The Discounted Cash Flow (DCF) Program uses the algorithm described in Internal Rate of Return Revisited.  I am pleased  to calculate and return cash flow data for noncommercial purposes.  It will save time and improve quality though if you submit your data in format.  If received in format, you can expect it back from the same session it is received.  DCF program output is in ASCII text readable by just about any word processor or spreadsheet.
 
Sample Problems

Sample problems are available for:
 

Input in Output Format

Table 1 illustrates DCF Program output for sample problem S05C.DCF.  If your browser supports it, required input data are underlined in red.  Optional administrative data are in green italics.  Calculated data are in a normal black fixed or variable font.
 

Table 2 below is spreadsheet input format.  Use any popular, reasonably current format and attach it to your E-mail.  Do not use commas or other non-numeric symbols.  No entry is required for zero.
 

Table 3.  DCF Program Spreadsheet Input

	A	B	C	D	E
1	S05C - Conflicting IRR/NPV	S05C.DC?
2	R. Martin
3	11-20-1997		Term Value:	0.0
4	(study period) 3	(period 1-9) 1	(discount method 1-3) 1
5		Expenditures	Revenues
6		1000		20
7			3600	20
8		4300		20
9			1760	20
10

 Notes are at the bottom of Table 3.

Cell B1 is an optional filename.  Use MS DOS file name conventions and a DC? extension.

Row 4 can be confusing.  Cell A4 is the number of study periods excluding period zero (0).  In this problem, 3 means years 0 through 3 or four years of data.  If you enter data (expenditure, revenue or a discount rate) in period 0, it will be incorportated, otherwise not.  Cell B4 is a number 1 through 9 inclusive, corresponding to data periods.  Number 1 is for annual; 9 is for daily,  See the Note at the bottom of Table 3 for 2 through 8.  Cell C4 is the discounting method.  It selects the equation used: 1 for End-of-(period), 2 for Continuous, and 3 for Middle-of-(period).

Cell D3 is the Terminal Value (TV), if any.  TV is calculated the same as the last period except that TV always uses End-of-(period) discounting regardless of the discount method selected.

Cells B6 through B9 are cash outflows (expenditures, payments, purchases, etc.).  These entries are subtracted to arrive at Net Cash Flow in Table 1.  Negative entries using a minus (-) sign are okay though and they will be added to arrive at Net Cash Flow.  Cells C6 through C9 are inflows (revenues, receipts, receipts, etc.).
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Cells D6 through D9 are periodic discount rates in percent.  They must be positive rates not greater than 999 percent.

Comma-Separated Value Input

Table 3 is comma-separated input format.  Either attach it to your E-mail or optionally include it as clear text in the body of your E-mail..  It may find it useful to copy the contents of Table 3 and replace the data with your own.  Make sure you have the required three commas per row and that your data are in the correct relative positon.  Blank spaces are no problem so long as numbers are intact..
 

1. The  Discounted Cash Flow program (DCF.EXE, MS DOS) calculates IRR to the specifications implicit in Internal Rate of Return Revisited. The files referred to in the paper are demonstration and sample files. Sample DCF files S05A.TXT through S05P.TXT provide the relevant calculations for the tables and figures in this paper. The other 49 groups of sample problems are listed in Table 1. IRR is the same rate solved for in virtually all time-value-of-money calculations.
2. Internal rate of either payment or outflow would be okay. Using the DCF program, total net cash flow, total discounted cash flow (NPV), and uniform periodic revenue with and without terminal value all show the direction of the flows (+/-). Also, "(outflow)" just before IRR indicates negative cash flows. IRR calculations cease and the reason printed if the program detects a noninterest or nonsense zone. NPV, on the other hand, is determined by the data entered. The DCF program deals only with positive rates from the point of view of either lender or borrower.
3. Discounting equations used:
End-of-(period):  1/(1+r)^I
Continuous:  (EXP(r)-1)/(r*EXP(r*I))
Middle-of-(period):  ((1/(1+r)^(I-1))+(1/(1+r)^(I)))/2
Where I is the period being evaluated, r is the discount rate, and EXP is the natural base e logarithm.  Rates are expressed in annual percent.
4. If the implied rate is close to 697.14 percent, such as 720 percent, the DCF program could settle on either of the two rates. Otherwise the DCF program will cease calculation and present the 697.14 percent IRR; e.g., it will not enter the nonsense zone. Multiple sign changes are flagged with a "(Sign +/-: n)," where n is the number of times signs changed.
5. The DCF program calculates the first (smallest) positive IRR possible, but operating only in the relevant range. If cash flows are net-negative, "(outflow)" is printed before the IRR in the DCF output report. It calculates the first IRR consistent with NPV converging on zero with an increasing discount rate. It ceases calculation and notifies you if it enters a noninterest/nonsense zone.
6. The DCF program attempts only to calculate an IRR up to 1,000 percent using annual discounting or proportionally greater using shorter periods. S05Q.TXT demonstrates a very high rate of return.

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