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## EVALUATING THE PERFORMANCE OF AN INVESTMENT CENTER

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**EVALUATING THE PERFORMANCE OF AN INVESTMENT CENTER**ROE ROI EVA**THE ALTERNATIVES**• Return on Equity [ROE] • Earnings [cash flows] divided by shareholders’ equity [Balance sheet assets minus liabilities] • Return on Investment [ROI] • Earnings [cash flows?] divided by assets [usually Balance Sheet Assets] • Economic Value Added [EVA] - Cash Flows divided by Capital less the Cost of Capital multiplied by Capital**Return on Equity [ROE]The FIRM Perspective**Return on equity encompasses the three main financial "levers" by which management can poke and prod the organization to excel -- profitability, Asset Management, and Leverage. Definition An Example**Return on Equity [ROE]The SHAREHOLDER’S Perspective**Businesses that generate high returns relative to their shareholder's equity are businesses that pay their shareholders off handsomely, creating substantial assets for each dollar invested. By relating the earnings generated to the shareholder's equity, an investor can quickly see how much cash is created from the existing assets. If the return on equity is 20%, for instance, then twenty cents of assets are created for each dollar that was originally invested. As additional cash investments increase the asset side of the balance sheet, this number ensures that additional dollars invested to not appear to be dollars of return from previous investments. The best & Worst ROE**RETURN ON EQUITY**(Income) (Assets)(Liabilities) Profit Margin Turnover Leverage Operating MarginInventory Turns Debt-to- Whatever Gross Margin Days Sales Out. Times Interest Earned By looking at trends in return on equity and analyzing the components, the investor is forced to not only examine the Statement of Operations, or the Income Statement, but also to balance this against the left and right sides of the Balance Sheet.**Return on Investment (ROI)**• ROI is good because targets can be adjusted to focus managers’ attentions on key success factors and also because every manager can be measured by the same metric. • ROI is bad because under certain circumstances it causes managers to make decisions that are bad for their organization. Two situations are critical: • the ROI target is not consistent with the entity’s capital cost, in which case the investment center manager will under-invest [sometimes over-invest] in assets. • the depreciation rate used in calculating ROI is not the true economic rate of depreciation, in which case managers may make bad decisions about both the maintenance and the acquisition of assets. ROI versus ROE**An Example**Calculated using book values and tax depreciation rates, the accounting rate of return is: Rac(t) = Accounting Income (t)/ Accounting Book Value (t) BUT Rac is the true ROI (R), if and only if and tax depreciation rates = the true rate of depreciation (D) are equal. For example, if R = .05 and D = .15, if the depreciation rate used is .2, even though the true R is constant and equals .05, the measured Rac is -.06 in Year 1 and .08 in Year 2 (.91 in year 20) (assume I =100 in t-1, so real income = 4.5 in year 1 and 3.6 in year 2).**Economic Value Added (EVA)**• EVA measures the value created from investments. • Returns on capital should be defined in terms of true cash flows resulting from investments. • The cost of capital is the weighted average of the costs of the different financing instruments used to finance investments. • EVA is measured in dollar values, not the percentage difference in returns. • It is closest in both theory and construct to the net present value of a project in capital budgeting, as opposed to IRR. • The value of a firm, in DCF terms is the EVA of projects in place plus the present value of the EVA of future projects.**An Example (a)**Assume that you have a firm with IA = 100 In each year 1-5, assume that ROCA = 15% D I = 10 (Investments at beginning of each year) WACCA = 10% ROC(New Projects) = 15% WACC = 10% Assume that all of these projects will have infinite lives. After year 5, assume that * Investments will grow at 5% a year forever * ROC on projects will be equal to the cost of capital (10%)**An Example (b)**Capital Invested in Assets in Place = $ 100 EVA from Assets in Place = (.15 - .10) (100)/.10 = $ 50 + PV of EVA from New Investments in Year 1 = [(.15 - .10)(10)/.10] = $ 5 + PV of EVA from New Investments in Year 2 = [(.15 - .10)(10)/.10]/1.12= $ 4.55 + PV of EVA from New Investments in Year 3 = [(.15 - .10)(10)/.10]/1.13= $ 4.13 + PV of EVA from New Investments in Year 4 = [(.15 - .10)(10)/.10]/1.14 = $ 3.76 + PV of EVA from New Investments in Year 5 = [(.15 - .10)(10)/.10]/1.15= $ 3.42 ……… Value of Firm = $ 170.86**Invested Capital (1)**• How do you measure the capital invested in assets? • Many firms use the book value of capital invested as their measure of capital invested. To the degree that book value reflects accounting choices made over time, this may not be reflect the economic value of the investment. • In some cases, capital and the after-tax operating income have to be adjusted to reflect true capital invested.**Invested Capital (2)**Normally the charge for invested capital is the book value of working capital plus fixed capita times a discount rate, which reflects the entity’s average nominal cost of capitol. This approach contains three errors: HC is used rather than replacement cost; a nominal rather than a real rate is used (not adjusted for inflation), and an average rate is used rather than a marginal rate. The BEST way to measure the use of invested capital would be to measure the market rental that could be earned on each item. However, the market won’t provide that info on assets that are specific to the firm -- I.e., those that have the greatest value to the firm.**Invested Capital (3)**For example, Public utility regulators throughout the United States use the following procedure to convert the replacement price of a wasting asset into a periodic rental price. This approach differs in two significant ways from standard business practice: it uses current replacement cost and it adjusts the rate of depreciation for investments in maintenance. It also applies different depreciation rates to different kinds of assets. R(t) = rental price for one unit of equipment at time t, p(t) = purchase price of one piece of equipment at time t, K(t) = amount of equipment remaining at time t, if n units were purchased at time 0, r = discount rate d = rate of depreciation (which is defined as the rate at which the equipment declines in its productive capacity, a function of use, wear and tear, and maintenance levels; d = -K’/K, where an apostrophe indicates differentiation with respect to time).**Invested Capital (4)**It is a fundamental law of capital theory that the price of an asset equals the discounted present value of the rentals one could obtain from the asset. If K(t) units of equipment remain at time t, then the total rental at time t would be R(t) K(t). Therefore: p(t=0) = ºxoR(t) K(t) e-rt dt, when K(0) = 1. This formula for the asset price applies not just at time 0, but at any time y. Hence: K(y) p(y) = ºxyR(t) K(t) e-r(t-y) dt, By taking the derivative of this equation with respect to y, one obtains: K’(y) p(y) + K(y) p’(y) = r(y) K(y) + r ºxyR(t) K(t) e-r(t-y) dt = R(y) k(y) + r[p(y)] K(y), Hence: R(y) = (r + d - [p’/p]) p(y). This means that that the rental rate per asset equals interest foregone, plus depreciation, minus any price appreciation or decline.**Invested Capital (5)**The basic notion is that R(y) = (r + d - [p’/p]) p(y). This means that that the rental rate per unit of asset R(y) equals interest foregone (r), plus depreciation (d, which is defined as the rate at which the equipment declines in its productive capacity, a function of use, wear and tear, and maintenance levels; d = -K’/K, where an apostrophe indicates differentiation with respect to time), minus any price appreciation or decline (p’/p). Summing those rates and multiplying them times the replacement price of the asset in time y, gives us the economic rent per unit in time y. For example, if we started with 2 units of investment: p(y) = 100 (replacement cost per unit) p'(y) = 8 d = .1 (where k' = .the change in life of the asset remaining 05, k =.5 the life of the asset remaining) r = .05 R(y) = .07 R(y)P(y) = .07(100) = 7, the rent per unit Hence the total asset rent is 14 = 2(7)**Returns**How do you measure return on capital? * Again, the accounting definition of return on capital may not reflect the economic return on capital. * In particular, the operating income has to be cleansed of any expenses which are really capital expenses (in the sense that they create future value). One example would be R& D. * The operating income also has to be cleansed of any cosmetic or temporary effects. How do you estimate cost of capital? * DCF valuation assumes that cost of capital is calculated using market values of debt and equity. * If it assumed that both assets in place and future growth are financed using the market value mix, the EVA should also be calculated using the market value. * If instead, the entire debt is assumed to be carried by assets in place, the book value debt ratio will be used to calculate cost of capital. Implicit then is the assumption that as the firm grows, its debt ratio will approach its book value debt ratio.