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]
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EVALUATING THE PERFORMANCE OF AN INVESTMENT CENTER
- Cash Flows divided by Capital less the Cost of Capital multiplied by Capital
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.
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
Operating MarginInventory TurnsDebt-to-Whatever
Gross MarginDays 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.
ROI versus ROE
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).
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%)
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
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.
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).
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),
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.
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)
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.