Responsibility budgets should be matched to the operating cycle of the responsibility center in question. They are usually incremental. This means that they presume some kind of a base plus an increment, which is adjusted for circumstance (volume and price changes, scheduled savings, etc.) The result for discretionary expense centers is a spending plan, for engineered expense centers a flexible spending plan (i.e., the budget has two components, a discretionary component and a component that varies directly with volume), and for cost or profit centers a performance target or goal. These budgets say what a responsibility manager is responsible for doing &endash; spending, meeting required output levels, or managing costs. For a cost center, the target will be a unit-cost standard, usually called a standard cost. For a quasi-profit center, the target will be expressed as a quasi profit measure: (Standard Cost [units delivered] &endash; Actual Unit Cost [units delivered]). For a profit center, revenue &endash; cost of goods sold.

The real difference between kinds of centers is not in how they are evaluated, what the manager is responsible for, but the authority delegated to responsibility managers with respect to the use and acquisition of assets. Expense centers must have all proposed outlays approved by a higher level. The only difference between discretionary and engineered expense centers is that prior approval is granted for acquisitions needed to adjust to changes in production rates, volume, or mix.

The budget of an investment center is also a target or goal &endash; usually return on assets (ROA or ROI) or residual income (RI). The main difference between investment centers and all other responsibility centers is that the former approves its own capital budgets.

Capital budgeting is concerned with changes that have multi-cycle consequences for the responsibility center in question &endash; investment in new plant or equipment, a new product development, a major process enhancement, etc. In the absence of liquidity constraints, capital budgeting should be carried out continuously. Where cost and profit centers are concerned, some higher authority must approve these kinds of projects. And, each time a project is approved, the targets for the current cycle should be adjusted accordingly, as should future year targets.

IN CONTRAST, investment center mangers can make these kinds of decisions without the approval of a higher authority. Their budgets are expressed in terms of performance targets expressed in terms of their skill in managing assets: ROA, EVA.

ROA (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. It is bad because under certain circumstances it causes managers to make decisions that are bad for their organization. Two situations are critical: The first is where the ROA target is not consistent with the entity’s capital cost, in which case the investment center manager will under-invest in assets. The second case is where the depreciation rate used in calculating ROA 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.

When R is the true rate of return on an investment, true depreciation (D) is equal to the difference between true _ and R. For example, suppose that $1 of investment today yields profits of ¹_oe^-Dt at time t:

$1 = º_o^x ¹_oe^-Dt e^-Rt ¶t, or 1 = ¹_o/(R+D), or R = P_o &endash; D

Calculated using book values and tax depreciation rates, the accounting rate of return is:

R_ac(t) = Accounting Income (t)/ Accounting Book Value (t)

Hence R = R_ac, if and only if and tax depreciation rates = R. For example, if R = .05 and D = .1, if the depreciation rate used is .2, even though the true R is constant and equals .05, the measured R_ac is -.03 in Year 1 and .91 in Year 20.

Economic Value Added (EVA), which is the currently popular term for the traditional accounting concept of residual income (RI), subtracts from operating income a charge for invested capital.

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, which are assumed to be self-correcting. 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 alternative way to measure the use of invested capital would be to measure the market rental that could be earned on each item. 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,

(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) = º^x _o R(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) = º^x_y R(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 º^x_y R(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.