The NPV Framework: A Rigorous Buy-vs-Rent Comparison

The 5% rule is a fast heuristic. For a rigorous comparison over a specific holding period, discount every future cash flow of each option back to today and compare — the Net Present Value (NPV) approach Tabner (2016)¹⁴⁴ applies to the buy-versus-rent question.

Over a holding period of $T$ years, at discount rate $r$, the NPV of owning is:

where $P_0$ is the all-in purchase price (including transaction costs), $R_t$ the imputed rent you collect by not paying a landlord, $C_t$ the year-$t$ cost of ownership (mortgage interest, maintenance, property tax, insurance), and $P_T$ the expected net sale price after $T$ years. The NPV of renting the same home is just the discounted stream of rent paid:

with $L_t$ the rent in year $t$. Buying is the better financial choice only when ${\text{NPV}}_{\text{own}}>{\text{NPV}}_{\text{rent}}$.

Run it once on the $2 million house from the 5%-rule example, held seven years, bought all-cash with 2% buying costs ($P_0=\$2.04$M) and sold with 6% costs; imputed rent $90,000 and carrying costs $50,000, both growing 3%. Both NPVs are negative — housing is consumption either way — so the verdict is whichever costs less:

Same house, same rent, and the verdict swings $630,000 on two assumptions you supply. That is not a defect of the framework — it is the framework telling you where the argument actually lives: in the discount rate and the appreciation guess, exactly the two dials the sales pitch sets for you.

Tabner’s central finding squares with the heuristics above: households generally need a holding period of five to ten years to reach a break-even NPV. Stay fewer than five years and the transaction costs of buying and selling never amortize, so renting usually wins. Two forces in the model deserve emphasis, because the quick rule of thumb understates them:

Inflation works for the owner

A fixed-rate mortgage payment stays flat in nominal terms while rents climb year after year; inflation also lifts the nominal sale price $P_T$. By the Fisher Effect, nominal rates adjust to expected inflation, so a fixed-rate owner captures wealth from the lender in real terms. Ownership is a partial inflation hedge; renting is not.

The discount rate decides the verdict

If $r$ is the risk-free rate, ownership looks attractive. If $r$ instead reflects the equity returns you forgo by locking capital in drywall — your true opportunity cost — the bar rises sharply. Tabner discounts at a household-savings rate close to risk-free, which flatters ownership; adjust it upward for an apples-to-apples comparison.

Tax treatment shifts the result too, though less than folklore claims: mortgage interest and property tax are deductible only if you itemize, and since the TCJA’s larger standard deduction most homeowners no longer do (section “Homeownership Taxes”).

Finally, NPV is not destiny. A buyer who places high personal value on ownership — stability, control, the freedom to renovate — may rationally accept a modestly negative NPV and treat the shortfall as the consumption cost of that lifestyle; a home is consumption first. A financially constrained buyer should instead read a negative NPV as a signal to consume less house, not to manufacture optimism. A solidly positive NPV is a margin of safety against the costs and uncertainties the model cannot fully capture.