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In Ben Graham's The Intelligent Investor, I read that "the public-utility enterprises have been a chief victim of inflation, being caught between a great advance in the cost of borrowed money and the difficulty of raising the rates charged under the regulatory process". Why is the cost of borrowed money rising if inflation decreases the value of each dollar? And why is it difficult to raise the rates charged under the regulatory process?

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Isn't it pretty self-explanatiory? Because they're "...caught between a great advance in the cost of borrowed money and the difficulty of raising the rates charged under the regulatory process".

In other words, they have to pay out more to buy stuff because of inflation, but the price they can charge for their goods is set by a bunch of bureaucrats (e.g. Public Service Commissions in the US), who don't like raising rates. Therefore, they may need to borrow more money so that they can stay in business (which they're generally legally obligated to do) because their ongoing income no longer covers costs.

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Why is the cost of borrowed money rising if inflation decreases the value of each dollar?

If the utility already locked in a fixed long-term borrowing rate, inflation would not hurt. But higher interest rates for new, rolled-over, or variable-rate debt will increase the debt service burden.

And why is it difficult to raise the rates charged under the regulatory process?

Utility rate increases are subject to political scrutiny and unpopular with the public even if they are commensurate with the cost of other goods and services. Regulators may be tempted to make a show of "holding the line" on utility rates. There will be sympathy for seniors on fixed incomes trying to heat their homes, etc.

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