James R. Martin, Ph.D., CMA
Professor Emeritus, University of South Florida
MAAW's Textbook Table of Contents
CONTENTS
Introduction  ROI Main Heading  DuPont Formula Graphic Illustration  Methods of Increasing ROI  ROI Read diagram  Relationships Between Sales, Capital Turnover Ratio and Return on Sales Ratio (ROS)  Equations for X and S Needed for a Desired ROS  Some Questions to Emphasize the ROS Relationships  Equations For X and S Needed For a Desired ROI  ROI Equations for Multiple Product Companies  Possible Investment Bases for ROI  How to Measure Assets for ROI Calculation  Residual Income and EVA®  Transfer Pricing  Appendix 141: Conflict Between Choosing Capital Projects and Evaluating Results  Appendix 142: What is inputoutput accounting?  Footnotes  Multiple Choice Questions The purpose of this chapter is to: 1) discuss two common performance measurements for investment centers and the various relationships between these measurements, 2) present some equations related to these measurements that can be used for planning purposes, 3) discuss a number of issues related to how these measurements are calculated and 4) discuss the transfer pricing problem that arises when investment centers sell products or services to each other.Return on investment or ROI = Net Income ÷ Investment
An alternative formulation of ROI based on Du Pont's formula is as follows:
ROI = (Capital Turnover Ratio)(Profit Margin on Sales)
= (Sales ÷ Investment)(Net Income ÷ Sales)
The Profit Margin is the Rate of Return on Sales (ROS) and measures
management's ability to control the spread between prices and costs.
Productivity and cost control are reflected in this measure as well as other
factors such as the sales level.
A more detailed view of the Du Pont ROI formula appears in the
graphic illustration below^{1}.
1. Increasing Capital Turnover (CTR)
a. Increase sales with the same the investment
base.
b. Decrease the investment base with the
same sales level.
2. Increasing Profit Margin or Return on Sales (ROS)
a. Increase prices with no unfavorable
effects on sales.
b. Decrease cost with no unfavorable
effects on quality or increase in assets.
c. Increase sales with no changes in prices or costs.
CMR = (PV) ÷ P
or 1  V÷P
CMR after taxes = (1T)(CMR) = (1T)[(PV) ÷ P]
or (1T)(1  V÷P)
Exhibit 141 

Using Units (X)  Using Sales Dollars (S) 
The Return on Sales Ratio before taxes is ROS = NIBT ÷ PX ROS = [(PV)X  TFC] ÷ PX When X > 0 ROS = [(PV) ÷ P]  (TFC ÷ PX) ROS = CMR  [(TFC÷P) ÷ X] For Cal Company: (See Chapter 11). P =10, V = 6, TFC = $120,000. ROS = [(106) ÷ 10]  (120,000÷10) ÷ X) ROS = .4  (12,000 ÷ X) For example, what is the return on sales before taxes when 60,000 units are produced and sold? ROS before taxes = .4  (12,000 ÷ 60,000) = .4  .2 = .2 or 20% 
The Return on Sales Ratio before taxes is ROS = NIBT ÷ S ROS = [S  (V÷P)(S)  TFC] ÷ S When S > 0 For Cal Company: ROS = (1.6)  (120,000÷S) For example, what is the return on sales before taxes when sales = $600,000? ROS before taxes = .4  (120,000÷600,000) 
The Return on Sales Ratio after taxes is ROS = NIAT ÷ PX ROS = [(1T)(PV)(X)  (1T)(TFC)] ÷ PX When X > 0 ROS = [(1T)(PV) ÷ P]  [(1T)(TFC) ÷ PX] ROS = (1T)(CMR)  [(1T)(TFC÷P) ÷ X] For Cal Company: ROS = [(1.4)(106)÷10]  [(1.4)(120,000÷10) ÷X] ROS = .24  (7,200 ÷ X) For example, what is the return on sales after taxes when 60,000 units are produced and sold? ROS after taxes = .24  (7,200 ÷ 60,000) = .24  .12 = .12 or 12%. 
The Return on
Sales Ratio after taxes is ROS = NIAT ÷ S ROS = [(1T)(S  (V÷P)(S)  TFC)] ÷ S When S > 0 For Cal Company: ROS = .24  (72,000÷S) For example, what is the return on sales after taxes when Sales = $600,000? ROS after taxes = .24  (72,000 ÷ 600,000) 
Exhibit 142 

Using Units (X)  Using Sales Dollars (S) 
ROS
before taxes = CMR  [(TFC÷P) ÷ X] Stated in terms of X: ROS  CMR =  (TFC÷P) ÷ X X(ROS  CMR) = TFC÷P X = (TFC÷P) ÷ (ROSCMR) AT the BEP ROS = 0 X = 12,000 ÷ (0.4) X = 30,000 units 
ROS before taxes = CMR  (TFC÷S) Stated in terms of S: ROS  CMR = TFC÷S S(ROSCMR) = TFC S = TFC ÷ (ROSCMR) AT the BEP ROS = 0 S = 120,000 ÷ (0.4) S = $300,000 
If the desired ROS
before taxes is 20% X = 12,000 ÷ (.2.4) X = 12,000 ÷ .2 X = 60,000 units 
If the desired
ROS after taxes is 20% S = 120,000 ÷ (.2.4) S = 120,000 ÷ .2 S = $600,000 
The after tax equation for X  The after tax equation for S 
X = (1T)(TFC÷P) ÷ (1T)(ROSCMR)  S = (1T)(TFC) ÷ (1T)(ROSCMR) 
Unit Sales  Capital Turnover Ratio  ROS After Taxes  ROI After Taxes 
10,000  0.2  .48  .096 
20,000  0.4  .12  .048 
30,000  0.6  0  0 
40,000  0.8  .06  .048 
50,000  1.0  .096  .096 
60,000  1.2  .12  .144 
70,000  1.4  .137  .1918 
80,000  1.6  .15  .240 
90,000  1.8  .16  .288 
100,000  2.0  .168  .336 
Note that although the function for ROS is nonlinear, the function for ROI is linear. This is because Net Income before and after taxes are linear functions in CVP analysis. See Figure 1118 for a graphic view of Cal Company's CVP analysis. Also note that increasing sales automatically increases the ROS, CTR and ROI even though the CMR remains constant in the conventional linear analysis. The ROS increases at a decreasing rate, while the CTR and ROI increase at a constant rate. The CMR affects the ROI through the effect it has on the ROS.
Exhibit 143 

Using Units (X)  Using Sales Dollars (S) 
ROI before taxes =
NIBT ÷ I ROI = [(PV)(X)  TFC] ÷ I X = [(I)(ROI) + TFC] ÷ (PV) For Cal Company: P =10, V = 6, X
= [(500,000)(ROI) + 120,000] ÷ (106) How many units need to be produced and sold to generate a ROI of 24% before taxes? X
= (125,000)(.24) + 30,000 
ROI before taxes =
NIBT ÷ I ROI = [(1V÷P)(S)  TFC] ÷ I S = [(I)(ROI) + TFC] ÷ CMR For Cal Company: P = 10, V = 6, CMR = .4, S = [(500,000)(ROI) + 120,000] ÷ .4 How many sales dollars are needed to generate a ROI of 24% before taxes? S = (1,250,000)(.24) + 300,000 
ROI after taxes =
NIAT ÷ I ROI = [(1T)(PV)(X)(1T)(TFC)] ÷ I X = [(I)(ROI) + (1T)(TFC)] ÷ (1T)(PV) For Cal Company: P =10, V = 6, T = .4 X =[(500,000)(ROI) + (.6)(120,000)] ÷(.6)(.4) How many units need to be produced and sold to generate a ROI of 14.4% after taxes? X = [(500,000)(.144) + 72,000] ÷ 2.4 X = 60,000 units. 
ROI after taxes =
NIAT ÷ I ROI = [(1T)(1V÷P)(S)  (1T)(TFC)] ÷ I S = [(I)(ROI) + (1T)(TFC)] ÷ (1T)(CMR) For Cal Company: P =10, V = 6, CMR
= .4, S = [(500,000)(ROI) + (.6)(120,000)] ÷(.6)(.4) How many sales dollars are needed to generate a ROI of 14.4% after taxes? S = [(500,000)(.144) + 72,000] ÷ .24 S = $600,000 
Equations for Multiple Product Companies
All of the equations presented above (for ROS, ROI and X and S for a desired ROS and ROI) can be converted to multiproduct situations. We simply need to use weighted averages for contribution margin per unit and the CMR as in the multiproduct CVP analysis in Chapter 11, and define X and S in the equations as mixed units and mixed sales dollars. When P and V are involved, these measures also need to be stated in terms of weighted averages.
Sandlot Cap Company Two Products ExampleThe Sandlot Cap Company produces baseball caps in two categories referred to as regular logo (X1) and special logo (X2). Sales prices, variable costs and sales mix ratios are provided below.
Product  Price  Variable Cost Per Unit  Mix Ratio Based on Units 
X1 X2 
$4 
$3 5 
.75 .25 
The company’s total fixed costs are $300,000, total assets are $1,000,000 and the tax rate is 40%. The mix ratios above indicate that 75% of the units sold are X1s and 25% are X2s. Mix ratios based on sales dollars are .6 for X1 and .4 for X2. These ratios represent each products proportion of the weighted average price. (See Chapter 11 for the CVP analysis related to this company). Based on the simplifying assumptions of conventional linear CVP analysis, determine the following.
1. The number of caps that need to be produced and sold to
earn a 30% ROI before taxes?
2. The number of sales dollars needed to
earn a 30% ROI before taxes? Solve this in dollars, rather than using your answer to question 1.
3. The number of caps that need to be produced and sold to earn an 18% ROI after taxes?
4. The number of sales dollars needed to
earn an 18% ROI after taxes? Solve this in dollars, rather than using your answer to question 3.
5. What are the return on sales and capital turnover ratios when ROI after taxes
is 18%?
The solutions to these problems appear below. Note that the equations in Exhibit 144 are the same as those in Exhibit 143, except X becomes mixed units and S becomes mixed sales dollars.
Exhibit 144 

Using Mixed Units (X)  Using Mixed Sales Dollars (S) 
1. X = [(I)(ROI)
+ TFC] ÷ (PV) X1 = (.75)(400,000) = 300,000 
2. S = [(I)(ROI) +
TFC] ÷ CMR S = [(1,000,000)(.3) + 300,000] ÷ .3 S = 600,000 ÷ .3 S = 2,000,000 mixed sales dollars S1 = (.6)(2,000,000) = $1,200,000 
3. X =
[(I)(ROI) + (1T)(TFC)] ÷ (1T)(PV) X = [(1,000,000)(.18) + (1.4)(300,000)] ÷ (1.4)(1.50) X = (180,000 + 180,000) ÷ .90 X = 400,000 mixed units 
4. S =
[(I)(ROI) + (1T)(TFC)] ÷ (1T)(CMR) S = [(1,000,000)(.3) + (1.4)(300,000)] ÷ (1.4)(.3) S = (180,000 + 180,000) ÷ .18 S = 2,000,000 mixed sales dollars 
5. ROS after taxes = NIAT ÷ Sales
NIAT = (1T)(TFC) + (PV)(X)
NIAT = (1.4)(300,000) + (1.5)(X)
NIAT = 180,000 + (.9)(400,000)
NIAT = $180,000
ROS = 180,000 ÷ PX
ROS = 180,000 ÷ (5)(400,000)
ROS = 180,000 ÷ 2,000,000
ROS = .09 or 9%
CTR = Sales ÷ Total
Assets
CTR = 2,000,000 ÷ 1,000,000
CTRatio = 2
Checking:
ROI = (ROS)(CTR)
ROI = (.09)(2) = .18
Note and Summary of Equations
Although the conventional linear analysis presented above ignores various nonproduction related cost drivers revealed in activitybased costing, it emphasizes the fact that increasing sales volume is the most effective way to increase profitability. When sales increases, the ROS, CTR and ROI all increase automatically in the absence of a substantial increase in fixed costs.
Equations Developed and Used in the Analysis Above  
Using Units (X) 
Using Sales Dollars (S) 
ROS = CMR  [(TFC÷P) ÷ X]  ROS = CMR  (TFC÷S) 
ROS = (1T)(CMR)  [(1T)(TFC÷P) ÷ X]  ROS = (1T)(CMR)  (1T)(TFC÷S) 
X = (TFC÷P) ÷ (ROSCMR)  S = TFC ÷ (ROSCMR) 
X = (1T)(TFC÷P) ÷ (1T)(ROSCMR)  S = (1T)(TFC) ÷ (1T)(ROSCMR) 
ROI = [(PV)(X)  TFC] ÷ I  ROI = [(1V÷P)(S)  TFC] ÷ I 
X = [(I)(ROI) + TFC] ÷ (PV)  S = [(I)(ROI) + TFC] ÷ CMR 
ROI = [(1T)(PV)(X)(1T)(TFC)] ÷ I  ROI = [(1T)(1V÷P)(S)  (1T)(TFC)] ÷ I 
X = [(I)(ROI) + (1T)(TFC)] ÷ (1T)(PV)  S = [(I)(ROI) + (1T)(TFC)] ÷ (1T)(CMR) 
Possible Investment Bases for ROI
The question concerning how the investment should be measured is controversial. Various possibilities include the following.
1. Total assets available. This is considered to be the best overall measurement if the manager has control over all the assets. However, there is a problem in determining how to value the assets. This problem is discussed below.
2. Total assets employed. These are operating assets currently used. Since this base excludes excess or idle assets such as vacant land or construction in progress it may be appropriate if some of the assets are not under the control of the manager.
3. Net Working Capital plus other assets), i.e., Total Assets Less Current Liabilities. This measurement increases the ROI because it reduces the investment base and allows for the use of short term credit in the manager's performance measurement.
4. Stockholder's Equity or Net Worth. This basis provides a measure of both operating performance and financial leverage. The measurement of financial leverage is the difference between the ROI and the ROSE. Using ROSE creates a bias to increase debt or leverage and risk.
How to Measure Assets for ROI Calculation
The question concerning how assets should be valued is also controversial? Some possibilities include:
1. Gross Book Value, i.e., historical cost. This may encourage managers to dispose of old assets too soon, where assets are still useful, but not very efficient, i.e., disposal value < present value of expected net cash inflows. This measurement favors old divisions with lower cost during inflationary periods.
2. Net Book Value, i.e., historical cost less depreciation. Since the ROI would tend to increase as the asset is depreciated (i.e., because the investment base decreases, the capital turnover ratio would increase), using net book value may encourage managers to keep old assets too long, i.e., beyond the point where the disposal value > present value of the expected net cash inflows. If new assets were purchased, the ROI would decline. This method also favors older divisions.
3. Replacement Cost or Current Cost, i.e., cost of identical assets or similar assets that would provide the same level of service. This may be more equitable for comparing different age divisions, but creates the problem of determining current value for all assets. Total present value (i.e., discounted expected future net cash inflows) or appraisal value can be used to approximate current cost.
RI Alternative to ROI
Residual Income (RI) was developed as an alternative to the return on investment (ROI) measurement to overcome some problems discussed below.
RI = Net Income  Minimum Desired Net Income.
The minimum desired rate of return used in the RI calculation is usually referred to as the cost of capital. The cost of capital is a weighted average measure of the cost of long term debt and stockholders equity.
A relatively new term for this measurement is Economic Value
Added (EVA®). This is the Stern
Stewart trademarked version of the concept defined as adjusted operating
income minus a capital charge. Stern Steward recommend a fairly large number of
adjustments although the main concept of Residual Income and EVA® are
the same. An underlying assumption is that a manager’s
actions only add economic value when the resulting profits exceed the cost of
capital.
Maximizing ROI and RI or EVA® are different objectives
Using ROI as a performance measurement may cause many managers to reject profitable projects if the projects would tend to lower the ROI. As a result, a conflict arises between the goals of the manager and the goals of the organization, i.e., goal congruence is not obtained.
Example:
Assume a firm has a minimum desired rate of return of 15 percent after taxes. Recent results show the following for a division:
Assume that Net Income after taxes = $20,000 and Total Assets = $100,000.
ROI = 20%
RI = ($20,000  15,000) = $5,000.
Would a manager evaluated on the basis of the ROI accept a new project with an expected return of 16, 18 or 19 percent? Probably not, since it would reduce the division's overall ROI below 20%.
Would the manager accept the project if RI is used as the evaluation measurement. Yes, since the return is above 15%, it would increase the division's residual income.
Separate Problem for RI users
Using Residual Income avoids the problem stated above, but creates a different problem. Using RI makes it difficult to compare the performance of different size divisions.
A partial solution is to compare each division against a negotiated budget for that division. Different size divisions and different aged divisions cannot be adequately compared with either measurement ROI or RI.
Decentralization means the freedom to make decisions. Decentralization can transform a profit center into an investment center. Centralization can transform an investment center into a profit center or transform a profit center into a cost center.
Potential Benefits from Decentralization
1. Better decisions can be made at the local level.
2. Provides more incentives to segment managers.
3. Encourages internal competition.
4. Provides top management with more time for strategic
planning and other policy decisions.
Cost of Decentralization
1. Lack of Goal congruence.
2. Conflicts between divisions.
3. Redundant activities.
The greater the interdependence between divisions, the greater the likelihood that the costs of decentralization will be greater than the benefits.
Transfer Prices
A transfer price refers to the price used for intracompany transfers, i.e., transfers between segments of a company. The term transfer pricing normally means pricing transfers between divisions, but could be used in any situation where the output of one segment (e.g., department, operation, process) becomes the input for another segment within the same company.
Three Decisions
A transfer pricing situation usually involves three questions or decisions.
1. Should the transfer take place? This is essentially a (Make
or Buy) question.
Should the company make the item or
outsource, i.e., purchase
it on the outside market?
This is a relevant cost problem (also referred to a
differential or incremental cost). The key
is which costs will be different under
the two alternatives, i.e., make inside and transfer, or
buy from outside the
company?
2. If the answer to question one is yes, then what transfer
price should be used?
3. Should the central office interfere in establishing the
transfer price?
Objectives of Transfer Prices
The overall objective is to establish a transfer price that will motivate effort and goal congruence. There are at least three underlying objectives.
1. To aid in Evaluating Division Performance, i.e., investment centers or profit centers. If the divisions are treated as investment centers, then Return on Investment (ROI) and Residual Income (RI) are the relevant measurements. For profit centers, contribution margin, segment margin, or netincome would be a more appropriate measurement.
2. To maintain Division Autonomy. Since autonomy means decentralization and freedom to make decisions, it is also an ingredient in motivating effort. Remember, however, that effort and goal congruence are different. Managers may exert considerable effort in pursuing their own goals that conflict with the goals of the firm. Central office interference in a transfer pricing dispute will affect autonomy and effort. The dilemma is that goal congruent behavior may not be obtained withor without interference.
3. To provide the buying segment with the information necessary for the make or buy question. Intracompany profits included in a transfer price make it impossible for the buying division to answer the make or buy question.
Possible Transfer Prices
1. Market prices. A market price is considered best if the
market is perfectly competitive, i.e., if a single buyer or seller cannot affect
the price. Generally intracompany transfers at market prices accomplish
objectives 1 and 2, but not 3. Unfortunately, several problems occur when trying
to use market prices:
a. Most markets are not perfectly competitive. In other words,
the demand curve and price structure may shift if the firm buys outside.
b. Market prices may not exist for some products.
c. A market price may not be comparable because of differences
in quality, credit terms, or extra services provided.
d. Price quotations may not be reliable because they are based
on temporary distress or dumping conditions.
e. A market price may not be relevant because the selling
division would not have the same transportation cost, accounting cost for A/R,
credit etc. as an outside supplier.
f. Information for the make or buy decision would not be
available to the buying division.
2. Full cost. All manufacturing, selling and administrative cost are included.
The problems that occur when full cost is used as a transfer
price include:
a. Transfer prices based on full cost do not accomplish any of
the objectives stated above.
The selling division could not be evaluated as a
profit center or investment center since it is treated as a cost center.
b. The seller would be motivated to over allocate cost to the
product transferred.
c. If actual cost are transferred, the cost of inefficiency
will be passed along to the buying division. Thus, standard cost make better
transfer prices although standards may be rigged.
d. The buyer would not have the differential cost information
needed for the overall firm make or buy decision. The irrelevant (mostly common
fixed cost) of the seller become relevant
cost to the buyer.
3. Full Cost Plus. All manufacturing, selling and administrative cost plus a markup for profit. Standard cost plus would be better than actual cost plus to motivate the seller to be an efficient cost producer. The same problems in 2 are applicable here. Motivation for over allocation is still present. Transfers at standard could motivate the seller to rig the standard.
4. Variable cost. All variable manufacturing, selling and administrative cost. This may come close to accomplishing objective 3, since variable cost may approximate differential cost. It should be noted however, that variable cost and differential cost are not the same since some fixed cost may also be relevant, i.e., change if the product is purchased outside rather than produced inside. Objectives 1 and 2 would not be obtained since the other problems listed under 2 and 3 are applicable here, lack of motivation for profits, potential for cost over allocation etc.
5. Variable cost plus. This may be a little better than 4, but the plus should be kept separate to allow for a ball park make or buy decision. Objectives 1 and 2 would not be fully obtained.
6. Negotiated price. Negotiated prices may be best if:
a. An imperfect market exist) for the product making it
difficult, if not impossible, to determine the appropriate market price.
b. The seller has excess capacity), thus the transfer becomes
a differential cost problem to the seller. Any transfer price above the seller's
differential cost would benefit the seller.
c. There is no external market) for the product, thus no
market price.
In these cases the buyer and seller may negotiate a price that allows both parties to share in the benefits of the transfer. This may accomplish objectives 1 and 2, but not 3. A problem with this approach is that managers may spend a substantial amount of time and effort negotiating transfer prices.
7. Dual Price. Use two transfer prices. Give the seller credit for selling at market price or full cost plus a reasonable markup, but charge the buyer with variable cost (i.e., approximate differential or additional outlay cost). Charge the difference to a central account. This approach may not motivate either the seller or the buyer to be efficient.
Very General Rule:
Optimum Price = Additional Outlay Cost + Opportunity Cost
Opportunity Cost = Market Price  Additional Outlay Cost
Opportunity Cost is the contribution margin that the seller would earn if the product could be sold on the outside market.
If the seller has excess capacity, i.e., cannot sell additional units on the outside market, then the seller's opportunity cost is zero. Thus, it is argued that the seller should transfer the product at cost. A problem may arise however, since the seller has no incentive to produce the extra product.
Maximum Price = Market Price
Minimum Price = Additional outlay cost, i.e., differential cost.
Transfer pricing is a classic catch22 situation, a problem without a definitive answer.
Additional Problems with Multinational Transfer Pricing
1. Taxes rates in different countries.
The firm's strategy is to shift income from the high tax country to the low tax country. If the buying division is in a low tax country, then transfers would be made at the lowest cost possible. If the seller is in a low tax country transfers would be made at high prices.
2. Foreign Laws preventing income and dividend repatriations.
If there are restrictions on the buying division payments of dividends and transfers of income to the central office, then transfers of products to the buyer would be made at high prices. Transfers from the foreign division would be made a low prices.
Appendix 141: Conflict Between Choosing Capital Projects and Evaluating Results
The traditional recommended approach for choosing Capital Budgeting projects involves using discounted cash flow methods. These include the net present value method (NPV) and the internal rate of return (IRR). The IRR is the discount rate that makes the present value of the cash inflows from an investment equal to the present value of the cash outflows.
Frequently the IRR is used to choose projects and the ROI is used to evaluate performance. A conflict arises because the ROI (accounting rate of return) and IRR are different measurements. The IRR is an average time adjusted rate over the life of the project. The ROI is based on a single year and reflects returns based on conventional depreciation methods, i.e., usually net book value.
Possible Solutions To Conflict Between IRR and ROI
1. Use Compound Interest Depreciation. (Also called the Annuity Method.)
2. Use a Dual Planning Model.
Compound Interest Depreciation
Cash inflows are made up of two parts:
1. Interest Return = (Beginning Book Value)(IRR)
2. Depreciation = Recovery of Principal = Expected Cash Inflow  Interest Return from 1.
Example:
Cost of Project = $7,132. Two year life.Annual net cash inflow = $4,000.
IRR 8% ($7,132/4000 = 1.783)
Interest Return Year 1 = ($7,132)(.08) = $571.00
Depreciation Year 1 = $4,000  571 = $3,429.00
Interest Return Year 2 = ($7,132  3,429)(.08) = $296.24
Depreciation Year 2 = $4,000  296.24 = $3,703.76
Comparison of Compound Interest depreciation with Straight line and Sumoftheyearsdigits.
Assume actual cash flows are equal to expected cash flows.
Compound Interest 
Straight Line 
Sumoftheyearsdigits 

Year 1 
Year 2 
Year 1 
Year 2 
Year 1 
Year 2 

Actual Net Cash Inflow  $4,000  $4,000  $4,000  $4,000  $4,000  $4,000 
Depreciation  3,429  3,704  3,566  3,566  4,755  2,377 
Net Income  $571  $296  $434  $434  $(755)  $1,623 
ROI = NI ÷ Net Book Value  571÷7,132 = 8% 
296÷3,704 = 8% 
434÷7,132 = 6% 
434÷3,566 = 12% 
(755)÷7,132 = 11% 
1,623÷2,377 = 68% 
Now assume that the actual net cash inflows are not equal to expected net cash inflows. Under the compound interest method, a net cash inflow in a given year that is different from the expected amount will cause the ROI to be different from the estimated IRR. For example, suppose the net cash inflow for year 2 above is $3,900. Under the compound interest method the ROI drops to 5.3%. The other depreciation methods do not provide this signal, i.e., that the interanal rate of return is below the expected return.
Compound Interest 
Straight Line 
Sumoftheyearsdigits 

Year 1 
Year 2 
Year 1 
Year 2 
Year 1 
Year 2 

Actual Net Cash Inflow  $4,000  $3,900  $4,000  $3,900  $4,000  $3,900 
Depreciation  3,429  3,704  3,566  3,566  4,755  2,377 
Net Income  $571  $196  $434  $334  $(755)  $1,523 
ROI = NI ÷ Net Book Value  571÷7,132 = 8% 
196÷3,704 = 5.3% 
434÷7,132 = 6% 
334÷3,566 = 9.4% 
(755)÷7,132 = 11% 
1,523÷2,377 = 64% 
Why the Compound Interest Method is not used
1. The method is hard to understand and not consistent with external reporting.
2. The depreciation charge increases over the life of the
asset. This seems to violate the
matching concept.
3. There is a possibility of negative depreciation in some years.
The Dual Planning Model
Plan with the DCF model and evaluate with the accounting rate of return model. In other words, choose capital budgeting projects using the DCF methods (IRR and NPV), but restate the expected results in terms of the accounting rate of return (ROI). Then compare actual ROI with expected ROI to evaluate performance.
^{1 }Johnson, H. T. and R. S. Kaplan. 1987. Relevance Lost: The Rise and Fall of Management Accounting. Boston: Harvard Business School Press. The graphic is adapted from Figure 41, page 85. (See the Summary of Chapter 4 for more on how Dupont used the ROI measurement).
^{2} See Read, R. B. 1954. Return on investment  A guide to management decisions. N.A.C.A. Bulletin (June); Danfy, R. J. 1975. Analyzing the return on investment. Management Accounting (September): 3132; and National Association of Accountants. Return on Capital as a Guide to Managerial Decisions. NAA Research Report No. 35: 33.
Appendix 142: What is inputoutput accounting?
Performance Measurements Main Page