How to Calculate a Rate-of-Return Regulated Price
A regulated utility's allowed revenue equals its operating costs plus the allowed rate of return times its rate base, and the regulated price is that revenue divided by units sold.
The Rate-of-Return Regulation formula
Calculator
Enter the rate base, operating costs and allowed return to get allowed revenue and the price per unit it implies.
Depreciated value of the capital the regulator has accepted into service.
Wages, fuel, maintenance and depreciation the utility may recover.
Percentage the regulator lets the utility earn on its rate base.
Quantity customers are expected to buy over the year.
Set this to zero to see the price before any new investment.
Spreading allowed revenue over the units sold sets the price at $2.12, which lands near average total cost rather than marginal cost.
- Allowed profit (millions)
- $36
- Allowed revenue (millions)
- $106
- Price after the extra capital
- $2.21
- Price rise from the extra capital
- $0.09
The approved return on the rate base comes to $36 million, and that is the whole of the utility's permitted profit.
Operating costs plus the allowed return gives $106 million of revenue the price has to raise.
With the larger rate base the same customers pay $2.21 for the same quantity.
Building capital nobody asked for adds $0.09 per unit to the bill and adds to allowed profit at the same time, which is why this method is accused of rewarding over-investment.
How to calculate Rate-of-Return Regulation, step by step
- 1Find the rate base. The rate base is the depreciated value of the capital in service that the regulator has accepted, so spending it rejects as imprudent earns nothing.
- 2Apply the allowed rate of return. Multiply the rate base by the approved percentage. That dollar figure is the profit the utility is permitted to earn on its capital.
- 3Add the approved operating costs. Wages, fuel, maintenance and depreciation the regulator allows. Allowed revenue is operating costs plus the allowed return.
- 4Divide by the units customers will buy. Allowed revenue divided by expected quantity gives the price per unit, which lands near average total cost rather than marginal cost.
- 5Test what happens when the rate base grows. Add capital without adding sales and the allowed return rises with it, so both the utility's profit and the customer's price go up. That incentive is the standing objection to this method.
Worked example: Rate-of-Return Regulation
A water utility has a rate base of $400 million, approved operating costs of $70 million a year and an allowed return of 9%. Its allowed profit is 0.09 × 400 = $36 million, so allowed revenue is 70 + 36 = $106 million. Selling 50 million units gives a regulated price of 106 ÷ 50 = $2.12 per unit. Now let it add $50 million of capital without delivering another drop of water: allowed revenue becomes 70 + (0.09 × 450) = $110.5 million and the price rises to $2.21, so the new equipment lifted the firm's profit and the customer's bill by $0.09 a unit at the same time.
Rate-of-Return Regulation questions
What is a rate base?
The rate base is the value of the capital a utility has invested to serve customers, usually measured at original cost less accumulated depreciation, and counting only the assets the regulator has accepted as prudent. It is the figure the allowed rate of return is applied to, so what goes into it decides how much profit the firm is permitted.
Why does this method encourage over-investment?
Because allowed profit is a percentage of the capital base, every extra dollar of accepted capital raises the profit the utility may earn, whether or not customers needed the equipment. Regulators push back by auditing spending and refusing to admit assets they judge unnecessary into the rate base.
Why not simply order the monopoly to charge marginal cost?
Where a natural monopoly's average cost is still falling, marginal cost sits below average total cost, so a price equal to marginal cost loses money on every unit and the firm would need a subsidy to survive. Pricing near average total cost keeps it solvent, at the cost of leaving some deadweight loss in place.
How does a price cap differ from rate-of-return regulation?
Rate-of-return regulation builds the price up from the firm's own costs, so savings are passed through to customers and the firm keeps little of what it cuts. A price cap fixes the maximum price in advance and lets the firm keep whatever it saves, which sharpens the incentive to cut costs but leaves more risk with the firm.
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