Three ways to value the same thing

Three people value the same warehouse on the same morning.

The first adds up the rent it will collect and asks what that stream is worth to someone who wants 8% a year. She says 118,000. The second looks at four similar warehouses sold nearby in the last year and says 145,000. The third prices the land, the steel and the labour to put up an identical building and says 96,000.

Nobody has made a mistake. They answered three different questions.

Method one: what the cash is worth

The only method that is about the asset rather than about the market.

An asset that hands you cash for a number of years is arithmetically identical to a loan you have made, seen from the other side of the table. The lender hands over a lump today and receives instalments; you hand over a price today and receive rent. Same structure, same maths, opposite chairs.

That means a repayment calculator is a valuation calculator with the labels changed. Give it the return you require and the length of the stream, and the amount it says you could lend is the amount you could pay.

Debt amortisation

≈ Hypothetical model, not a forecast

The full repayment schedule for a fixed-rate debt paid off in equal instalments.

It assumes

• The rent arrives in full every year for twenty years and never once misses.
• The building is worth exactly nothing at the end of the lease.
• Eight percent is the return you require, not a return anyone has promised.
• Nothing is spent on repairs, insurance or management along the way.

It ignores

• Arrangement fees, late fees and early-repayment charges
• Any rate that moves, resets or reverts partway through
• Payment holidays, arrears and renegotiation
• Tax relief on interest, which exists in some places and not others

A warehouse is let on a twenty-year lease at 12,000 a year, after which the building is worth nothing. You require 8% a year. Move the price until the yearly payment sits between 12,000 and 12,100 — that price is the most this stream is worth to you.

Amount borrowed100,000

Payment each period

10,185

Number of payments

20

Total handed over

203,704

Of which interest

103,704

Interest as a share of everything paid

0.509

Balance at the end

0

• Capital not yet returned
• Return earned so far

◷ Not there yet — keep moving the controls.

The answer lands near 118,000. Two things about it are worth more than the number itself.

The first is that the required return is an input, not a fact. Ask for 6% and the same rent is worth about 138,000; ask for 12% and it is worth about 90,000. The asset did not change. Nothing about the warehouse knows what return you want. This is why two careful people can value the same stream differently and both be right, and why "what is it worth" is an incomplete question until somebody says worth to whom.

The second is what the chart shows. Each 12,000 payment is part return and part your own capital coming back. Early on it is mostly return; by the end it is mostly capital. An owner who counts the whole 12,000 as income for twenty years and then finds the building is worthless has spent their capital and called it a yield.

Predict

The lease is renegotiated: same 12,000 a year, but for forty years instead of twenty. Holding the required return at 8%, roughly what happens to the value?

Choose one answer

It doubles — twice as many paymentsIt rises by roughly a fifthIt is unchanged, since the yearly cash is the sameIt falls, because the money is locked up longer

Lock in answer

Method two: what the neighbours sold for

Comparables answer a different question: not what the cash is worth, but what someone recently paid.

This is the method almost everyone actually uses, for the good reason that it requires no forecast. It is also the method that transmits errors fastest. If the last four buyers were wrong about the future of the area, the comparable tells you so with complete confidence and to two decimal places.

Comparables are strongest where the objects are genuinely alike and the sales are genuinely recent — the same street, the same specification, the same month. They weaken with every adjustment you have to make, and by the time you are adjusting for four differences at once, you are no longer measuring, you are guessing in a spreadsheet.

Method three: what it would cost to build

Replacement cost answers a third question: what would it take to make another one of these?

It sets a ceiling in a market where supply can respond. If a warehouse trades for 145,000 and a new one costs 96,000 to put up, the sensible move for anyone who wants a warehouse is to build. Enough people doing that pulls the price back towards the cost of building, and the gap between the two is a good estimate of how much of the price is scarcity rather than the object.

Where supply cannot respond, replacement cost says almost nothing. Nobody can build another well-located city block, and nobody can rebuild a brand or a thirty-year customer relationship at any price. For those assets the replacement figure is a lower bound and a curiosity.

Check

A business trades for six times what it would cost to build a competitor from scratch, and the gap has held for a decade. What is the most useful reading?

Choose one answer

The business is overvalued and the price will converge on the build costSomething the money cannot buy is holding competitors outThe replacement cost has been calculated wronglyReplacement cost does not apply to businesses

Check answer

›When the three methods agreeOptional

Agreement between the three is comfortable and slightly uninformative. It usually means an ordinary asset in a functioning market, priced about where everyone expects.

Disagreement is where the content is, and each pattern of disagreement has a characteristic meaning. Cash-flow value far below comparables says buyers are paying for something other than the current cash — growth, scarcity, or someone else's willingness to pay more later. Comparables far below replacement cost says the market expects the need to shrink, and nobody will be building anything here for a while. Replacement cost far below both says there is a barrier, and it is worth naming before you rely on it.

None of those three readings is a conclusion. Each one is a question sharp enough to be worth a week.

Worth remembering

• The three valuation methods answer three different questions: what the cash is worth, what others paid, and what building another would cost.
• Discounting a cash stream is the same arithmetic as a loan schedule, seen from the lender's side.
• The required return is an input chosen by the buyer, so two careful people can value one stream very differently.
• At around 8% a year, cash arriving beyond roughly thirty years contributes very little to the value today.
• A durable gap between market price and replacement cost is a barrier to entry, expressed as a number.