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Investments can be revenue-generating investments (such as the Home Depot opening

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a new store) or they can be cost saving investments (as would be the case if Boeing
adopted a new system to manage inventory). Some projects have large up-front costs
(as is the case with the Boeing Super Jumbo), while other projects may have costs
spread out across time. A good investment rule will provide an answer on all of these
different kinds of investments.
Does there have to be only one investment decision rule? While many firms analyze
projects using a number of different investment decision rules, one rule has to dominate.
In other words, when the investment decision rules lead to different conclusions on
whether the project should be accepted or rejected, one decision rule has to be the tie-
breaker and can be viewed as the primary rule.

Accounting Income Based Decision Rules
Many of the oldest and most established investment decision rules have been
drawn from the accounting statements and, in particular, from accounting measures of
income. Some of these rules are based on income to equity investors (i.e., net income)
while others are based on pre-debt operating income.

Return on Capital
The return on capital on a project measures the returns earned by the firm on it is
total investment in the project. Consequently, it is a return to all claimholders in the firm
on their collective investment in a project. Defined generally,


Earnings before interest and taxes
Return on Capital (Pre-tax) =
Average Book Value of Total Investment in Project

Earnings before interest and taxes (1- tax rate)
Return on Capital (After-tax) =
Average Book Value of Total Investment in Project
To illustrate, consider a 1-year project, with an initial investment of $ 1 million, and
earnings before interest and taxes of $300,000. Assume that the project has a salvage
value at the end of the year of $800,000, and that the tax rate is 40%. In terms of a time
line, the project has the following parameters:




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Earnings before interest & taxes = $ 300,000

Book Value = $ 1,000,000 Salvage Value = $ 800,000

Average Book Value of Assets = $(1,000,000+$800,000)/2 = $ 900,000

The pre-tax and after-tax returns on capital can be estimated as follows:
$ 300,000
= 33.33%
Return on Capital (Pre-tax) =
$ 900,000
$ 300,000 (1- 0.40)
= 20%
Return on Capital (After-tax) =
$ 900,000
While this calculation is rather straightforward for a 1-year project, it becomes more
involved for multi-year projects, where both the operating income and the book value of
the investment change over time. In these cases, the return on capital can either be
estimated each year and then averaged over time or the average operating income over
the life of the project can be used in conjunction with the average investment during the
period to estimate the average return on capital.
The after-tax return on capital on a project has to be compared to a hurdle rate that
is defined consistently. The return on capital is estimated using the earnings before debt
payments and the total capital invested in a project. Consequently, it can be viewed as
return to the firm, rather than just to equity investors. Consequently, the cost of capital
should be used as the hurdle rate.
If the after-tax return on capital > Cost of Capital -> Accept the project
If the after-tax return on capital < Cost of Capital -> Reject the project
For instance, if Disney in the example, above, had a cost of capital of 10%, it would view
the investment in the new software as a good one.

Illustration 5.7: Estimating and Using Return on Capital in Decision Making: Disney
and Bookscape
In illustration 5.4 and 5.5, we estimated the operating income from two projects -
an investment by Bookscape in an on-line book ordering service and an investment in a
theme park in Bangkok by Disney. We will estimate the return on capital on each of these




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investments using these estimates of operating income. Table 5.7 summarizes the
estimates of operating income and the book value of capital at Bookscape.
Table 5.7: Return on Capital on Bookscape On-line
1 2 3 4 Average
After-tax Operating Income $120,000 $183,000 $216,300 $252,930 $193,058
BV of Capital: Beginning $1,150,000 $930,000 $698,000 $467,800
BV of Capital: Ending $930,000 $698,000 $467,800 $0
Average BV of Capital $1,040,000 $814,000 $582,900 $233,900 $667,700
Return on Capital 11.54% 22.48% 37.11% 108.14% 28.91%
The book value of capital each year includes the investment in fixed assets and the non-
cash working capital. If we average the year-specific returns on capital, the average
return on capital is 44.82% but this number is pushed up by the extremely high return in
year 4. A better estimate of the return on capital is obtained by dividing the average after-
tax operating income over the four years by the average capital invested over the four
years, which yields a return on capital of 28.91%. Since this exceeds the cost of capital
that we estimated in illustration 5.2 for this project of 22.76%, the return on capital
approach would suggest that this is a good project.
In table 5.8, we estimate operating income, book value of capital and return on
capital for Disney™s theme park investment in Thailand. The operating income estimates
are from exhibit 5.1:
Table 5.8: Return on Capital for Disney Theme Park Investment
After-tax
Operating BV of Capital: BV of Capital: Average BV
Year Income Beginning Ending of Capital ROC
1 $0 $2,500 $3,500 $3,000 NA
2 -$165 $3,500 $4,294 $3,897 -4.22%
3 -$77 $4,294 $4,616 $4,455 -1.73%
4 $75 $4,616 $4,524 $4,570 1.65%
5 $206 $4,524 $4,484 $4,504 4.58%
6 $251 $4,484 $4,464 $4,474 5.60%
7 $297 $4,464 $4,481 $4,472 6.64%
8 $347 $4,481 $4,518 $4,499 7.72%
9 $402 $4,518 $4,575 $4,547 8.83%
10 $412 $4,575 $4,617 $4,596 8.97%
$175 $4,301 4.23%



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The book value of capital includes the investment in fixed assets (capital expenditures),
net of depreciation, and the investment in working capital that year and the return on
capital each year is computed based upon the average book value of capital invested
during the year. The average after-tax return on capital over the 10-year period is 4.21%.
Here, the return on capital is lower than the cost of capital that we estimated in
illustration 5.2 to be 10.66% and this suggests that Disney should not make this
investment.

Return on Equity
The return on equity looks at the return to equity investors, using the accounting
net income as a measure of this return. Again, defined generally,
Net Income
Return on Equity =
Average Book Value of Equity Investment in Project
To illustrate, consider a 4-year project with an initial equity investment of $ 800, and the
following estimates of net income in each of the 4 years:


Net Income $ 140 $ 170 $ 210 $ 250




BV of Equity $ 700 $ 600 $ 500 $ 400
$ 800


38.18% 55.56%
26.15%
18.67%
Return on Equity

Like the return on capital, the return on equity tends to increase over the life of the
project, as the book value of equity in the project is depreciated.
Just as the appropriate comparison for the return on capital is the cost of capital,
the appropriate comparison for the return on equity is the cost of equity, which is the rate
of return equity investors demand.
Decision Rule for ROE Measure for Independent Projects
If the Return on Equity > Cost of Equity -> Accept the project
If the Return on Equity < Cost of Equity -> Reject the project



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The cost of equity should reflect the riskiness of the project being considered and the
financial leverage taken on by the firm. When choosing between mutually exclusive
projects of similar risk, the project with the higher return on equity will be viewed as the
better project.

Illustration 5.8: Estimating Return on Equity - Aracruz Cellulose
Consider again the analysis of the paper plant for Aracruz Cellulose that we
started in illustration 5.6. Table 5.9 summarizes the book value of equity and the
estimated net income (from exhibit 5.3) for each of the next ten years in thousands of real
BR.
Table 5.9: Return on Equity: Aracruz Paper Plant
Beg. Ending BV of Average
Net BV: Capital BV: Working BV: BV:
Year Income Assets Depreciation Exp. Assets Capital Debt Equity Equity ROE
0 0 0 250,000 250,000 35,100 100,000 185,100
1 9,933 250,000 35,000 0 215,000 37,800 92,142 160,658 172,879 5.75%
2 20,171 215,000 28,000 0 187,000 40,500 83,871 143,629 152,144 13.26%
3 29,500 187,000 22,400 0 164,600 42,750 75,166 132,184 137,906 21.39%
4 37,213 164,600 17,920 0 146,680 42,750 66,004 123,426 127,805 29.12%
5 39,896 146,680 14,336 50,000 182,344 42,750 56,361 168,733 146,079 27.31%
6 35,523 182,344 21,469 0 160,875 42,750 46,212 157,413 163,073 21.78%
7 35,874 160,875 21,469 0 139,406 42,750 35,530 146,626 152,020 23.60%
8 36,244 139,406 21,469 0 117,938 42,750 24,287 136,400 141,513 25.61%
9 36,634 117,938 21,469 0 96,469 42,750 12,454 126,764 131,582 27.84%
10 37,044 96,469 21,469 0 75,000 0 0 75,000 100,882 36.72%
23.24%

To compute the book value of equity in each year, we first compute the book value of the
fixed assets (plant and equipment), add to it the book value of the working capital in that
year and subtract out the outstanding debt. The return on equity each year is obtained by
dividing the net income in that year by the average book value of equity invested in the
plant in that year. The increase in the return on equity over time occurs because the net
income rises, while the book value of equity decreases. The average real return on equity
of 22.91% on the paper plant project is compared to the real cost of equity for this plant,
which is 11.40%, suggesting that this is a good investment.




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Assessing Accounting Return Approaches
How well do accounting returns measure up to the three criteria that we listed for a
good investment decision rule? In terms of maintaining balance between allowing
managers to bring into the analysis their judgments about the project and ensuring
consistency between analysis, the accounting returns approach falls short. It fails because
it is significantly affected by accounting choices. For instance, changing from straight
line to accelerated depreciation affects both the earnings and the book value over time,
thus altering returns. Unless these decisions are taken out of the hands of individual
managers assessing projects, there will be no consistency in the way returns are measured
on different projects.
Does investing in projects that earn accounting returns exceeding their hurdle
rates lead to an increase in firm value? The value of a firm is the present value of
expected cash flows on the firm over its lifetime. Since accounting returns are based upon
earnings, rather than cash flows, and ignore the time value of money, investing in
projects that earn a return greater than the hurdle rates will not necessarily increase firm
value. Conversely, some projects that are rejected because their accounting returns fall
short of the hurdle rate may have increased firm value. This problem is compounded by
the fact that the returns are based upon the book value of investments, rather than the
cash invested in the assets.
Finally, the accounting return works better for projects that have a large up-front
investment and generate income over time. For projects that do not require a significant
initial investment, the return on capital and equity has less meaning. For instance, a retail
firm that leases store space for a new store will not have a significant initial investment,
and may have a very high return on capital as a consequence.
Note that all of the limitations of the accounting return measures are visible in the
last two illustrations. First, the Disney example does not differentiate between money
already spent and money still to be spent; rather, the sunk cost of $ 0.5 billion is shown in
the initial investment of $3.5 billion. Second, in both the Bookscape and Aracruz
analyses, as the book value of the assets decreases over time, largely as a consequence of
depreciation, the operating income rises, leading to an increase in the return on capital.
With the Disney analysis, there is one final and very important concern. The return on


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capital was estimated over 10 years but the project life is likely to be much longer. After
all, Disney™s existing theme parks in the United States are more than three decades old
and generate substantial cashflows for the firm still. Extending the project life will push
up the return on capital and may make this project viable.
Notwithstanding these concerns, accounting measures of return endure in
investment analysis. While this fact can be partly attributed to the unwillingness of
financial managers to abandon familiar measures, it also reflects the simplicity and
intuitive appeal of these measures. More importantly, as long as accounting measures of

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