Investing is simply the act of committing money now with the expectation of receiving more in the future. The amount committed, or the price of the investment is known. What will be collected in the future, however, is the value of the investment and discovered through analysis. This Guide to Discounted Cash Flow Part 1 shows the way to do that.
The estimate of value, or the amount to be received, is often the missing link to successful investing for the individual investor. The previous two articles on valuation here and here discussed relative valuation methods. Now we take on Discounted Cash Flow another valuation method with tremendous advantages for the investor.
Discounted Cash Flow (DCF)
Warren Buffett summarized John Burr Williams’s formula for value in the Berkshire Hathaway 1992 Annual Report. Paraphrasing, he wrote: “The value of any stock, bond, or business today is determined by the cash inflows and outflows. Then discount the cash flows at the interest rate expected during the remaining life of the asset.”
The cash flow is discounted for three main reasons, (1) account for the time value of money (TVM), (2) adjust for the risk of the investment, and (3) consider the opportunity cost of the investment.

Time Value of Money
Time is an essential element in investing. What you receive from the investment “during the remaining life” is, of course, a future event. And, the longer you have to wait for money, the less it is worth.
Money is more valuable now than in the future due to inflation. Receiving $10,000 today is better than $10,000 ten years from now. That is because, in ten years, the purchasing power of the money is reduced by the rate of inflation.

Risk
Not all businesses or investment opportunities have the same level of risk. For example, the likelihood of receiving cash from the US Treasury is higher than earning money from a new startup company. The startup is a riskier investment because of the uncertainty of its future performance.
A higher discount rate reflects riskier investments and a lower one safer investments. The 10year US Treasury bond interest rate is often used as the riskfree rate because of the reliability of payment. The risk free discount rate is increased with the risk of other investments.

Opportunity Cost
Opportunity costs are the benefits one misses out on when choosing one investment over another. Investors make better decisions when they understand the cost of the opportunity they will miss out on if they choose a different investment.
We’ll use an example below to illustrate how to reflect the opportunity cost of an investment in the discount rate.
Net Present Value (NPV)
Discounted Cash Flow is the sum all “future” cash flows discounted back to the present and sometimes called the “Present Value.” “Net Present Value” also subtracts the initial cost of the investment from the Discounted Cash Flow.
A positive NPV means the investor gets back more than paid after discounting the cash flows. And, a negative NPV means the investor will receive less than paid after discounting the cash flows.
For example, a 10% discount rate consists of 2% for inflation and 8% for the required investor’s return. A Net Present Value of $1000, the investor means the investor receives an 8% real return in a 2% inflation period plus an extra $1000.
The Advantage of Discounted Cash Flow
The DCF analysis is a valuation method that considers essential elements of investment. And, it is an absolute valuation method that determines the underlying intrinsic value of the investment itself.
Recall that marketbased relative valuations compare the price of similar investments. They depend on variables external to the investment in question — variables like the overall market level and the external companies used in the comparison.
The DCF valuation offers tremendous advantages to the investor. They can patiently wait for the price of the investment to fall below the intrinsic value. When it does, they can then opportunistically buy it on sale with a suitable Margin of Safety.
Conversely, when the market price of the investment rises to the intrinsic value, the investor knows it is fairly priced and can decide to sell or hold based on objective information.
Intrinsic value takes the market out of the equation and values the investment on its cash flow merits regardless of the market. The DCF valuations tend to be more stable, changing with the business’ longterm cash flows rather than market sentiment.
The Disadvantage of Relative Valuations
The market volatility and cyclical changes in the business sector cause a relative valuation to fluctuate with the market.
Investors then tend to buy as market prices and sell when they decrease. The “follow the herd” behavior contradicts a cardinal rule of investing; “buy low and sell high.”
Relative valuations also assume the comparable investments are similar. This ignores the fact that the business in the same industry or sector can have drastically different performance levels.
For example, online retailer Amazon is significantly different than brick and mortar Walmart and Target. And, these two perform considerably better than JCPenney and Sears. So, you need to know enough about the relative companies to determine which ones are comparable.
The DCF valuation is independent of what other “similar” investments are selling for in the marketplace. There is no need to look at competitors in the industry or complementary sectors, although it may be insightful to do so.
The absolute valuation method focuses on the characteristics of the particular company. And, isolates it from what the market may think it, or its’ sector, might be worth on any given day.
There is an underlying assumption: The intrinsic value of the business will eventually be recognized by other investors and reflected in the market price of the shares.
Simplifying Discounted Cash Flow
The Discounted Cash Flow model is robust and can be used to value anything that produces income or a stream of cash flow, including; bonds, shares, entire businesses, or single projects.
Determining the intrinsic value of a wide range of investments can get complicated. For example, a company’s valuation requires estimates of the weighted average cost of capital, future sales, expenses, margins, and cash flows. These are difficult determinations even for company insiders.
Reducing the many variables required for more extensive applications reduces it to the variables faced by the individual investor. And, those are the investor’s time value of money, risk tolerance, and opportunity cost.
Sometimes it is not easy to see the forest for the trees. Warren Buffett is one of the world’s greatest investors. He reduces complex investing topics down into simple folksy stories understood by the rest of us.
Monish Pabrai is another one. He is an outstanding investor, teacher, and author of the mustread investing book, “The Dhandho Investor.” He, too, has a knack for explaining complicated ideas in ways that we can easily understand through the use of simplified examples.
So, we’ll use the insights of these investing mentors and apply their principle of keeping it simple. Every person has to accomplish things in their way. One way is to find people like Buffett and Pabrai with the insight to simplify what others complicate for the rest of us.
The goal here is to show how individual investors can reduce the potential complexity of DCF valuations to create a reasonable approximation of value.
The Discounted Cash Flow Equation
Here is the complicated version of the formula. It shows that we need to predict future cash flows and discount them back to the present at a discount rate. For simplicity, we define cash flow as cash from operations less capital expenditures.
Here’s the equation:
Where:
 PV0 = Present value at time 0
 CFn = Cash flow in period n
 r (or sometimes k) = Interest rate (or discount rate) in period n
 N = Number of periods
A Simplified Business Example
Monish Pabrai provides good examples in his book, “The Dhandho Investor,” that we can use as templates for our purposes.
Imagine a neighborhood bagel shop for sale, and the owner’s asking price is $300,000. A prospective buyer estimates the free cash flow generated by the business is $80,000 per year. And, the buyer believes the bagel shop will sell for $300,000 after ten years.
But the buyer has another investment to consider: a bond that pays 6% interest per year. That is an alternative to investing in the bagel shop. Is the buyer better off with the bagel shop or the relatively secure 6% bond? How do the two investments compare?
A [free online calculator] was used to do the DCF calculations. The table shows buying the bagel shop at $300,000 has a Net Present Value of about $456,000 with the future cash flow from the business discounted at 6%. Add back the $300,000 purchase price to show the intrinsic value of the bagel shop is $756,000 ($456,000 + $300,000 = $756,000).
Buying the bagel shop at $300,000 is paying about 40% of the shop’s intrinsic value ($300K/$756K = 39.7%). The bagel shop is a better investment with a 60% margin of safety. The buyer receives the 6% return plus and additional $456,000 in present value over ten years.
The Alternative Investment Example
We can see this if we look at the DCF analysis on the 6 percent yielding bond. Like the bagel shop, the bond investment has a present value of $300,000. However, the bond yield of 6% results in an annual interest payment of $18,000 per year. With the bond discounted at 6% per year, there is $0 of additional present value.
Add back the $300,000 purchase price shows the intrinsic value of the bond is $300,000 ($0 + $300,000 = $300,000). The bond has no margin of safety when discounted at the expected return.
Investing in the bagel shop is better than putting the cash in a 6 percent yielding bond provided the expected cash flows, and future sale price is reasonably accurate.
And, this is no different than looking at buying shares of a company on the stock exchange compared to a bond yielding 6% as we’ll see in the next article on Discounted Cash Flow.
What we Learned:
The estimate of value is often the missing link to successful investing.
Discounting the cash flows of any investment (stock, bond, business, or project) at an appropriate rate during its life determines the intrinsic value.
Discounted Cash Flow is the fundamental valuation method with tremendous advantages for the investor. It provides an objective basis for evaluating investments.
Discounted Cash Flow considers three primary investment factors:
 the time value of money,
 the risk of the investment, and
 the opportunity cost of the investment.
We can reduce the potential complexity of DCF valuations considerably and create a reasonable estimate of value that helps our investing tremendously.