ACCA - P5 Study text - Emile Woolf INT - 2010
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Chapter 15: Decentralisation and divisional performance
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Residual income (RI)
Measuring residual income
Imputed interest (notional interest)
Residual income and investment decisions
Advantages and disadvantages of residual income
3 Residual income (RI)
Residual income (RI) is another way of measuring the performance of an investment
centre.
Residual income = Divisional profit minus Imputed interest charge.
Notes
Divisional profit is an accounting measurement of profit, after depreciation charges
are subtracted.
The interest charge is calculated by applying a cost of capital to the division’s net
investment (net assets). The appropriate measure of net investment is the average
investment during the period.
3.1 Measuring residual income
Residual income is measured in either of the following ways:
Managerial evaluation
$
Controllable profit A
Less notional interest on average controllable investment B
Controllable residual income A – B
Divisional/economic evaluation
$
Traceable profit A
Less notional interest on average traceable investment B
Divisional residual income A – B
3.2 Imputed interest (notional interest)
Residual income is calculated by deducting an amount for imputed interest (also
called notional interest) from the accounting profit for the division.
Imputed interest (notional interest) is the division’s capital employed, multiplied by:
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the organisation’s cost of borrowing, or
the weighted average cost of capital of the organisation, or
a special risk-weighted cost of capital to allow for the special business risk
characteristics of the division. A higher interest rate would be applied to
divisions with higher business risk.
3.3 Residual income and investment decisions
If investment centres are evaluated on the basis of residual income, their managers
will be motivated to undertake new investments that increase residual income and
to avoid new investments that would reduce residual income.
However, the investment decisions will often be different to what the decision
would be if ROI is used. Residual income increases if the annual profit exceeds the
notional interest charge.
Investments with an average annual profit higher than the cost of capital are
undertaken.
Investments with an average annual profit lower than the cost of capital are
rejected.
Example
The difference between the ROI and residual income can be illustrated by returning
to the previous example.
Division A Division B
Average investment (controllable investment) $100,000 $100,000
Average annual profit after depreciation $16,000 $11,000
Current controllable ROI of the division 18% 9%
Cost of capital of the company 13% 13%
Division A decision
Using RI as a basis for the investment decision, Division A would invest in their
project, because RI would increase.
Division A
$
Average annual profit after depreciation
16,000
Notional interest (13% × $100,000)
13,000
Increase in average annual RI 3,000
Average annual return on capital from the project (16%) is higher than the
company’s cost of capital. This is why the average annual residual income increases.
Division B decision
Using RI as a basis for the investment decision, Division B would not invest in their
project, because RI would fall.
Chapter 15: Decentralisation and divisional performance
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Division B
$
Average annual profit after depreciation 11,000
Notional interest (13% × $100,000)
13,000
Fall in average annual RI (2,000)
Average annual return on capital from the project (11%) is less than the company’s
cost of capital. This is why the average annual residual income falls.
The decisions by Division A and Division B whether or not to invest should be
based on a DCF evaluation. There is insufficient information to calculate the project
NPV. However, using residual income for investment decisions is more likely than
using ROI to result in a decision that agrees with the decision based on DCF
analysis.
In the above example, it is almost certain that a DCF analysis would show that the
Division B investment has a negative NPV. The decision using DCF would be to
reject the investment, and the decision based on RI is consistent with this.
3.4 Advantages and disadvantages of residual income
Advantages of RI
There are several advantages in using RI as a measure of the performance of an
investment centre.
It relates the profit of the division to the capital employed, by charging an
amount of notional interest on capital employed, and the division manager is
responsible for both profit and capital employed.
Divisional managers are made aware, through the charge for imputed interest,
that investments have a financing cost.
RI is a flexible measure of performance, because a different cost of capital can be
applied to investments with different risk characteristics.
As explained above, measuring performance with RI is more likely to encourage
managers to make investment decisions that are consistent with DCF-based
investment decisions.
Disadvantages of RI
There are also disadvantages in using RI as a measure of the performance of an
investment centre.
RI is an accounting-based measure, and suffers from the same problem as ROI in
defining capital employed.
Its main weakness is that it is difficult to compare the performance of different
divisions using RI. Larger divisions should earn a bigger RI. A small division
making RI of $50,000 might actually perform much better than a much larger
division whose RI is $100,000.
RI is not easily understood by management, especially managers with little
accounting knowledge.
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There may be problems in deciding a suitable rate of interest for the imputed
interest charge.
Example
The performance of a divisional manager is evaluated by RI. The company’s cost of
capital is 10%.
The manager is considering whether to invest in a project to buy an asset costing
$600,000. The asset would have a three-year life and no residual value. Cash flows
from the investment would be $500,000 in each year.
Required
(a) Calculate the RI for each of the three years of the project, using net book value
(NBV) at the start of the year as capital employed.
(b) Calculate the NPV of the project. Assume that cash flows occur at the end of
each year.
Answer
(a) Residual income
Year 1 Year 2 Year 3
$ $ $
Opening net book value 600,000 400,000 200,000
Annual depreciation 200,000 200,000 200,000
$ $ $
Profit 300,000 300,000 300,000
Notional interest (10%) 60,000 40,000 20,000
Residual income 240,000 260,000 280,000
(b) NPV
Year Cash flow Discount factor at 10% Present value
$ $
0 (600,000) 1.000 (600,000)
1 – 3 500,000 2.487 1,243,500
+ 643,500
Chapter 15: Decentralisation and divisional performance
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Divisional performance and depreciation
ROI or RI: the problem with depreciation
Annuity-based depreciation
4 Divisional performance and depreciation
4.1 ROI or RI: the problem with depreciation
If straight-line depreciation is used and capital employed is based on carrying
values (net book values) ROI and RI will rise over time if:
annual profits are constant and
assets are not replaced, and existing assets remain in use as they get older.
In the early years of an investment project, the ROI or RI might be very low. If a
divisional manager is concerned about the effect that this would have on the
division’s ROI or RI for the next year or two, the manager might refuse to invest in
the project. This is because performance in the next year or so might be much worse,
even though the project might be expected to earn a high return over its full
economic life.
Example
Palace Division is a part of the Crystal Group. Its manager has the authority to
invest in new capital expenditure, within limits set by head office. The senior
management team of the division is considering an investment of $4.2 million. This
would have a residual value of zero after four years. Net cash inflows from the
investment would be $1.4million for each of the next four years.
The cost of capital for the Palace Division is 10%. It is the group’s policy to use
straight-line depreciation when measuring divisional profit.
For measurement purposes and reporting purposes, ‘capital’ is defined as the
opening net book value at the start of each year.
Required
For this particular investment:
(a) Calculate residual income each year
(b) Calculate the Return on Investment each year
(c) Calculate the NPV of the investment
(d) State whether the decision would be in the best interests of the company if the
manager makes the decision on the basis of the effect of the investment on:
(i) RI or
(ii) ROI.
Ignore taxation.
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Answer
(a) Residual income
Year 1 Year 2 Year 3 Year 4
$000 $000 $000 $000
Opening net book value 4,200
3,150
2,100 1,050
Annual depreciation 1,050
1,050
1,050 1,050
$
$
$ $
Profit before depreciation
1,400
1,400
1,400 1,400
1,050
1,050
1,050 1,050
350
350
350 350
Notional interest (10%) 420
315
210 105
Residual income (70)
35
140 245
The total residual income over the four years is $350,000 (profit of $1,400,000
minus notional interest charges of $1,050,000).
(b) Return on Investment
Capital is defined here as the value of the net assets at the beginning of the
year.
Year 1 Year 2 Year 3 Year 4
$000 $000 $000 $000
Opening net book value 4,200
3,150
2,100 1,050
Annual depreciation 1,050
1,050
1,050 1,050
$
$
$
Profit before depreciation
1,400
1,400
1,400 1,400
1,050
1,050
1,050 1,050
Profit 350
350
350 350
Return on investment (ROI)
8.3%
11.1%
16.7% 33.3%
The average return on investment = average annual profit/average
investment = $350,000/$2,100,000 = 16.7%.
(c) NPV
Year
Cash flow
Discount
factor at
10%
Present
value
$ $
0 Capital expenditure
4,200,000
1.000
4,200,000
1 - 4 Net cash flow 1,400,000
3.170
4,438,000
Net present value
+ 238,000
(d) Ignoring risk and uncertainty in the forecast cash flows, the decision should be
to undertake the capital investment, because the NPV is positive. In theory,
undertaking the project will add to shareholders’ wealth by this amount.
If the management of Palace Division are concerned about the short-term
performance of the division, they might decide not to undertake the
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investment. This is because the ROI will be less than 10% in Year 1 and the
residual income would be negative.
However, if the management team takes a longer-term view, and considers
performance over the full four years, they would undertake the investment,
because the average annual ROI on the new investment would be 16.7% and
the average annual increase in residual income for the division would be
$87,500.
Unfortunately, decision-making often focuses on the short term, and there is a
possibility that the investment will not be undertaken in order to prevent a fall
in ROI or residual income.
Conflicts with NPV
This previous example should demonstrate that on occasions there may be a conflict
between NPV and ROI/RI.
NPV gives the correct decision under the assumption that we want to maximise
shareholder wealth.
NPV cannot be used to assess historical performance, but ROI and residual income
do not always indicate the most appropriate investment decision. This raises the
question: Is there any way in which ROI or residual income could be made more
consistent with NPV in the assessment of new capital investments?
4.2 Annuity-based depreciation
The problem might sometimes be overcome if annuity-based depreciation is used to
measure ROI and RI, instead of straight-line depreciation. However, this approach
is only valid if the annual cash flows from an investment project are expected to be a
constant amount each year (and are not low in the early years of the investment
project).
An annual depreciation charge is calculated as follows:
Assume that the investment is purchased using a bank loan at the company’s
cost of capital.
Convert this loan into an annuity (constant annual cash flow). To do this, divide
the cost by the DCF annuity factor for the number of years of the project.
This annuity or equivalent annual cash flow consists of an interest charge and a
loan repayment. The loan repayment element is assumed to be the depreciation
charge for the year.
This depreciation charge, which increases each year over the life of the project, is
used to calculate the division’s profit for the year.
Annual equivalent cash flow (annuity) = Depreciation + Interest
Annuity depreciation = Annual equivalent cash flow – Notional interest on capital
employed.
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Example 1
An investment centre invests $3,170,000 in capital equipment that is expected to
have a four-year life. The DCF cost of capital is 10%. The investment centre’s
performance is measured by ROI, but annuity depreciation is used for the centre’s
capital assets.
For the new equipment annual depreciation will be calculated as follows:
The DCF annuity factor for four years at 10% is about 3.170 (from DCF tables).
The annuity cost of the new equipment is therefore $3,170,000/3.170 =
$1,000,000.
This annuity cost consists of an interest charge and depreciation.
The depreciation charge is calculated as the difference between the total annuity
cost($1,000,000)andtheannualinterest,asfollows.
Year Opening
balance
Interest at 10% Annuity Balance at
end of year
$ $
$
$
1 (3,170,000) (317,000)
1,000,000
(2,487,000)
2 (2,487,000) (248,700)
1,000,000
(1,735,700)
3 (1,735,700) (173,570)
1,000,000
(909,270)
4 (909,270) (90,927)
1,000,000
(197)
Theclosingbalance atthe endofthefouryearsshouldbe $0.The$197arises from
roundingerrorsintheannuitydiscountfactor.
The annual depreciation charge is the difference between the annuity cost of
$1,000,000 and the interest charge each year. So it is $683,000 in Year 1, rising to
$751
,300inYear2,$816,430inYear3and$909,073inYear4.
Example 2
Palace Division is a part of the Crystal Group. Its manager has the authority to
invest in new capital expenditure, within limits set by head office. The senior
management team of the division is considering an investment of $4.2 million. This
would have a residual value of zero after four years. Net cash inflows from the
investment would be $1.4million for each of the next four years.
The cost of capital for the Palace Division is 10%. It is the group’s policy to use
annuity depreciation when measuring divisional profit.
For measurement purposes and reporting purposes, ‘capital’ is defined as the
opening net book value at the start of each year.
The equivalent annual charge or annuity =
Cost of investment
DCF factor for years 1− 4 at 10%
=
$4.2 million
3.170
= $1, 324, 921 (say, $1,325,000).
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Residual income
Year 1 Year 2 Year 3 Year 4
$000 $000 $000 $000
Cash flow 1,400
1,400
1,400 1,400
Depreciation + notional interest 1,325
1,325
1,325 1,325
Residual income 75
75
75 75
The residual income is now constant in every year, and a positive value. The
investment adds to RI each year.
The decision, based on residual income and using annuity depreciation, would be to
undertake the investment project. This is consistent with the NPV assessment.
ROI
For an ROI calculation, we must separate the equivalent annual charge into the
interest charge and the depreciation element (the balance).
Year
Investment at the
start of the year
Interest at 10%
Equivalent
annual charge
Depreciation
charge (=total
annual charge
minus interest)
$ $ $ $
1 4,200,000
420,000
1,324,921 904,921
2 3,295,079
329,508
1,324,921 995,413
3 2,299,666
229,967
1,324,921 1,094,954
4 1,204,712
120,471
1,324,921 1,204,450
5 0**
** Allowing for rounding errors in the discount factor.
Year 1 Year 2 Year 3 Year 4
$ $ $ $
Cash flow 1,400,000
1,400,000
1,400,000 1,400,000
Depreciation 904,921
995,413
1,094,954 1,204,450
Profit 495,079
404,587
305,046 195,550
Investment 4,200,000
3,295,079
2,299,666 1,204,450
ROI 11.8%
12.3%
13.3% 16.2%
The ROI exceeds the cost of capital (10%) in each year. The decision by the
divisional manager, based on ROI, would therefore be to undertake the investment.
This decision would be consistent with the NPV assessment.
The project, which has a positive NPV, will therefore be accepted under both ROI
and RI when depreciation is charged by the annuity method. It is important to
recognise, however, that this conclusion is valid only if:
the cash flows in each year of the project are constant (and are not fairly low in
the first year or early years of the project), and
the investment does not have any residual value at the end of its life.
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Economic Value Added (EVA)
Profits and adding value to a business
The potential benefits of EVA
Measuring economic value added (EVA)
Using EVA
Possible problems with EVA
5 Economic Value Added (EVA)
5.1 Profits and adding value to a business
In theory, if a company makes a profit, the value of its shares ought to increase by
the amount of the profit (less any dividends paid to shareholders). In practice, this
does not happen.
One reason for this is that in order to make a profit, capital is invested. Capital is a
resource which has a cost. The actual creation of extra value should therefore be the
profit less the cost of capital invested. Residual income is the accounting profit
earned by a division less a notional charge for capital employed. In theory, there is a
connection between residual income and the expected increase in the value of a
business.
Suppose for example that a company has $10 million in cash and keeps it in a bank
deposit account earning 2% per year interest. The cash will earn interest of $200,000
less tax in one year, and this will be reported as income. However although keeping
money in a low-interest account adds to accounting profit, it does not ’add value’ to
the company (or ‘create value’), because the cost of capital needed to finance the
cash is probably higher than 2%. The management writer Peter Drucker once wrote
that: ‘until a business returns a profit that is greater than its cost of capital, it
operates at a loss.’
There is a second – and more important – reason why profits are not a good
measure of the expected increase in the value of a business. This is that profit
measured by accounting conventions is not a proper measure of ‘real’ economic
profit.
It can be argued that if
economic profit is measured, instead of accounting profit,
we will arrive at a better measurement of the increase in the value of a business
during a given period of time.
A management consultancy firm, Stern Stewart, devised a method of measuring
economic profit, which they have called economic value added or EVA. The term
‘EVA’ is a trademark of the Stern Stewart organisation.