Page info: *Author:Mathiesen, H. *Document version:2.5. *Copyright 1997-2017, ViamInvest.Legal notice.



 

Exhibition: The nature of accounting returns v. market returns

 

 

1††††††† Introduction

 

This exhibition describes the nature of accounting based v. market based measures of financial performance. The description is aided by a stylized case that illustrates and calculates the impact of a performance event on various financial performance measures. One of the points of this exhibition is that statistical studies that use market returns as an indicator of performance typically only will be meaningful if they are structured as event studies. The reason is that in market equilibrium all firms of equal risk must earn the same return at any particular point in time. This is so because of arbitrage. Market returns are based on expectations regarding the entire future of the firm. Therefore, any change in performance must be discrete and effect only one period, see firm A versus firm B in figure 1 below. In contrast, accounting returns are based on measurement regarding historical periods. Therefore, any permanent change in the performance of a firm will result in higher accounting returns in all future periods, see calculations below.

 

Figure 1: An unexpected performance event

 

This figure plots the logarithm of the market value against time for both Firm A and Firm B. The case is based on assumptions, formulas and calculations as fully reported and discussed below.

 

 

2††††††† Case Assumptions

 

The assumptions behind the situation in figure 1 are the following:

1.      To begin with, Firm A and Firm B earn a free cash flow (FCF) of $1 per year. However, primo 1995 Firm A unexpectedly invent something that boosts its FCF to $1.3 per year. The free cash flow is more precisely defined as the cash flow free to honor returns on debt and equity under the going concern assumption. For details see Copeland, Koller and Murrin [1996, page 140].

2.      Firm A and Firm B each have a weighted average cost of capital (WACC) of 10% per year. For simplicity they are 100% equity-financed so that the WACC is also equal to the equityís cost of capital. For information about calculating WACC under more general circumstances click here.

3.      The firm is expected to operate forever (the so-called going concern assumption).

4.      All stock market investors are perfectly informed. The implication is that the firmís fundamental present value (PV) will be equal to its market value (footnote 1).

5.      All of the FCF is paid to shareholders as dividends ultimo each year.

6.      Firm A and Firm B are started by making an initial investment of $10 primo 1993.

7.      Both firms have zero growth and total reinvestments equals total depreciations say $2 per year. Two important implications follow. Implication 1: The FCF will equal the net operating profit less adjusted taxes (NOPLAT) since FCF = NOPLAT + Investments Ė Depreciations (footnote 2). Implication 2: For each year the firmsí invested capital will be equal to the firmsí initial investment, which is $10. Invested capital is defined as all the capital that has been invested in the business operations of the corporation, Copeland, Koller and Murrin [1996, page 164].

8.      For simplification there are zero taxes.

9.      Each firm has ten outstanding shares.

10.  There is zero inflation and no technological progress. The implication is that the replacement value of invested capital is equal to the book value of invested capital.

 

 

3††††††† Performance Formulas

 

Given the above assumptions the following performance measures can be calculated for the two firms:

         ROICt or return on invested capital = NOPLATt / Invested capitalt.

         Earning per sharet, EPS = NOPLATt / Numbers of outstanding sharest.

         Economic profitt = NOPLAPt - (Invested capitalt*WACCt).

         Present value of the firm, PVt. Under the given assumptions (in particular the going concern assumption) it is calculated as FCFt / WACCt using Gordonís growth formula with growth equal to zero. For proof of Gordonís growth formula click here. For calculations of present value under more general circumstances click here.

         Market value = PV given Assumption 4.

         Market returnt is the percentage growth of the firmís market value assuming that all dividends are reinvested. This is the same as the slope a in Figure 1 in Chapter 5 and since market value is equal to PV (given the perfect information assumption) it is calculated as (PVt + Dt - PVt-1) / PVt-1 where Dt is dividends.

         Abnormal market return, ARt = (Market returnt - WACCt). It should be noted that the WACCt only is the relevant cost of capital because both firms are 100% equity financed.

         Cumulated abnormal return, where d1 and d2 respectively are the starting and the ending dates of the cumulated period.

         Tobinís qt = Market valuet / Replacement value of invested capitalt.

 

For thorough definitions of accounting concepts such as NOPLAT, FCF see Copeland, Koller and Murrin [1996]. Otherwise, click here to see a table with the essential accounting concepts.


 

4††††††† Calculations

 

Table 1: Firm A and Firm B

 

Given the mentioned assumptions in Section 2 and given the definitions of the different performance measures in Section 3 it is simple to calculate the performance measures. These calculations are shown for the two hypothetical firms for the period 1993 to 1997. The CAR values are calculated with 1993 as the initial year (d1).

 

Firm A

1993

1994

1995

1996

1997

Dividends = FCF = NOPLAT (ultimo)

$1

$1

$1.3

$1.3

$1.3

Accounting return, ROIC

10%

10%

13%

13%

13%

Earnings per share, EPS

$0.1

$0.1

$0.13

$0.13

$0.13

Economic profit

$0

$0

$0.3

$0.3

$0.3

Market value = PV (primo)

$10

$10

$13

$13

$13

Market return

10%

10%

43%

10%

10%

Abnormal market return, AR

0%

0%

33%

0%

0%

Cumulated abnormal return, CAR

0%

0%

33%

33%

33%

Tobinís q

1

1

1.3

1.3

1.3

Firm B

1993

1994

1995

1996

1997

Dividends = FCF = NOPLAT (ultimo)

$1

$1

$1

$1

$1

Accounting return, ROIC

10%

10%

10%

10%

10%

Earnings per share, EPS

$0.1

$0.1

$0.1

$0.1

$0.1

Economic profit

$0

$0

$0

$0

$0

Market value = PV (primo)

$10

$10

$10

$10

$10

Market return

10%

10%

10%

10%

10%

Abnormal market return, AR

0%

0%

0%

0%

0%

Cumulated abnormal return, CAR

0%

0%

0%

0%

0%

Tobinís q

1

1

1

1

1

Footnotes

 

Footnote 1) In the real world the market value may differ from the fundamental PV for a number of reasons. The most important is that investors are differentiated according to how much information they have about how to calculate the fundamental PV. For an exhibition on stock pricing when information about value is costly click here.

Footnote 2) To be more specific, NOPLAT is equal to earnings before interest and taxes (EBIT) less of cash taxes on EBIT. For more information see Copeland, Koller and Murrin [1996, page 140].

 

-Copyright 1997-2017, ViamInvest. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.Legal notice.