Cash flow is the movement of money into or out of a
business, project, or financial product. It is usually measured during a
specified, limited period of time. Measurement of cash flow can be used for
calculating other parameters that give information on a company's value and
situation.
1. To determine a
project's rate of return or value. The time
of cash flows into and out of projects are used as inputs in financial models
such as internal rate of return and net present value.
2. To determine problems
with a business's liquidity. Being profitable does not necessarily
mean being liquid. A company can fail because of a shortage of cash even while
profitable.
3. As an alternative
measure of a business's profits when it is believed that accrual accounting concepts do not
represent economic realities. For instance, a company may be notionally
profitable but generating little operational cash (as may be the case for a
company that barters its products rather than selling for cash). In such a
case, the company may be deriving additional operating cash by issuing shares
or raising additional debt finance.
4. Cash flow can be used
to evaluate the 'quality' of income generated by accrual accounting. When net income is composed of large
non-cash items it is considered low quality.
5. To evaluate the risks
within a financial product, e.g., matching cash requirements, evaluating
default risk, re-investment requirements, etc.
Cash flow notion is based loosely on
cash flow statement accounting standards. the term is flexible and can refer to
time intervals spanning over past-future. It can refer to the total of all
flows involved or a subset of those flows. Subset terms include net cash flow, operating cash flow and free cash flow.
Business' financials
The (total) net cash flow of a company
over a period (typically a quarter, half year, or a full year) is equal to the
change in cash balance over this period: positive if the cash balance increases
(more cash becomes available), negative if the cash balance decreases. The
total net cash flow is the sum of cash flows that are classified in three
areas:
1. Operational cash flows: Cash received or
expended as a result of the company's internal business activities. It includes
cash earnings plus changes to working capital. Over the medium term this must be net
positive if the company is to remain solvent.
2. Investment cash
flows:
Cash received from the sale of long-life assets, or spent on capital expenditure (investments,
acquisitions and long-life assets).
3. Financing cash flows: Cash received from
the issue of debt and equity, or paid out as dividends, share repurchases or debt repayments.
Examples
Description
|
Amount ($)
|
totals ($)
|
Cash flow from operations
|
+10
|
|
Sales (paid in cash)
|
+30
|
|
Incoming loan
|
+50
|
|
Loan repayment
|
-5
|
|
Taxes
|
-5
|
|
Cash flow from investments
|
-10
|
|
Purchased capital
|
-10
|
|
Total
|
0
|
The net cash flow only provides a
limited amount of information. Compare, for instance, the cash flows over three
years of two companies:
Company A
|
Company B
|
|||||
Year 1
|
Year 2
|
year 3
|
Year 1
|
Year 2
|
year 3
|
|
Cash
flow from operations
|
+20M
|
+21M
|
+22M
|
+10M
|
+11M
|
+12M
|
Cash
flow from financing
|
+5M
|
+5M
|
+5M
|
+5M
|
+5M
|
+5M
|
Cash
flow from investment
|
-15M
|
-15M
|
-15M
|
0M
|
0M
|
0M
|
Net
cash flow
|
+9M
|
+10M
|
+11M
|
+13M
|
+14M
|
+15M
|
Company B has a higher yearly cash
flow. However, Company A is actually earning more cash by its core activities
and has already spent 45M in long term investments, of which the revenues will
only show up after three years.
DISCOUNTED CASH FLOW
In finance, discounted cash flow (DCF)
analysis is a method of valuing a project, company, or asset using the concepts
of the time value of money. All future cash flows are estimated and discounted by using cost of
capital to give their present values (PVs). The sum of
all future cash flows, both incoming and outgoing, is the net present value (NPV), which is
taken as the value or price of the cash flows in question.[1]
Using DCF analysis to compute the NPV
takes as input cash flows and a discount rate and gives as output a present
value; the opposite process—takes cash flows and a price (present value) as
inputs, and provides as output the discount rate—this is used in bond markets
to obtain the yield.
Discounted cash flow analysis is widely
used in investment finance, real estate development, corporate financial management and patent valuation.
Contents
- 1 Discount rate
- 2 History
- 3 Mathematics
- 4 Example DCF
- 5 Methods of appraisal of a company or project
- 6 Shortcomings
- 7 See also
- 8 References
- 9 External links
- 10 Further reading
Discount rate
Main
article: Discounting
The most widely used method of discounting is exponential
discounting, which values future cash flows as "how much money would have
to be invested currently, at a given rate of return, to yield the cash flow in
future." Other methods of discounting, such as hyperbolic discounting, are studied in
academia and said to reflect intuitive decision-making, but are not generally
used in industry.
The discount rate used is generally the
appropriate weighted average cost of capital (WACC), that
reflects the risk of the cashflows. The discount rate reflects two things:
1. Time value of money (risk-free rate) – according to the
theory of time preference, investors would
rather have cash immediately than having to wait and must therefore be
compensated by paying for the delay
2. Risk premium – reflects the extra
return investors demand because they want to be compensated for the risk that
the cash flow might not materialize after all
History
Discounted cash flow calculations have
been used in some form since money was first lent at interest in ancient times.
Studies of ancient Egyptian and Babylonian mathematics suggest that they used
techniques similar to discounting of the future cash flows. This method of asset
valuation differentiated between the accounting book value, which is based on
the amount paid for the asset.[2] Following the stock
market crash of 1929, discounted cash flow analysis gained popularity as a
valuation method for stocks. Irving Fisher in his 1930 book The Theory of
Interest and John Burr Williams's 1938 text The Theory of Investment Value first formally
expressed the DCF method in modern economic terms.[3]
Mathematics
Discounted cash flows
The discounted cash flow formula is
derived from the future value formula for
calculating the time value of money and compounding
returns.
![DCF = \frac{CF_1}{(1+r)^1} + \frac{CF_2}{(1+r)^2} + \dotsb +
\frac{CF_n}{(1+r)^n}](file:///C:/Users/User/AppData/Local/Temp/msohtmlclip1/01/clip_image001.gif)
![FV = DCF \cdot (1+r)^n](file:///C:/Users/User/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif)
Thus the discounted present value (for
one cash flow in one future period) is expressed as:
![DPV = \frac{FV}{(1+r)^n}](file:///C:/Users/User/AppData/Local/Temp/msohtmlclip1/01/clip_image003.gif)
Where:
- DPV is the discounted present value of the future cash flow (FV), or FV adjusted for the delay in receipt;
- FV is the nominal value of a cash flow amount in a future period;
- r is the interest rate or discount rate, which reflects the cost of tying up capital and may also allow for the risk that the payment may not be received in full;[4]
- n is the time in years before the future cash flow occurs.
Where multiple cash flows in multiple
time periods are discounted, it is necessary to sum them as follows:
![DPV = \sum_{t=0}^{N} \frac{FV_t}{(1+r)^{t}}](file:///C:/Users/User/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif)
For each future cash flow (FV)
at any time period (t) in years from the present time, summed over all
time periods. The sum can then be used as a net present value figure. If the
amount to be paid at time 0 (now) for all the future cash flows is known,
then that amount can be substituted for DPV and the equation can be
solved for r, that is the internal rate of return.
All the above assumes that the interest
rate remains constant throughout the whole period.
If the cash flow stream is assumed to
continue indefinitely, the finite forecast is usually combined with the
assumption of constant cash flow growth beyond the discrete projection period.
The total value of such cash flow stream is the sum of the finite discounted
cash flow forecast and the Terminal value (finance).
Continuous cash flows
For continuous cash flows, the
summation in the above formula is replaced by integration:
![DPV= \int_0^T FV(t) \, e^{-\lambda t} dt \,,](file:///C:/Users/User/AppData/Local/Temp/msohtmlclip1/01/clip_image005.gif)
Where
is now the rate
of cash flow, and
.
![FV(t)](file:///C:/Users/User/AppData/Local/Temp/msohtmlclip1/01/clip_image006.gif)
![\lambda = log(1+r)](file:///C:/Users/User/AppData/Local/Temp/msohtmlclip1/01/clip_image007.gif)
Example DCF
To show how discounted cash flow
analysis is performed, consider the following simplified example.
- John Doe buys a house for $100,000. Three years later, he expects to be able to sell this house for $150,000.
Simple subtraction suggests that the
value of his profit on such a transaction would be $150,000 − $100,000 = $50,000,
or 50%. If that $50,000 is amortized over the three years, his implied
annual return (known as the internal rate of return) would be about
14.5%. Looking at those figures, he might be justified in thinking that the
purchase looked like a good idea.
1.1453 x 100000 = 150000
approximately.
However, since three years have passed
between the purchase and the sale, any cash flow from the sale must be
discounted accordingly. At the time John Doe buys the house, the 3-year US Treasury Note rate is 5% per
annum. Treasury Notes are generally considered to be inherently less risky than
real estate, since the value of the Note is guaranteed by the US Government and
there is a liquid market for the
purchase and sale of T-Notes. If he hadn't put his money into buying the house,
he could have invested it in the relatively safe T-Notes instead. This 5% per
annum can therefore be regarded as the risk-free interest rate for the relevant
period (3 years).
Using the DPV formula above
(FV=$150,000, i=0.05, n=3), that means that the value of $150,000 received in
three years actually has a present value of $129,576 (rounded off). In other
words we would need to invest $129,576 in a T-Bond now to get $150,000 in 3
years almost risk free. This is a quantitative way of showing that money in the
future is not as valuable as money in the present ($150,000 in 3 years isn't
worth the same as $150,000 now; it is worth $129,576 now).
Subtracting the purchase price of the
house ($100,000) from the present value results in the net present value of the whole
transaction, which would be $29,576 or a little more than 29% of the purchase
price.
Another way of looking at the deal as
the excess return achieved (over the risk-free rate) is (114.5 - 105)/(100 + 5)
or approximately 9.0% (still very respectable).
But what about risk?
We assume that the $150,000 is John's
best estimate of the sale price that he will be able to achieve in 3 years time
(after deducting all expenses, of course). There is of course a lot of
uncertainty about house prices, and the outcome may end up higher or lower than
this estimate.
(The house John is buying is in a
"good neighborhood," but market values have been rising quite a lot
lately and the real estate market analysts in the media are talking about a
slow-down and higher interest rates. There is a probability that John might not
be able to get the full $150,000 he is expecting in three years due to a
slowing of price appreciation, or that loss of liquidity in the real estate
market might make it very hard for him to sell at all.)
Under normal circumstances, people entering
into such transactions are risk-averse, that is to say that they are prepared
to accept a lower expected return for the sake of avoiding risk. See Capital asset pricing model for a further
discussion of this. For the sake of the example (and this is a gross
simplification), let's assume that he values this particular risk at 5% per
annum (we could perform a more precise probabilistic analysis of the risk, but
that is beyond the scope of this article). Therefore, allowing for this risk,
his expected return is now 9.0% per annum (the arithmetic is the same as
above).
And the excess return over the
risk-free rate is now (109 - 105)/(100 + 5) which comes to approximately 3.8%
per annum.
That return rate may seem low, but it
is still positive after all of our discounting, suggesting that the investment
decision is probably a good one: it produces enough profit to compensate for
tying up capital and incurring risk with a little extra left over. When
investors and managers perform DCF analysis, the important thing is that the
net present value of the decision after discounting all future cash flows at
least be positive (more than zero). If it is negative, that means that the
investment decision would actually lose money even if it appears to
generate a nominal profit. For instance, if the expected sale price of John
Doe's house in the example above was not $150,000 in three years, but $130,000
in three years or $150,000 in five years, then on the above assumptions
buying the house would actually cause John to lose money in
present-value terms (about $3,000 in the first case, and about $8,000 in the
second). Similarly, if the house was located in an undesirable neighborhood and
the Federal Reserve Bank was about to raise
interest rates by five percentage points, then the risk factor would be a lot
higher than 5%: it might not be possible for him to predict a profit in
discounted terms even if he thinks he could sell the house for $200,000
in three years.
In this example, only one future cash
flow was considered. For a decision which generates multiple cash flows in
multiple time periods, all the cash flows must be discounted and then summed
into a single net present value.
References
2. O.E.H. Neugebaner,
The Exact Sciences in Antiquity (Copenhagen :Ejnar Mukaguard, 1951) p.33 (1969).
O.E.H. Neugebaner, The Exact Sciences in Antiquity (Copenhagen :Ejnar
Mukaguard, 1951) p.33. US: Dover Publications. p. 33. ISBN 0486223329.
3. Fisher, Irving.
"The theory of interest." New York 43 (1930).