occurs at regular intervals over a specified period of time. For example, € 1,000 a year for 10 years.
- A "growing annuity" is cash flow that is designed to grow at a constant rate over a specified period of time. For example, € 1,000 per year with a growth rate of 3 percent per year for the next 10 years.
- A "perpetual annuity" is a steady flow of cash at regular intervals that will last forever. For example, a preferential title that pays $ 1,000 a year forever.
- A "growing perpetual annuity" is a cash flow that is destined to grow at a constant rate forever. For example, a stock that pays € 2.20 in dividends this year and is expected to grow by 4% per year forever.
Step 3. Use the formula to calculate discounted cash flow:
- For a "simple cash flow": present value = cash flow in the future period / (1 + discount rate) ^ time period. For example, the present value of $ 1,000 over 10 years, with a discount rate of 6.3 percent, is $ 1,000 / (1 + 0.065) ^ 10 = $ 532.73.
- For an "annuity": present value = annual cash flow * (1-1 / (1 + discount rate) ^ number of periods) / Discount rate. For example, the present value of 1,000 euros per year for 10 years, with a discount rate of 6.3 percent, is 1,000 * (1-1 / (1 + 0, 063) ^ 10) /0.063 = 7,256, 60 euros.
- For an "increasing annuity": present value = annual cash flow * (1 + g) * (1- (1 + g) ^ n / (1 + r) ^ n) / (rg), where r = rate of discount, g = growth rate, n = number of periods. For example, the present value of 1,000 euros per year with a growth rate of 3 percent per year for the next 10 years, with a discount rate of 6.3 percent, is 1,000 * (1 + 0.03) * (1- (1 + 0.03) ^ 10 / (1 + 0, 063) ^ 10) / (0.063-0.03) = 8.442, 13 euros.
- For a "perpetual annuity": present value = cash flow / discount rate. For example, the present value of a preferred stock that pays 1,000 euros per year forever, with a discount rate (interest rate) of 6.3 percent, is 1,000 / 0, 063 = 15,873.02 euros.
- For a "growing perpetual annuity": present value = expected cash flow next year / (discount rate-expected growth rate). For example, the present value of a stock that pays € 2.20 in dividends this year and is expected to grow by 4% per year forever (reasonable assumption for 3M), assuming a discount rate of 6, 3 percent, it is 2.20 * (1.04) / (0.063-0.04) = 99.48 euros.
Advice
- The discounted cash flow analysis for an increasing perpetual annuity can be used to determine market expectations for a security. For example, considering that 3M pays € 2.20 in dividends, it has a discount rate = rate of return on equity = 0.063 and the current price is € 84, what is the expected growth rate of the market for 3M? Solving for g in 2.20 * (1 + g) / (0.063-g) = 84, we get g = 3.587 percent.
- You can also use the numerous online Discounted Cash Flow or DCF calculators, like this one.
