# Four (4) Different Ways to Calculate DCF Based ‘Equity Cash Flow (ECF)’ – Part 1 of 4

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Over the next several days, I will present

**4 different methods**of correctly calculating

**Equity Cash Flow (ECF)**using

**R**. The valuation technique of discounted cash flow (

**DCF**) estimates equity value (

**E**) as the present value of forecasted

**ECF**. The appropriate discount rate for this flow definition is the cost of equity capital (

**Ke**).

**‘ECF – Method 1’**is defined as follows:

where

Note:

**ECF**is not simply ‘dividends.’ A common misconception is that discounted dividends (

**DIV**) provide equity value. An example of this is the common ‘dividend growth’ equity valuation model found in many corporate finance texts. All ‘dividend growth’ models that discount dividends (

**DIV**) at the cost of equity capital (

**Ke**) are incorrect unless forecasted

**1)**marketable securities (

**MS**) balances are zero, and

**2)**there is no

**issuance**or

**repurchase**of equity shares.

The data assumes a

**5-year year**hypothetical

**capital project**. A single

**revenue producing asset**is purchased at the end of ‘

**Year 0**‘ and is sold at the end of ‘

**Year 5**.’ The

**$500,000**asset is purchased assuming

**50% debt**and

**50% equity**financing.

Further, the data used to estimate

**ECF**in this example are taken from

**fully integrated pro forma financial statements**and other relevant data assumptions including the corporate tax rate. This particular example only requires financial data from integrated

**pro forma income statements**and

**balance sheets**. These 2 pro forma financial statements are shown below with the relevant data rows highlighted.

**https://www.dropbox.com/s/xwy97flxe99gqr9/financials.pdf?dl=0**

The above link provides access to a

The relevant data used to calculate

**ECF**are initially placed in a tibble.

library(tidyverse) data <- tibble(Year = c(0:5), div = c(0, 2379, 7068, 13102, 16295, 1249876), MS = c(0, 0, 7226, 350948, 698648, 0), ii = c(0, 0, 0, 253, 12283, 24453), pic = c(250000, 250000, 250000, 250000, 250000, 0), T_ = c(0.25, 0.40, 0.40, 0.40, 0.40, 0.40)) data

An

**R**function is created to rotate the data in standard financial data presentation format (each data line item occupies a single row instead of a column)

rotate <- function(r) { p <- t(as.matrix(as_tibble(r))) return(p) }

**View the rotated data**.

rotate(data)

An

**R**function reads in the appropriate data, performs the necessary calculations, and outputs the data. The

**R**output is then placed in a spreadsheet to formatting purposes.

**‘ECF – Method 1’ R function**

ECF_1 <- function(a) { ECF1 <- tibble( T_ = a$T_, pic = a$pic, chg_pic = pic - lag(pic, default=0), MS = a$MS, ii = a$ii, Year = c(0:(length(T_)-1)), div = a$div, net_new_equity = -chg_pic, chg_MS = MS - lag(MS, default=0), ii_AT = -ii*(1-T_), ECF1 = div + net_new_equity + chg_MS + ii_AT ) ECF1 <- rotate(ECF1) return(ECF1) }

**View R Output**

ECF_method_1 <- ECF_1( data) ECF_method_1

**Excel formatting applied to R Output**

It is quite evident there is far more than just dividends (

**DIV**) involved in the proper calculation of

**ECF**. Use of a

**‘dividend growth’ equity valuation model**in this instance would result in

**significant**

**model error**.

This

**ECF**calculation example is taken from my newly published textbook, ‘

**Advanced Discounted Cash Flow (DCF) Valuation using R**.’ It is discussed in far greater detail along with development of the integrated financials using

**R**as well as numerous, advanced

**DCF**valuation modeling approaches – some never before published.

Reference my website for further details.

**https://www.leewacc.com/**

Next up, ‘ECF – Method 2’ …

Brian K. Lee, MBA, PRM, CMA, CFA

Next up, ‘ECF – Method 2’ …

Brian K. Lee, MBA, PRM, CMA, CFA

Four (4) Different Ways to Calculate DCF Based ‘Equity Cash Flow (ECF)’ – Part 1 of 4 was first posted on June 14, 2021 at 6:10 pm.

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