Discounted Cash Flow (DCF) Models
Securities such as stocks and bonds are valued for the potential future cash flows they
generate. Similarly, investments in real assets or capital budgeting projects are
undertaken when the NPV, a type of DCF model, is positive. In general then a DCF
model involves a cash flow (CF) stream and a discount rate(s). In practice both the CF
stream and rate(s) are not known and must be estimated, so it is important to understand
the best estimation techniques which can vary from case to case.
To apply DCF models effectively we must understand what it means to discount and why
we even do it in the first place. There is a lot more to the answer than just “time value of
money” or “a dollar now is worth more than a dollar in the future”. For example, if an
investment opportunity promises us a $110 cash flow one year from now and we wish to
know what that promise is worth in cash today, we might discount (or reduce) the $110
at, say 10%, for one year giving us a present value (PV) of $100. The key to
understanding why we discount and at what rate involves our opportunity cost of capital.
Suppose this $110 promise (a year from now) is in the form of a loan contract we are
considering buying (this is the same as lending or investing money) with cash we have on
hand. How much would we be willing to pay for the $110 promised to us one year from
today? That would depend on the minimum rate of return we need on the money we use
to buy the loan contract which in turn depends on the rate of return on our alternative
investment set. In particular, it would depend on the best rate we could find for our
money on any other comparable investment opportunity.
Assume then that we have scoured the universe for the best rate of return our dollar
investment can earn and determine it to be 10% in investment X. In other words, we have
the opportunity to invest any (reasonable) amount of money at a promised rate of 10%
per annum. That 10% would mean that an investment of $100 today should produce a
($100) (1+10%) = $110 cash inflow one year from now. Thus, if the loan contract
promising us $110 a year from now required us to pay more than $100 today to own it we
would be better off spending only $100 on investment X for the same thing. Another way
of thinking about this is that if we purchase the loan contract with our money we give up
the opportunity to invest it at 10% in X. This 10% in essence is our opportunity cost of
capital.
So, when we discount (reduce) a future cash flow we are really trying to determine how
much we would have to invest in X, our next best alternative investment, to get the same
future cash flow as promised by the loan contract, the investment opportunity being
valued. Since discounting is the reverse, or inverse, process of compounding, the value of
the loan contract to us today is its present value:
PV0 = FVn/ (1 + i)n = $110/(1+10%)1 = $100
That in a nutshell is our DCF model applied to value a simple loan contract. But all of
this reasoning is predicated on the assumption that the loan contract and investment X are
comparable and reasonable substitutes, especially in terms of risk. After all, it’s only
fair to compare apples with apples. In the loan contract example the opportunity cost of
capital of 10% was at least conceptually determined by analyzing all alternative
investment opportunities with very similar characteristics to the cash flow stream of the
loan contract. In practice, the alternative investments would probably have been other
loans that matched as many of the characteristics of the loan contract as possible. These
general characteristics might include:
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Risk or uncertainty of the CF stream
Tax status (are the interest/profits taxable)
Timing of the cash flows (short, intermediate or long-term; duration)
Method of estimating CF stream (expected, conservative, aggressive,
promised)
In a DCF model the general rule of thumb is to match the characteristics of the cash flows
being discounted with the rate used to discount them. If the cash flows are after-tax then
use an after-tax opportunity cost of capital as the discount rate. If the cash flows are
expected use an expected discount rate. As in the loan contract example, if the cash flows
are promised then the discount rate should be a comparable promised rate, like yield to
maturity (YTM). If the cash flows are risky or uncertain the discount rate should be a
comparable Risk Adjusted Discount Rate (RADR).