28-08-2012, 01:04 PM
A Tutorial on the Discounted Cash Flow Model for Valuation of Companies
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Abstract
All steps of the discounted cash flow model are outlined. Essential steps are:
calculation of free cash flow, forecasting of future accounting data (income statements
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 equipment. There is an exemplifying valuation included (of a company called
McKay), as an illustration. A number of other valuation models (discounted dividends,
adjusted present value, economic value added, and abnormal earnings) are
also discussed. Earlier versions of this working paper were entitled “A Tutorial on
the McKinsey Model for Valuation of Companies”.
Introduction
This tutorial explains all the steps of the discounted cash flow model, prominently
featured in a book by an author team from McKinsey & Company (Tim Koller, Marc
Goedhart, and David Wessels: Valuation: Measuring and Managing the Value of Companies,
5th ed. 2010). 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. The discussion
proceeds by means of an extended valuation example. The company that is subject to
the valuation exercise is the McKay company.1
The McKay example in this tutorial is somewhat similar to the Preston example
(concerning a trucking company) in the first two editions of Valuation: Measuring and
Managing the Value of Companies (Copeland et al. 1990, Copeland et al. 1994). However,
certain simplifications have been made, for easier understanding of the model. In
particular, the capital structure of McKay is composed only of equity and debt (i. e.,
no convertible bonds, etc.). Also, McKay has no operating leases or capitalized pension
liabilities.2 McKay is a single-division company and has no foreign operations (and consequently
there are no translation differences). There is no goodwill and no minority
interest. The purpose of the McKay example is merely to present all essential aspects
of the discounted cash flow 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).
Model overview
Essential features of the discounted cash flow 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 discounted cash flow 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. Koller et al. 2010, pp. 102 - 103).
Historical financial statements and the calculation
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. In other words, the 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. A slightly puzzling feature of the historical financial statements may be noted:
The relationship between interest income and excess marketable securities. That is, there
is zero interest income in several years, even though excess marketable securities are
positive.
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. As required, the explicit forecast period is at least
as long as the economic life of the PPE (the latter is assumed to be 10 years in Section 7
and 11 years in a sensitivity analysis scenario in Section 12).
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
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).
Forecast assumptions relating to discount rates and
financing
Consider now the interest rate items in Table 8. The nominal borrowing rate is
“one plus the real rate multiplied by one plus expected inflation minus one”. McKay’s
real borrowing rate is apparently forecasted to be 5.60% in all future years. Expected
inflation has already earlier been forecasted to remain at 3% in future years. The nominal
borrowing rate is hence (1+0.0560)×(1+0.03)−1 = 8.77% (rounded).15 Incidentally, the
forecasted nominal borrowing rate is assumed to be the going market rate for companies
in McKay’s risk class. This means that the market value of the interest-bearing debt is
equal to the book value. In the valuation of the equity as a residual, the book value of
the interest-bearing debt is subtracted from the value of the firm’s assets. This procedure
is correct only because of the equality between market and book debt values when the
nominal borrowing rate is the same as the going market rate (cf. Jennergren 2005 on debt
valuation when this assumption does not hold).
For calculating the WACC, the cost of equity capital, also referred to as the required
rate of return on equity, is also needed. The real cost of equity capital is apparently
assumed to be 11.40%. The nominal cost of equity capital then becomes (1 + 0.1140) ×
(1+0.03)−1 = 14.74% (rounded). It should be emphasized that the cost of equity capital,
as well as the borrowing rate, is not independent of the debt and equity weights that enter
into the WACC. In fact, the nominal borrowing rate in row 177 and the nominal cost of
equity in row 179 are valid under the assumption that the WACC weights are 50% debt
and 50% equity.16 If those debt and equity weights are varied, then the borrowing rate and
cost of equity capital should be varied as well. However, the precise relationship between,
on the one hand, the debt and equity weights entering into the WACC and, on the other
hand, the borrowing rate and cost of equity capital that also enter into the WACC is for
the time being (until Section 14 below) left unspecified in this tutorial.