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All steps of the McKinsey model are outlined. Essential steps are: calculation
of free cash flow, forecasting of future accounting data (profit and loss accounts and
balance sheets), and discounting of free cash flow. There is particular emphasis on
forecasting those balance sheet items which relate to Property, Plant, and Equip-
ment. There is an exemplifying valuation included (of a company called McKay),
as an illustration

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A Tutorial on the McKinsey Model for

Valuation of Companies

L. Peter Jennergren ∗

Fourth revision, August 26, 2002

SSE/EFI Working Paper Series in Business Administration No. 1998:1

Abstract

All steps of the McKinsey model are outlined. Essential steps are: calculation

of free cash ﬂow, forecasting of future accounting data (proﬁt and loss accounts and

balance sheets), and discounting of free cash ﬂow. There is particular emphasis on

forecasting those balance sheet items which relate to Property, Plant, and Equip-

ment. There is an exemplifying valuation included (of a company called McKay),

as an illustration.

Key words: Valuation, free cash ﬂow, discounting, accounting data

JEL classiﬁcation: G31, M41, C60

∗Stockholm School of Economics, Box 6501, S - 11383 Stockholm, Sweden. The author is indebted to

Joakim Levin, Per Olsson, Kenth Skogsvik, and Tomas Hjelstr¨

om for discussions and comments. Minor

corrections made September 29, 2004, and February 9, 2005.

1

1

Introduction

This tutorial explains all the steps of the McKinsey valuation model, also referred to

as the discounted cash ﬂow model and described in Tom Copeland, Tim Koller, and Jack

Murrin: Valuation: Measuring and Managing the Value of Companies (Wiley, New York;

1st ed. 1990, 2nd ed. 1994, 3rd ed. 2000). The purpose is to enable the reader to set up a

complete valuation model of his/her own, at least for a company with a simple structure

(e. g., a company that does not consist of several business units and is not involved in

extensive foreign operations). The discussion proceeds by means of an extended valuation

example. The company that is subject to the valuation exercise is the McKay company.

The McKay example in this tutorial is somewhat similar to the Preston example (con-

cerning a trucking company) in Copeland et al. 1990, Copeland et al. 1994. However,

certain simpliﬁcations have been made, for easier understanding of the model. In par-

ticular, the capital structure of McKay is composed only of equity and debt (i. e., no

convertible bonds, etc.). The purpose of the McKay example is merely to present all

essential aspects of the McKinsey model as simply as possible. Some of the historical

income statement and balance sheet data have been taken from the Preston example.

However, the forecasted income statements and balance sheets are totally diﬀerent from

Preston’s. All monetary units are unspeciﬁed in this tutorial (in the Preston example in

Copeland et al. 1990, Copeland et al. 1994, they are millions of US dollars).

This tutorial is intended as a guided tour through one particular implementation of

the McKinsey model and should therefore be viewed only as exemplifying: This is one way

to set up a valuation model. Some modelling choices that have been made will be pointed

out later on. However, it should be noted right away that the speciﬁcation given below

of net Property, Plant, and Equipment (PPE) as driven by revenues is actually taken

from Copeland et al. 2000. The previous editions of this book contain two alternative

model speciﬁcations relating to investment in PPE (cf. Section 15 below; cf. also Levin

and Olsson 1995).

In one respect, this tutorial is an extension of Copeland et al. 2000: It contains a more

detailed discussion of capital expenditures, i. e., the mechanism whereby cash is absorbed

by investments in PPE. This mechanism centers on two particular forecast assumptions,

[this year’s net PPE/revenues] and [depreciation/last year’s net PPE].1 It is explained

below how those assumptions can be speciﬁed at least somewhat consistently.

On a

related note, the treatment of deferred income taxes is somewhat diﬀerent, and also more

detailed, compared to Copeland et al. 2000. In particular, deferred income taxes are

related to a forecast ratio [timing diﬀerences/this year’s net PPE], and it is suggested

how to set that ratio.

1Square brackets are used to indicate speciﬁc ratios that appear in tables in the spreadsheet ﬁle.

2

There is also another extension in this tutorial: An alternative valuation model is

included, too, the abnormal earnings model. That is, McKay is valued through that

model as well.

The McKay valuation is set up as a spreadsheet ﬁle in Excel named MCK 1.XLS.

That ﬁle is an integral part of this tutorial. The model consists of the following parts (as

can be seen by loading the ﬁle):

Table 1. Historical income statements,

Table 2. Historical balance sheets,

Table 3. Historical free cash ﬂow,

Table 4. Historical ratios for forecast assumptions,

Table 5. Forecasted income statements,

Table 6. Forecasted balance sheets,

Table 7. Forecasted free cash ﬂow,

Table 8. Forecast assumptions,

Value calculations.

Tables in the spreadsheet ﬁle and in the ﬁle printout that is included in this tutorial are

hence indicated by numerals, like Table 1. Tables in the tutorial text are indicated by

capital letters, like Table A.

The outline of this tutorial is as follows: Section 2 gives an overview of essential model

features. Section 3 summarizes the calculation of free cash ﬂow. Section 4 is an introduc-

tion to forecasting ﬁnancial statements and also discusses forecast assumptions relating

to operations and working capital. Sections 5, 6, and 7 deal with the speciﬁcation of

the forecast ratios [this year’s net PPE/revenues], [depreciation/last year’s net PPE], and

[retirements/last year’s net PPE]. Section 8 considers forecast assumptions about taxes.

Further forecast assumptions, relating to discount rates and ﬁnancing, are discussed in

Section 9. Section 10 outlines the construction of forecasted ﬁnancial statements and

free cash ﬂow, given that all forecast assumptions have been ﬁxed. Section 11 outlines a

slightly diﬀerent version of the McKay example, with another system for accounting for

deferred income taxes.2 The discounting procedure is explained in Section 12. Section 13

gives results from a sensitivity analysis, i. e., computed values of McKay’s equity when cer-

tain forecast assumptions are revised. Section 14 discusses the abnormal earnings model

and indicates how McKay’s equity can be valued by that model. Section 15 discusses

two further discounted cash ﬂow model versions, one of which may in a certain sense be

considered “exact”. The purpose is to get a feeling for the goodness of valuations derived

2This version of the McKay example is contained in the Excel ﬁle MCK 1B.XLS. A printout from that

ﬁle is also included in this tutorial. The two versions of the McKay example are equivalent as regards

cash ﬂow and resulting value. In other words, it is only the procedure for computing free cash ﬂow that

diﬀers (slightly) between them.

3

by means of the McKinsey model, in particular the sensitivity to changes in certain model

parameters. Section 16 contains concluding remarks. There are two appendices. Appen-

dix 1 discusses how a data base from Statistics Sweden can be used as an aid in specifying

parameters related to the forecast ratios [this year’s net PPE/revenues], [depreciation/last

year’s net PPE] and [retirements/last year’s net PPE]. Appendix 2 is a note on leasing.

The point is that payments associated with leases can be viewed as pertaining either to

the ﬁrm’s operations, or to its ﬁnancing. If one is consistent, both views lead to the same

valuation result. A similar remark also applies to payments associated with pensions.

2

Model Overview

Essential features of the McKinsey model are the following:

1. The model uses published accounting data as input. Historical income statements

and balance sheets are used to derive certain critical ﬁnancial ratios. Those historical

ratios are used as a starting point in making predictions for the same ratios in future

years.

2. The object of the McKinsey model is to value the equity of a going concern. Even so,

the asset side of the balance sheet is initially valued. The value of the interest-bearing debt

is then subtracted to get the value of the equity. Interest-bearing debt does not include

deferred income taxes and trade credit (accounts payable and other current liabilities).

Credit in the form of accounts payable is paid for not in interest but in higher operating

expenses (i. e., higher purchase prices of raw materials) and is therefore part of operations

rather than ﬁnancing. Deferred income taxes are viewed as part of equity; cf. Sections 9

and 10. It may seem like an indirect approach to value the assets and deduct interest-

bearing debt to arrive at the equity (i. e., it may seem more straight-forward to value

the equity directly, by discounting future expected dividends). However, this indirect

approach is the recommended one, since it leads to greater clarity and fewer errors in the

valuation process (cf. Copeland et al. 2000, pp. 150-152).

3. The value of the asset side is the value of operations plus excess marketable secu-

rities. The latter can usually be valued using book values or published market values.

Excess marketable securities include cash that is not necessary for operations. For valu-

ation purposes, the cash account may hence have to be divided into two parts, operating

cash (which is used for facilitating transactions relating to actual operations), and ex-

cess cash. (In the case of McKay, excess marketable securities have been netted against

interest-bearing debt at the date of valuation. Hence there are actually no excess mar-

ketable securities in the McKay valuation. This is one of the modelling choices that were

alluded to in the introduction.)

4. The operations of the ﬁrm, i. e., the total asset side minus excess marketable secu-

4

rities, are valued by the WACC method. In other words, free cash ﬂow from operations

is discounted to a present value using the WACC. There is then a simultaneity problem

(actually quite trivial) concerning the WACC. More precisely, the debt and equity values

enter into the WACC weights. However, equity value is what the model aims to determine.

5. The asset side valuation is done in two parts: Free cash ﬂow from operations is

forecasted for a number of individual years in the explicit forecast period. After that,

there is a continuing value derived from free cash ﬂow in the ﬁrst year of the post-horizon

period (and hence individual yearly forecasts must be made for each year in the explicit

forecast period and for one further year, the ﬁrst one immediately following the explicit

forecast period). The explicit forecast period should consist of at least 7 - 10 years (cf.

Copeland et al. 2000, p. 234). The explicit forecast period can be thought of as a transient

phase during a turn-around or after a take-over. The post-horizon period, on the other

hand, is characterized by steady-state development. This means that the explicit forecast

period should as a minimal requirement be suﬃciently long to capture transitory eﬀects,

e. g., during a turn-around operation.

6. For any future year, free cash ﬂow from operations is calculated from forecasted

income statements and balance sheets. This means that free cash ﬂow is derived from a

consistent scenario, deﬁned by forecasted ﬁnancial statements. This is probably the main

strength of the McKinsey model, since it is diﬃcult to make reasonable forecasts of free

cash ﬂow in a direct fashion. Financial statements are forecasted in nominal terms (which

implies that nominal free cash ﬂow is discounted using a nominal discount rate).

7. Continuing (post-horizon) value is computed through an inﬁnite discounting for-

mula. In this tutorial, the Gordon formula is used (cf. Brealey and Myers 2002, pp. 38

and 64-65). In other words, free cash ﬂow in the post-horizon period increases by some

constant percentage from year to year, hence satisfying a necessary condition for inﬁnite

discounting. (The Gordon formula is another one of the modelling choices made in this

tutorial.)

As can be inferred from this list of features, and as will be explained below, the

McKinsey model combines three rather diﬀerent tasks: The ﬁrst one is the production

of forecasted ﬁnancial statements. This is not trivial. In particular, it involves issues

relating to capital expenditures that are fairly complex. (The abnormal earnings model

uses forecasted ﬁnancial statements, just like the McKinsey model, so the ﬁrst task is

actually the same for that model as well).

The second task is deriving free cash ﬂow from operations from ﬁnancial statements.

At least in principle, this is rather trivial. In fairness, it is not always easy to calculate free

cash ﬂow from complicated historical income statements and balance sheets. However, all

ﬁnancial statements in this tutorial are very simple (and there is, in any case, no reason

to forecast accounting complexities if the purpose is one of valuation). The third task is

5

discounting forecasted free cash ﬂow to a present value. While not exactly trivial, this task

is nevertheless one that has been discussed extensively in the corporate ﬁnance literature,

so there is guidance available. This tutorial will explain the mechanics of discounting

in the McKinsey model. However, issues relating to how the relevant discount rates are

determined will largely be brushed aside. Instead, the reader is referred to standard text

books (for instance, Brealey and Myers 2002, chapters 9, 17, and 19).

3

Historical Financial Statements and the Calcula-

tion of Free Cash Flow

The valuation of McKay is as of Jan. 1 year 1. Historical input data are the income

statements and balance sheets for the years −6 to 0, Tables 1 and 2. Table 1 also includes

statements of retained earnings. It may be noted in Table 1 that operating expenses

do not include depreciation (i. e., operating expenses are cash costs). At the bottom of

Table 2, there are a couple of ﬁnancial ratio calculations based on historical data for the

given years. Short-term debt in the balance sheets (Table 2) is that portion of last year’s

long-term debt which matures within a year. It is clear from Tables 1 and 2 that McKay’s

ﬁnancial statements are very simple, and consequently the forecasted statements will also

have a simple structure. As already mentioned earlier, McKay has no excess marketable

securities in the last historical balance sheet, i. e., at the date of valuation.

From the data in Tables 1 and 2, historical free cash ﬂow for the years −5 to 0

is computed in Table 3. Each annual free cash ﬂow computation involves two balance

sheets, that of the present year and the previous one, so no free cash ﬂow can be obtained

for year −6. Essentially the same operations are used to forecast free cash ﬂow for

year 1 and later years (in Table 7). The free cash ﬂow calculations assume that the

clean surplus relationship holds. This implies that the change in book equity (including

retained earnings) equals net income minus net dividends (the latter could be negative,

if there is an issue of common equity). The clean surplus relationship does not hold,

if PPE is written down (or up) directly against common equity (for instance). Such

accounting operations may complicate the calculation of free cash ﬂow from historical

ﬁnancial statements (and if so, that calculation may not be trivial). However, there is no

reason to forecast deviations from the clean surplus relationship in a valuation situation.

EBIT in Table 3 means Earnings Before Interest and Taxes. NOPLAT means Net Op-

erating Proﬁts Less Adjusted Taxes. Taxes on EBIT consist of calculated taxes according

to the income statement (from Table 1) plus [this year’s tax rate]×(interest expense)

minus [this year’s tax rate]×(interest income). Interest income and interest expense are

taken from Table 1. The tax rate is given in Table 4. Calculated taxes according to the

income statement reﬂect depreciation of PPE over the economic life. Change in deferred

6

income taxes is this year’s deferred income taxes minus last year’s deferred income taxes.

In the McKay valuation example, it is assumed that deferred income taxes come about

for one reason only, timing diﬀerences in depreciation of PPE. That is, ﬁscal depreciation

takes place over a period shorter than the economic life.

Working capital is deﬁned net. Hence, working capital consists of the following balance

sheet items: Operating cash plus trade receivables plus other receivables plus inventories

plus prepaid expenses minus accounts payable minus other current liabilities. Accounts

payable and other current liabilities are apparently considered to be part of the operations

of the ﬁrm, not part of the ﬁnancing (they are not interest-bearing debt items). Change

in working capital in Table 3 is hence this year’s working capital minus last year’s working

capital. Capital expenditures are this year’s net PPE minus last year’s net PPE plus this

year’s depreciation. Depreciation is taken from Table 1, net PPE from Table 2. It should

be emphasized that depreciation in Table 1 (and forecasted depreciation in Table 5) is

according to plan, over the economic life of the PPE.

Free cash ﬂow in Table 3 is hence cash generated by the operations of the ﬁrm, after

paying taxes on operations only, and after expenditures for additional working capital and

after capital expenditures. (“Additional working capital” could of course be negative. If

so, free cash ﬂow is generated rather than absorbed by working capital.) Hence, free cash

ﬂow represents cash that is available for distribution to the holders of debt and equity in

the ﬁrm, and for investment in additional excess marketable securities. Stated somewhat

diﬀerently, free cash ﬂow is equal to ﬁnancial cash ﬂow, which is the utilization of free

cash ﬂow for ﬁnancial purposes. Table 3 also includes a break-down of ﬁnancial cash ﬂow.

By deﬁnition, free cash ﬂow must be exactly equal to ﬁnancial cash ﬂow.

As suggested in the introduction (Section 1), certain payments may be classiﬁed as

pertaining either to free cash ﬂow (from operations), or to ﬁnancial cash ﬂow. In other

words, those payments may be thought of as belonging either to the operations or the

ﬁnancing of the ﬁrm. This holds, in particular, for payments associated with capital

leases. If one is consistent, the resulting valuation should of course not depend on that

classiﬁcation. This issue is further discussed in Appendix 2.

We now return brieﬂy to the ﬁnancial ratios at the end of Table 2. Invested capi-

tal is equal to working capital plus net PPE. Debt at the end of Table 2 in the ratio

[debt/invested capital] is interest-bearing (short-term and long-term). The ﬁnancial ratio

[NOPLAT/invested capital] is also referred to as ROIC (Return on Invested Capital). It

is a better analytical tool for understanding the company’s performance than other return

measures such as return on equity or return on assets, according to Copeland et al. (2000,

pp. 165-166). Invested capital in the ratio [NOPLAT/invested capital] is the average of

last year’s and this year’s. It is seen that McKay has on average provided a fairly modest

rate of return in recent years. It can also be seen from Table 3 that the free cash ﬂow has

7

been negative, and that the company has handled this situation by increasing its debt.

It is also evident from the bottom of Table 2 that the ratio of interest-bearing debt to

invested capital has increased substantially from year −6 to year 0.

Table 4 contains a set of historical ﬁnancial ratios. Those ratios are important, since

forecasts of the same ratios will be used to produce forecasted income statements and

balance sheets. Most of the items in Table 4 are self-explanatory, but a few observations

are called for. Net PPE (which is taken from Table 2) enters into four ratios. In two of

those cases, [depreciation/net PPE] and [retirements/net PPE], the net PPE in question

is last year’s. In the other two cases, [net PPE/revenues] and [timing diﬀerences/net

PPE], the net PPE in question is this year’s. Retirements are deﬁned as depreciation

minus change in accumulated depreciation between this year and last year (accumulated

depreciation is taken from Table 2). This must hold, since last year’s accumulated de-

preciation plus this year’s depreciation minus this year’s retirements equals this year’s

accumulated depreciation.

The timing diﬀerences for a given year are measured between accumulated ﬁscal depre-

ciation of PPE and accumulated depreciation according to PPE economic life. For a given

piece of PPE that is about to be retired, accumulated ﬁscal depreciation and accumulated

depreciation according to economic life are both equal to the original acquisition value.

Consequently, non-zero timing diﬀerences are related to non-retired PPE only. The ratio

[timing diﬀerences/net PPE] in Table 4 has been calculated by ﬁrst dividing the deferred

income taxes for a given year by the same year’s corporate tax rate (also given in Table

4). This gives that year’s timing diﬀerences. After that, there is a second division by that

year’s net PPE.

4

Forecast Assumptions Relating to Operations and

Working Capital

Having recorded the historical performance of McKay in Tables 1 - 4, we now turn

to the task of forecasting free cash ﬂow for years 1 and later. Individual free cash ﬂow

forecasts are produced for each year 1 to 12. The free cash ﬂow amounts for years 1 to

11 are discounted individually to a present value. The free cash ﬂow for year 12 and all

later years is discounted through the Gordon formula, with the free cash ﬂow in year 12

as a starting value. Years 1 to 11 are therefore the explicit forecast period, and year 12

and all later years the post-horizon period.

Tables 5 - 8 have the same format as Tables 1 - 4. In fact, Table 5 may be seen as

a continuation of Table 1, Table 6 as a continuation of Table 2, and so on. We start

the forecasting job by setting up Table 8, the forecast assumptions. Using assumptions

(ﬁnancial ratios and others) in that table, and using a couple of further direct forecasts

8

of individual items, we can set up the forecasted income statements, Table 5, and the

forecasted balance sheets, Table 6. From Tables 5 and 6, we can then in Table 7 derive

the forecasted free cash ﬂow (just like we derived the historical free cash ﬂow in Table 3,

using information in Tables 1 and 2).

Consider now the individual items in Table 8. It should be noted in Table 8 that all

items are the same for year 12, the ﬁrst year of the post-horizon period, as for year 11,

the last year of the explicit forecast period. Since the ﬁrst year in the post-horizon period

is representative of all subsequent post-horizon years, all items are the same for every

post-horizon year as for the last year of the explicit forecast period. This is actually an

important condition (cf. Levin and Olsson 1995, p. 38): If that condition holds, then free

cash ﬂow increases by the same percentage (the nominal revenue growth rate for year

12 in Table 8, cell T137) between all successive years in the post-horizon period. This

means that a necessary condition for discounting by means of the Gordon formula in the

post-horizon period is satisﬁed.

The revenue growth in each future year is seen to be a combination of inﬂation and real

growth. Actually, in years 10 and 11 there is no real growth, and the same assumption

holds for all later years as well (in the application of the Gordon formula). The underlying

assumption in Table 8 is apparently that real operations will initially expand but will

eventually (in year 10) settle down to a steady state with no further real growth. Inﬂation,

on the other hand, is assumed to be 3% in all coming years (including after year 11). The

ratio of operating expenses to revenues is assumed to improve immediately, e. g., as a

consequence of a determined turn-around eﬀort. Apparently, it is set to 90% year 1

and all later years. To avoid misunderstandings, this forecast assumption (and the other

ones displayed in Table 8) are not necessarily intended to be the most realistic ones that

can be imagined. The purpose is merely to demonstrate the mechanics of the McKinsey

model for one particular scenario. A table in Levin and Olsson 1995 (p. 124; based on

accounting data from Statistics Sweden) contains information about typical values of the

ratio between operating expenses and revenues in various Swedish industries (cf. also

Appendix 1 for a further discussion of the Statistics Sweden data base).

A number of items in the forecasted income statements and balance sheets are di-

rectly driven by revenues. That is, those items are forecasted as percentages of revenues.

In particular, this holds for the working capital items. It is thus assumed that as rev-

enues increase, the required amounts of working capital of diﬀerent categories increase

correspondingly. It is not important whether revenues increase due to inﬂation or real

growth, or a combination of both. Working capital turns over very quickly, and therefore

it is a reasonable assumption that the working capital items are simply proportional to

revenues. The ratios between the diﬀerent categories of working capital and revenues for

future years in Table 8 have been set equal to the average values of the corresponding

9

historical percentages in Table 4. Again, this is only for illustrative purposes. Another

table in Levin and Olsson 1995 (p. 125), again based on data from Statistics Sweden,

reports average values of the ratio between (aggregate) working capital and revenues in

diﬀerent Swedish industries.

5

Forecast Assumptions Relating to Property, Plant,

and Equipment

The forecast assumptions relating to PPE will be considered next (this section and

the following two). The equations that determine capital expenditures may be stated as

follows (subscripts denote years):

(capital expenditures)t = (net PPE)t − (net PPE)t−1 + depreciationt,

(net PPE)t = revenuest × [this year’s net PPE/revenues],

depreciationt = (net PPE)t−1 × [depreciation/last year’s net PPE].

To this set of equations, we may add three more that are actually not necessary for the

model:

retirementst = (net PPE)t−1 × [retirements/last year’s net PPE],

(accumulated depreciation)t

= (accumulated depreciation)t−1 + depreciationt − retirementst,

(gross PPE)t = (net PPE)t + (accumulated depreciation)t.

In particular, this second set of three equations is needed only if one wants to produce

forecasted balance sheets showing how net PPE is related to gross PPE minus accumulated

depreciation. It should be noted that such detail is not necessary, since the ﬁrst set of

three equations suﬃces for determining net PPE, depreciation, and consequently also

capital expenditures.3

It is clear from the ﬁrst three equations that forecasts have to be made for two partic-

ular ratios, [this year’s net PPE/revenues] and [depreciation/last year’s net PPE]. Setting

those ratios in a consistent fashion involves somewhat technical considerations. In this

section and the following one, one way of proceeding, consistent with the idea of the

company developing in a steady-state fashion in the post-horizon period, will be outlined.

To begin with, the idea of the company developing in a steady-state fashion has to

be made more precise. As indicated in Section 4, the forecast assumptions should be

3If the historical ﬁnancial statements do not show gross PPE and accumulated depreciation, only net

PPE, then it seems pointless to try to include these items in the forecasted ﬁnancial statements. If so,

the second set of three equations is deleted. In the McKay case, the historical statements do indicate

gross PPE and accumulated depreciation. For that (aesthetic) reason, those items will also be included

in the forecasted statements.

10

Valuation of Companies

L. Peter Jennergren ∗

Fourth revision, August 26, 2002

SSE/EFI Working Paper Series in Business Administration No. 1998:1

Abstract

All steps of the McKinsey model are outlined. Essential steps are: calculation

of free cash ﬂow, forecasting of future accounting data (proﬁt and loss accounts and

balance sheets), and discounting of free cash ﬂow. There is particular emphasis on

forecasting those balance sheet items which relate to Property, Plant, and Equip-

ment. There is an exemplifying valuation included (of a company called McKay),

as an illustration.

Key words: Valuation, free cash ﬂow, discounting, accounting data

JEL classiﬁcation: G31, M41, C60

∗Stockholm School of Economics, Box 6501, S - 11383 Stockholm, Sweden. The author is indebted to

Joakim Levin, Per Olsson, Kenth Skogsvik, and Tomas Hjelstr¨

om for discussions and comments. Minor

corrections made September 29, 2004, and February 9, 2005.

1

1

Introduction

This tutorial explains all the steps of the McKinsey valuation model, also referred to

as the discounted cash ﬂow model and described in Tom Copeland, Tim Koller, and Jack

Murrin: Valuation: Measuring and Managing the Value of Companies (Wiley, New York;

1st ed. 1990, 2nd ed. 1994, 3rd ed. 2000). The purpose is to enable the reader to set up a

complete valuation model of his/her own, at least for a company with a simple structure

(e. g., a company that does not consist of several business units and is not involved in

extensive foreign operations). The discussion proceeds by means of an extended valuation

example. The company that is subject to the valuation exercise is the McKay company.

The McKay example in this tutorial is somewhat similar to the Preston example (con-

cerning a trucking company) in Copeland et al. 1990, Copeland et al. 1994. However,

certain simpliﬁcations have been made, for easier understanding of the model. In par-

ticular, the capital structure of McKay is composed only of equity and debt (i. e., no

convertible bonds, etc.). The purpose of the McKay example is merely to present all

essential aspects of the McKinsey model as simply as possible. Some of the historical

income statement and balance sheet data have been taken from the Preston example.

However, the forecasted income statements and balance sheets are totally diﬀerent from

Preston’s. All monetary units are unspeciﬁed in this tutorial (in the Preston example in

Copeland et al. 1990, Copeland et al. 1994, they are millions of US dollars).

This tutorial is intended as a guided tour through one particular implementation of

the McKinsey model and should therefore be viewed only as exemplifying: This is one way

to set up a valuation model. Some modelling choices that have been made will be pointed

out later on. However, it should be noted right away that the speciﬁcation given below

of net Property, Plant, and Equipment (PPE) as driven by revenues is actually taken

from Copeland et al. 2000. The previous editions of this book contain two alternative

model speciﬁcations relating to investment in PPE (cf. Section 15 below; cf. also Levin

and Olsson 1995).

In one respect, this tutorial is an extension of Copeland et al. 2000: It contains a more

detailed discussion of capital expenditures, i. e., the mechanism whereby cash is absorbed

by investments in PPE. This mechanism centers on two particular forecast assumptions,

[this year’s net PPE/revenues] and [depreciation/last year’s net PPE].1 It is explained

below how those assumptions can be speciﬁed at least somewhat consistently.

On a

related note, the treatment of deferred income taxes is somewhat diﬀerent, and also more

detailed, compared to Copeland et al. 2000. In particular, deferred income taxes are

related to a forecast ratio [timing diﬀerences/this year’s net PPE], and it is suggested

how to set that ratio.

1Square brackets are used to indicate speciﬁc ratios that appear in tables in the spreadsheet ﬁle.

2

There is also another extension in this tutorial: An alternative valuation model is

included, too, the abnormal earnings model. That is, McKay is valued through that

model as well.

The McKay valuation is set up as a spreadsheet ﬁle in Excel named MCK 1.XLS.

That ﬁle is an integral part of this tutorial. The model consists of the following parts (as

can be seen by loading the ﬁle):

Table 1. Historical income statements,

Table 2. Historical balance sheets,

Table 3. Historical free cash ﬂow,

Table 4. Historical ratios for forecast assumptions,

Table 5. Forecasted income statements,

Table 6. Forecasted balance sheets,

Table 7. Forecasted free cash ﬂow,

Table 8. Forecast assumptions,

Value calculations.

Tables in the spreadsheet ﬁle and in the ﬁle printout that is included in this tutorial are

hence indicated by numerals, like Table 1. Tables in the tutorial text are indicated by

capital letters, like Table A.

The outline of this tutorial is as follows: Section 2 gives an overview of essential model

features. Section 3 summarizes the calculation of free cash ﬂow. Section 4 is an introduc-

tion to forecasting ﬁnancial statements and also discusses forecast assumptions relating

to operations and working capital. Sections 5, 6, and 7 deal with the speciﬁcation of

the forecast ratios [this year’s net PPE/revenues], [depreciation/last year’s net PPE], and

[retirements/last year’s net PPE]. Section 8 considers forecast assumptions about taxes.

Further forecast assumptions, relating to discount rates and ﬁnancing, are discussed in

Section 9. Section 10 outlines the construction of forecasted ﬁnancial statements and

free cash ﬂow, given that all forecast assumptions have been ﬁxed. Section 11 outlines a

slightly diﬀerent version of the McKay example, with another system for accounting for

deferred income taxes.2 The discounting procedure is explained in Section 12. Section 13

gives results from a sensitivity analysis, i. e., computed values of McKay’s equity when cer-

tain forecast assumptions are revised. Section 14 discusses the abnormal earnings model

and indicates how McKay’s equity can be valued by that model. Section 15 discusses

two further discounted cash ﬂow model versions, one of which may in a certain sense be

considered “exact”. The purpose is to get a feeling for the goodness of valuations derived

2This version of the McKay example is contained in the Excel ﬁle MCK 1B.XLS. A printout from that

ﬁle is also included in this tutorial. The two versions of the McKay example are equivalent as regards

cash ﬂow and resulting value. In other words, it is only the procedure for computing free cash ﬂow that

diﬀers (slightly) between them.

3

by means of the McKinsey model, in particular the sensitivity to changes in certain model

parameters. Section 16 contains concluding remarks. There are two appendices. Appen-

dix 1 discusses how a data base from Statistics Sweden can be used as an aid in specifying

parameters related to the forecast ratios [this year’s net PPE/revenues], [depreciation/last

year’s net PPE] and [retirements/last year’s net PPE]. Appendix 2 is a note on leasing.

The point is that payments associated with leases can be viewed as pertaining either to

the ﬁrm’s operations, or to its ﬁnancing. If one is consistent, both views lead to the same

valuation result. A similar remark also applies to payments associated with pensions.

2

Model Overview

Essential features of the McKinsey model are the following:

1. The model uses published accounting data as input. Historical income statements

and balance sheets are used to derive certain critical ﬁnancial ratios. Those historical

ratios are used as a starting point in making predictions for the same ratios in future

years.

2. The object of the McKinsey model is to value the equity of a going concern. Even so,

the asset side of the balance sheet is initially valued. The value of the interest-bearing debt

is then subtracted to get the value of the equity. Interest-bearing debt does not include

deferred income taxes and trade credit (accounts payable and other current liabilities).

Credit in the form of accounts payable is paid for not in interest but in higher operating

expenses (i. e., higher purchase prices of raw materials) and is therefore part of operations

rather than ﬁnancing. Deferred income taxes are viewed as part of equity; cf. Sections 9

and 10. It may seem like an indirect approach to value the assets and deduct interest-

bearing debt to arrive at the equity (i. e., it may seem more straight-forward to value

the equity directly, by discounting future expected dividends). However, this indirect

approach is the recommended one, since it leads to greater clarity and fewer errors in the

valuation process (cf. Copeland et al. 2000, pp. 150-152).

3. The value of the asset side is the value of operations plus excess marketable secu-

rities. The latter can usually be valued using book values or published market values.

Excess marketable securities include cash that is not necessary for operations. For valu-

ation purposes, the cash account may hence have to be divided into two parts, operating

cash (which is used for facilitating transactions relating to actual operations), and ex-

cess cash. (In the case of McKay, excess marketable securities have been netted against

interest-bearing debt at the date of valuation. Hence there are actually no excess mar-

ketable securities in the McKay valuation. This is one of the modelling choices that were

alluded to in the introduction.)

4. The operations of the ﬁrm, i. e., the total asset side minus excess marketable secu-

4

rities, are valued by the WACC method. In other words, free cash ﬂow from operations

is discounted to a present value using the WACC. There is then a simultaneity problem

(actually quite trivial) concerning the WACC. More precisely, the debt and equity values

enter into the WACC weights. However, equity value is what the model aims to determine.

5. The asset side valuation is done in two parts: Free cash ﬂow from operations is

forecasted for a number of individual years in the explicit forecast period. After that,

there is a continuing value derived from free cash ﬂow in the ﬁrst year of the post-horizon

period (and hence individual yearly forecasts must be made for each year in the explicit

forecast period and for one further year, the ﬁrst one immediately following the explicit

forecast period). The explicit forecast period should consist of at least 7 - 10 years (cf.

Copeland et al. 2000, p. 234). The explicit forecast period can be thought of as a transient

phase during a turn-around or after a take-over. The post-horizon period, on the other

hand, is characterized by steady-state development. This means that the explicit forecast

period should as a minimal requirement be suﬃciently long to capture transitory eﬀects,

e. g., during a turn-around operation.

6. For any future year, free cash ﬂow from operations is calculated from forecasted

income statements and balance sheets. This means that free cash ﬂow is derived from a

consistent scenario, deﬁned by forecasted ﬁnancial statements. This is probably the main

strength of the McKinsey model, since it is diﬃcult to make reasonable forecasts of free

cash ﬂow in a direct fashion. Financial statements are forecasted in nominal terms (which

implies that nominal free cash ﬂow is discounted using a nominal discount rate).

7. Continuing (post-horizon) value is computed through an inﬁnite discounting for-

mula. In this tutorial, the Gordon formula is used (cf. Brealey and Myers 2002, pp. 38

and 64-65). In other words, free cash ﬂow in the post-horizon period increases by some

constant percentage from year to year, hence satisfying a necessary condition for inﬁnite

discounting. (The Gordon formula is another one of the modelling choices made in this

tutorial.)

As can be inferred from this list of features, and as will be explained below, the

McKinsey model combines three rather diﬀerent tasks: The ﬁrst one is the production

of forecasted ﬁnancial statements. This is not trivial. In particular, it involves issues

relating to capital expenditures that are fairly complex. (The abnormal earnings model

uses forecasted ﬁnancial statements, just like the McKinsey model, so the ﬁrst task is

actually the same for that model as well).

The second task is deriving free cash ﬂow from operations from ﬁnancial statements.

At least in principle, this is rather trivial. In fairness, it is not always easy to calculate free

cash ﬂow from complicated historical income statements and balance sheets. However, all

ﬁnancial statements in this tutorial are very simple (and there is, in any case, no reason

to forecast accounting complexities if the purpose is one of valuation). The third task is

5

discounting forecasted free cash ﬂow to a present value. While not exactly trivial, this task

is nevertheless one that has been discussed extensively in the corporate ﬁnance literature,

so there is guidance available. This tutorial will explain the mechanics of discounting

in the McKinsey model. However, issues relating to how the relevant discount rates are

determined will largely be brushed aside. Instead, the reader is referred to standard text

books (for instance, Brealey and Myers 2002, chapters 9, 17, and 19).

3

Historical Financial Statements and the Calcula-

tion of Free Cash Flow

The valuation of McKay is as of Jan. 1 year 1. Historical input data are the income

statements and balance sheets for the years −6 to 0, Tables 1 and 2. Table 1 also includes

statements of retained earnings. It may be noted in Table 1 that operating expenses

do not include depreciation (i. e., operating expenses are cash costs). At the bottom of

Table 2, there are a couple of ﬁnancial ratio calculations based on historical data for the

given years. Short-term debt in the balance sheets (Table 2) is that portion of last year’s

long-term debt which matures within a year. It is clear from Tables 1 and 2 that McKay’s

ﬁnancial statements are very simple, and consequently the forecasted statements will also

have a simple structure. As already mentioned earlier, McKay has no excess marketable

securities in the last historical balance sheet, i. e., at the date of valuation.

From the data in Tables 1 and 2, historical free cash ﬂow for the years −5 to 0

is computed in Table 3. Each annual free cash ﬂow computation involves two balance

sheets, that of the present year and the previous one, so no free cash ﬂow can be obtained

for year −6. Essentially the same operations are used to forecast free cash ﬂow for

year 1 and later years (in Table 7). The free cash ﬂow calculations assume that the

clean surplus relationship holds. This implies that the change in book equity (including

retained earnings) equals net income minus net dividends (the latter could be negative,

if there is an issue of common equity). The clean surplus relationship does not hold,

if PPE is written down (or up) directly against common equity (for instance). Such

accounting operations may complicate the calculation of free cash ﬂow from historical

ﬁnancial statements (and if so, that calculation may not be trivial). However, there is no

reason to forecast deviations from the clean surplus relationship in a valuation situation.

EBIT in Table 3 means Earnings Before Interest and Taxes. NOPLAT means Net Op-

erating Proﬁts Less Adjusted Taxes. Taxes on EBIT consist of calculated taxes according

to the income statement (from Table 1) plus [this year’s tax rate]×(interest expense)

minus [this year’s tax rate]×(interest income). Interest income and interest expense are

taken from Table 1. The tax rate is given in Table 4. Calculated taxes according to the

income statement reﬂect depreciation of PPE over the economic life. Change in deferred

6

income taxes is this year’s deferred income taxes minus last year’s deferred income taxes.

In the McKay valuation example, it is assumed that deferred income taxes come about

for one reason only, timing diﬀerences in depreciation of PPE. That is, ﬁscal depreciation

takes place over a period shorter than the economic life.

Working capital is deﬁned net. Hence, working capital consists of the following balance

sheet items: Operating cash plus trade receivables plus other receivables plus inventories

plus prepaid expenses minus accounts payable minus other current liabilities. Accounts

payable and other current liabilities are apparently considered to be part of the operations

of the ﬁrm, not part of the ﬁnancing (they are not interest-bearing debt items). Change

in working capital in Table 3 is hence this year’s working capital minus last year’s working

capital. Capital expenditures are this year’s net PPE minus last year’s net PPE plus this

year’s depreciation. Depreciation is taken from Table 1, net PPE from Table 2. It should

be emphasized that depreciation in Table 1 (and forecasted depreciation in Table 5) is

according to plan, over the economic life of the PPE.

Free cash ﬂow in Table 3 is hence cash generated by the operations of the ﬁrm, after

paying taxes on operations only, and after expenditures for additional working capital and

after capital expenditures. (“Additional working capital” could of course be negative. If

so, free cash ﬂow is generated rather than absorbed by working capital.) Hence, free cash

ﬂow represents cash that is available for distribution to the holders of debt and equity in

the ﬁrm, and for investment in additional excess marketable securities. Stated somewhat

diﬀerently, free cash ﬂow is equal to ﬁnancial cash ﬂow, which is the utilization of free

cash ﬂow for ﬁnancial purposes. Table 3 also includes a break-down of ﬁnancial cash ﬂow.

By deﬁnition, free cash ﬂow must be exactly equal to ﬁnancial cash ﬂow.

As suggested in the introduction (Section 1), certain payments may be classiﬁed as

pertaining either to free cash ﬂow (from operations), or to ﬁnancial cash ﬂow. In other

words, those payments may be thought of as belonging either to the operations or the

ﬁnancing of the ﬁrm. This holds, in particular, for payments associated with capital

leases. If one is consistent, the resulting valuation should of course not depend on that

classiﬁcation. This issue is further discussed in Appendix 2.

We now return brieﬂy to the ﬁnancial ratios at the end of Table 2. Invested capi-

tal is equal to working capital plus net PPE. Debt at the end of Table 2 in the ratio

[debt/invested capital] is interest-bearing (short-term and long-term). The ﬁnancial ratio

[NOPLAT/invested capital] is also referred to as ROIC (Return on Invested Capital). It

is a better analytical tool for understanding the company’s performance than other return

measures such as return on equity or return on assets, according to Copeland et al. (2000,

pp. 165-166). Invested capital in the ratio [NOPLAT/invested capital] is the average of

last year’s and this year’s. It is seen that McKay has on average provided a fairly modest

rate of return in recent years. It can also be seen from Table 3 that the free cash ﬂow has

7

been negative, and that the company has handled this situation by increasing its debt.

It is also evident from the bottom of Table 2 that the ratio of interest-bearing debt to

invested capital has increased substantially from year −6 to year 0.

Table 4 contains a set of historical ﬁnancial ratios. Those ratios are important, since

forecasts of the same ratios will be used to produce forecasted income statements and

balance sheets. Most of the items in Table 4 are self-explanatory, but a few observations

are called for. Net PPE (which is taken from Table 2) enters into four ratios. In two of

those cases, [depreciation/net PPE] and [retirements/net PPE], the net PPE in question

is last year’s. In the other two cases, [net PPE/revenues] and [timing diﬀerences/net

PPE], the net PPE in question is this year’s. Retirements are deﬁned as depreciation

minus change in accumulated depreciation between this year and last year (accumulated

depreciation is taken from Table 2). This must hold, since last year’s accumulated de-

preciation plus this year’s depreciation minus this year’s retirements equals this year’s

accumulated depreciation.

The timing diﬀerences for a given year are measured between accumulated ﬁscal depre-

ciation of PPE and accumulated depreciation according to PPE economic life. For a given

piece of PPE that is about to be retired, accumulated ﬁscal depreciation and accumulated

depreciation according to economic life are both equal to the original acquisition value.

Consequently, non-zero timing diﬀerences are related to non-retired PPE only. The ratio

[timing diﬀerences/net PPE] in Table 4 has been calculated by ﬁrst dividing the deferred

income taxes for a given year by the same year’s corporate tax rate (also given in Table

4). This gives that year’s timing diﬀerences. After that, there is a second division by that

year’s net PPE.

4

Forecast Assumptions Relating to Operations and

Working Capital

Having recorded the historical performance of McKay in Tables 1 - 4, we now turn

to the task of forecasting free cash ﬂow for years 1 and later. Individual free cash ﬂow

forecasts are produced for each year 1 to 12. The free cash ﬂow amounts for years 1 to

11 are discounted individually to a present value. The free cash ﬂow for year 12 and all

later years is discounted through the Gordon formula, with the free cash ﬂow in year 12

as a starting value. Years 1 to 11 are therefore the explicit forecast period, and year 12

and all later years the post-horizon period.

Tables 5 - 8 have the same format as Tables 1 - 4. In fact, Table 5 may be seen as

a continuation of Table 1, Table 6 as a continuation of Table 2, and so on. We start

the forecasting job by setting up Table 8, the forecast assumptions. Using assumptions

(ﬁnancial ratios and others) in that table, and using a couple of further direct forecasts

8

of individual items, we can set up the forecasted income statements, Table 5, and the

forecasted balance sheets, Table 6. From Tables 5 and 6, we can then in Table 7 derive

the forecasted free cash ﬂow (just like we derived the historical free cash ﬂow in Table 3,

using information in Tables 1 and 2).

Consider now the individual items in Table 8. It should be noted in Table 8 that all

items are the same for year 12, the ﬁrst year of the post-horizon period, as for year 11,

the last year of the explicit forecast period. Since the ﬁrst year in the post-horizon period

is representative of all subsequent post-horizon years, all items are the same for every

post-horizon year as for the last year of the explicit forecast period. This is actually an

important condition (cf. Levin and Olsson 1995, p. 38): If that condition holds, then free

cash ﬂow increases by the same percentage (the nominal revenue growth rate for year

12 in Table 8, cell T137) between all successive years in the post-horizon period. This

means that a necessary condition for discounting by means of the Gordon formula in the

post-horizon period is satisﬁed.

The revenue growth in each future year is seen to be a combination of inﬂation and real

growth. Actually, in years 10 and 11 there is no real growth, and the same assumption

holds for all later years as well (in the application of the Gordon formula). The underlying

assumption in Table 8 is apparently that real operations will initially expand but will

eventually (in year 10) settle down to a steady state with no further real growth. Inﬂation,

on the other hand, is assumed to be 3% in all coming years (including after year 11). The

ratio of operating expenses to revenues is assumed to improve immediately, e. g., as a

consequence of a determined turn-around eﬀort. Apparently, it is set to 90% year 1

and all later years. To avoid misunderstandings, this forecast assumption (and the other

ones displayed in Table 8) are not necessarily intended to be the most realistic ones that

can be imagined. The purpose is merely to demonstrate the mechanics of the McKinsey

model for one particular scenario. A table in Levin and Olsson 1995 (p. 124; based on

accounting data from Statistics Sweden) contains information about typical values of the

ratio between operating expenses and revenues in various Swedish industries (cf. also

Appendix 1 for a further discussion of the Statistics Sweden data base).

A number of items in the forecasted income statements and balance sheets are di-

rectly driven by revenues. That is, those items are forecasted as percentages of revenues.

In particular, this holds for the working capital items. It is thus assumed that as rev-

enues increase, the required amounts of working capital of diﬀerent categories increase

correspondingly. It is not important whether revenues increase due to inﬂation or real

growth, or a combination of both. Working capital turns over very quickly, and therefore

it is a reasonable assumption that the working capital items are simply proportional to

revenues. The ratios between the diﬀerent categories of working capital and revenues for

future years in Table 8 have been set equal to the average values of the corresponding

9

historical percentages in Table 4. Again, this is only for illustrative purposes. Another

table in Levin and Olsson 1995 (p. 125), again based on data from Statistics Sweden,

reports average values of the ratio between (aggregate) working capital and revenues in

diﬀerent Swedish industries.

5

Forecast Assumptions Relating to Property, Plant,

and Equipment

The forecast assumptions relating to PPE will be considered next (this section and

the following two). The equations that determine capital expenditures may be stated as

follows (subscripts denote years):

(capital expenditures)t = (net PPE)t − (net PPE)t−1 + depreciationt,

(net PPE)t = revenuest × [this year’s net PPE/revenues],

depreciationt = (net PPE)t−1 × [depreciation/last year’s net PPE].

To this set of equations, we may add three more that are actually not necessary for the

model:

retirementst = (net PPE)t−1 × [retirements/last year’s net PPE],

(accumulated depreciation)t

= (accumulated depreciation)t−1 + depreciationt − retirementst,

(gross PPE)t = (net PPE)t + (accumulated depreciation)t.

In particular, this second set of three equations is needed only if one wants to produce

forecasted balance sheets showing how net PPE is related to gross PPE minus accumulated

depreciation. It should be noted that such detail is not necessary, since the ﬁrst set of

three equations suﬃces for determining net PPE, depreciation, and consequently also

capital expenditures.3

It is clear from the ﬁrst three equations that forecasts have to be made for two partic-

ular ratios, [this year’s net PPE/revenues] and [depreciation/last year’s net PPE]. Setting

those ratios in a consistent fashion involves somewhat technical considerations. In this

section and the following one, one way of proceeding, consistent with the idea of the

company developing in a steady-state fashion in the post-horizon period, will be outlined.

To begin with, the idea of the company developing in a steady-state fashion has to

be made more precise. As indicated in Section 4, the forecast assumptions should be

3If the historical ﬁnancial statements do not show gross PPE and accumulated depreciation, only net

PPE, then it seems pointless to try to include these items in the forecasted ﬁnancial statements. If so,

the second set of three equations is deleted. In the McKay case, the historical statements do indicate

gross PPE and accumulated depreciation. For that (aesthetic) reason, those items will also be included

in the forecasted statements.

10

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