Discounted Cash Flow Analysis in 8 Steps

1. Develop an understanding of the Discounted Cash Flow (DCF) techniques in making capital investment and other financial decisions.

2. Practicing the DCF technique using a prepared Excel spreadsheet.

3. Practicing changing assumptions in an analysis in preparing “what it” analyses.

4. Gain experience using the Quantitative Literacy Checklist in understanding these
concepts.

I. The Eight Step Process for Preparing a DCF Analysis

A. Preparing a discounted cash flow analysis takes eight steps. As shown
here, both the Net Present Value and Internal Rate of Return are computed,
although some organizations compute only one or the other.

B. Step 1: Choose the time period involved in the investment
alternative.

1. When choosing the time period you will typically consider two
variables. The first variable is the length of time of the investment. For a
piece of equipment, it is usually the life of the equipment. After a period of
years, the equipment may be sold at which time the project is complete
and the final year will include the cash flow from the sale.

2. The second variable is to determine the number of periods in which
to divide the time. It is most common to use the number of years,
especially in analyzing projects that will last many years. One could use
months or quarters in analyzing investments, and this might be
appropriate with a financial security such as a bond. Using months or
quarters for equipment or project analysis, however, becomes unwieldy. It
is common to use timing of annual cash flows with the additional
assumption that the flow will occur at the end of the year. Flows in reality
will occur throughout the year; however the year end convention is
common and yields reasonably good results.

C. Step 2: Determine the cash flows involved.

1. Cash flows come in two general types: Inflows, or cash being
received; and outflows, or cash being expended or invested. Note that a
project that is expected to save expenses treats those savings as a cash
inflow.

2. Flows over time might be either as a single sum or as a series.
Thus, there are four typical patterns of cash flow for any investment.
a) Out In
b) Out Out Out Out . . . In
c) Out In In In . . .
d) Out Out Out Out . . . In In In . . .

3. The first out flow, if done today, in the present, is made in period
“0″. Subsequent flows will be noted in the subsequent periods.
D. Step 3: Determine the Net Cash Flow
1. This is determined by summing all of the net inflows and subtracting
the net outflows from these. To keep these amounts organized it is
common to treat all inflows as a positive number, and all outflows as a
negative number.

2. The end result is a series of net cash flow by period, starting with
period 0 and ending with the final period of the project; not one number,
but a series of numbers; one for each period.

E. Step 4: Select a discount rate in which to discount the future cash
flows to the present.

1. The discount rate is the “hurdle rate”, that is, the rate at which the
organization will place on this project so that if it “clears” this rate (as a
runner in track might clear a hurdle) the project will be deemed financially
attractive. If the project does not clear the parameters established by the
hurdle rate, the net present value of the project will be a negative number.
This will mean that the present value of all future inflows does not equal at
least the present value of the initial outflow, deeming the project financially
unattractive.

2. While a “hurdle rate” might vary by project depending on the amount of
risk involved, a common practice is to use an organization’s “cost of capital” as the discount rate. This cost of capital rate is the hypothetical
rate that must be earned on the investment such that the overall value of
the firm will not be changed. In for–profit companies it is a blend of the
amount of money it costs, net of taxes, to borrow cash (interest expense),
blended with the amount of money it costs associated with common stock.
(In this case it is a function of the dividends and stock appreciation
expected by the owners). In not–for–profits, because there is no stock, the
cost of capital is at least the cost of the organization’s debt, or the interest
rate on the debt it has.

3. Step 4c is not to worry about the rate selected in step 4a. There are
enough estimates involved in discounted cash flow analysis that the
selection of the rate is unlikely to make a significant impact on the
deciding the attractiveness of the investment as long as a reasonable rate
is used. Reasonable means no lower than the cost of the next dollar of
debt which would be paid.

F. Step 5: using the discount rate, compute the net present value of the
investment. This can be done in one of several ways.
1. Using a financial calculator, the net cash flows can be entered by year.
This method is long and tedious and is not particularly desirable. Still it
can be done, and somewhere in the instruction manual of the calculator is
a long explanation on how to accomplish this. Try it if you want to,
however, this is not recommended.

2. Using a financial present value table, the net present value of $1 can
be determined for each year. (You can also determine this using the
appropriate mathematical formula found in the text). Simply multiply this
factor by the net cash flow to get the discounted cash flow or that year.
Sum all of the years, including year 0 and the total will be the Net Present
Value.

3. Using a financial spreadsheet, both methods one and two can easily
be done. This is likely the most efficient way to do this task.
a) A spreadsheet such as Excel has NPV formulas which will
automatically compute the present value of a stream of cash flows
at a given discount rate.
b) The spreadsheet can also compute the appropriate discount
factors by year, multiply them by each year’s net cash flow, and
sum them to arrive at the net present value. If the spreadsheet is done appropriately, both methods can be done with the longer

manual calculations being done as a check.
G. Step 6: Determine if the sum of each year’s discounted present
value.
1. If the Net Present Value is greater or less than 0, then the project
adds value to the organization. If less than 0, the project reduces the
value of the organization.
H. Step 7: Using the cash flows identified, determine what discount rate
would be appropriate in order to make the net present value equal to zero.
1. This value by definition is the Internal Rate of Return (IRR) of the
project or investment. “Internal” because it typically will be a project that
an organization might undertake by purchasing equipment and doing
something inside of the organization to produce a product for sale, or to
save costs; “Rate of Return” because it is an expression of an interest
rate which can equate the flows of the investment with that of an external
investment such a bond or bank account.
a) If the internal rate of return of the project is greater than the
hurdle rate, then you have a “winner”. If less, the project is a
“loser”. The spread between the IRR and the hurdle rate is the
“Computational Risk” associated with the selection of the discount
rate. The larger the spread, the less the discount rate selected has
to do with the generation of a positive NPV.
A great advantage of using spreadsheets, in addition to their accuracy,
speed, and ease of use once you know the basics, is the ability to perform
“what if” analysis. If one changes assumptions, what will be the new
results? This type of exercise is termed “sensitivity analysis” and is
valuable in gaining insight as to the level of impact of changes made.
I. Step 8: Reflect on your answers, assumptions, and process.
1. Using concepts introduced in the Quantitative Literacy
Rubric/Checklist used in this course, think about the various results you
have calculated. Do they appear reasonable? What assumptions went
into this analysis that may give you some concern? What conclusions can
you make from this analysis? How will you communicate these results to
others?
II. Other analytical values determined by DCF analysis
A. The DCF analysis yields two are values that are sometimes uses in
analyzing investments.
1. The first is the “Profitability Index”. This is an index used to
compare one investment alternative with others. Values above one are desirable, with the higher the value, the financially better the alternative.
a) The computation for the Profitability Index is to take the NPV
for all future cash flows and divide that by the value of the initial
investment.
b) The second is the “Payback Period”. This value measures
the time it takes to recoup the investment inflows to a level to equal
the initial investment. This time is normally measured in years, with
shorter payback period being better than longer ones. For this
analysis, traditional payback calculations use undiscounted cash
flows, which is a drawback as it does not take into account the time
value of money. An alternative is to use discounted cash flows to
determine a discounted payback period.
III. Discounted cash flow analysis is often used in two types of
analysis.
A. The analysis of a capital investment. An investment might be a financial
investment, such as a bond, or it might be a piece of equipment, project, or new
service line which includes a combination of equipment and operating expenses.
B. The analysis of financing options, particularly when confronted with the
decision of purchasing a piece of equipment or leasing it.
C. In both cases, the fundamental seven–step process can be used.
IV. An example of using the DCF Eight Step Process
A. Using the accompanying spreadsheet as a template, compute the net
present value (NPV), the internal rate of return (IRR), the Profitability Index, and
the Payback Period using discounted cash flows, for a project with these
assumptions:
1. The initial price of a piece of equipment we’ll call “Project A” will be
for $100,000.
2. Gross revenues associated with the program using this equipment
will be $60,000 each year for 5 years.
3. Net revenues associated with a program using this equipment will
be $40,000 each year for 5 years, thus the deductions from revenue year
will be $20,000.
4. Expenses will be $10,000 each year for 5 years.
5. The equipment will be sold for $10,000 after the end of the five
years.

B. Change these variables and note the new results:
1. Changing the purchase price from $100,000 to $110,000 yields
these values.
2. Keeping the $100,000 purchase price, and decreasing the discount
rate from 10% to 8% yields these values.
The answers are noted below as well as on separate tabs of the
accompanying Excel Spreadsheet.

7 DK 11/4/22 v1.0
Answers to Project A Base Problem:
Net Present Value (NPV) = $19,933
Internal Rate of Return (IRR) = 17.23%
Profitability Index = 1.20
Payback Period using discounted cash flows = 4.20 years
Answers to change 1 — Increasing purchase price by $10,000:
Net Present Value (NPV) = $9,933
Internal Rate of Return (IRR) = 13.34%
Profitability Index = 1.09
Payback Period using discounted cash flows = 4.60 years
Observation: Increasing the purchase price lowers the NPV; lowers the
IRR; decreases the Profitability Index; and lengthens the Payback Period.
Answers to change 2 — keeping original purchase price and decreasing
discount rate from 10% to 8%:
Net Present Value (NPV) = $26,587
Internal Rate of Return (IRR) = 17.23%
Profitability Index = 1.27
Payback Period using discounted cash flows = 4.02 years

Assumptions:
For your analysis assume that the Center uses a 7% discount rate for projects
of this risk level, and that they will initially use a five–year time horizon. This is a
tax–exempt not–for–profit organization so there will not be any income tax effects
to consider in the calculations.
The business after buying the equipment is expected to generate gross revenues
of $140,000 each year in the first two years and is expected to be $190,000 each
year in the next two years, followed by $240,000 in the fifth year. The services
will be paid for by third parties and there is a demand for this new service. Since
the third–party payers will pay less than the full charge, assume that deductions
from revenue to average 20% of gross revenues in each of the five years. The
equipment cost is $425,000 and will cost $45,000 to install. After five years the
equipment will be retired, and it is expected that it could be sold for $60,000.
The costs for the service include part–time staffing costs of $13,000 and supply
costs of $10,000 in each of the first two years. For the following two years,
salaries are expected to be $15,000 and supplies are estimated to be $13,000;
and in the last year five, salaries are expected to be $22,000 and supplies are
expected to be $18,000. The equipment is under warranty in the first year so
there is no extra fee paid. A maintenance contract costing $6,500 per year will
be paid in years 2 through 5.

Name: _____________________
2 DK 11/10/22 v2.0
Required:
1. Use the template spreadsheet and 8–step process to enter the above
assumptions in the appropriate cells.
2. Compute the Net Present Value of Future Cash Flows, and the Internal
Rate of Return. Highlight in yellow those two answers on your
spreadsheet. Note those answers in the table below so that they are
in both places.
3. Note at the bottom of the schedule whether this is an attractive project
from a purely financial point of view based upon the numbers that you
calculated on the spreadsheet. Why did you make that decision? Note
your answers in the table below so that they are in both places.
Optional Additional Point Opportunity:
Copy your spreadsheet tab with your answer and label the new tab “Six
Years”. Add a Year 6 column and assume that year six cash inflows and
outflows will be the same as year 5, with the exception that the equipment
will be sold for $40,000 at the end of year 6 instead of $60,000 at the end
of year 5. Adjust any formulas in the cells as appropriate caused by
the addition of a year 6. Compute the new Net Present value and
Internal Rate of Return for this six–year project. Highlight those answers in
yellow on your spreadsheet. Note those answers in the table below so
that they are in both places