Theory of Returns
What you'll be able to do
By the end of this unit you will be able to:
- Decompose total return into income return (yield) and appreciation return (growth).
- Value a property two ways — direct capitalization and discounted cash flow (DCF).
- Read the relationship R₀ = r − g and explain what moves a cap rate.
- Build a clean PGI → NOI proforma and project it forward.
- Layer in debt and judge whether leverage is positive or negative for a deal.
Estimated time for the unit: ~90 minutes. Prerequisite: Unit 0.2 — Present Value Math.
Defining “return”
Return is the change in price of an investment over time, plus any income it generates. It can be positive (the investment was profitable) or negative (a loss). It is usually expressed as a percentage: profit divided by the amount originally invested.
Two ideas matter from the start:
- Price and return are opposite sides of the same coin. As the price you pay rises, your return falls — and vice versa. An investor who needs a higher return has to pay a lower price.
- Money is made when you buy, not when you sell. Once your purchase price is set, so is your expected return. But that expected return is not fully in your control: future cash flows depend on the market, so be prepared for volatility.
The two components of return
When a property produces rent and changes in value, total return over a period combines two pieces:
Rₜ = CFₜ / Vₜ₋₁ + (Vₜ − Vₜ₋₁) / Vₜ₋₁
- Income return (yield) — the return from net operating income:
yₜ = CFₜ / Vₜ₋₁. It comes from contractual leases, so it is relatively stable. - Appreciation return (growth) — the return from the rise in market value:
gₜ = (Vₜ − Vₜ₋₁) / Vₜ₋₁. It depends on future market conditions, so it carries most of the risk.
Total return = income return + appreciation return.
Worked example (from class)
A property is bought for €200,000 at t = 0. The landlord receives €7,000 rent and sells for €205,000 at t = 1.
- Income return = 7,000 / 200,000 = 3.5%
- Appreciation return = (205,000 − 200,000) / 200,000 = 2.5%
- Total return = 3.5% + 2.5% = 6.0%
For multi-period investments (the norm in real estate, which is long-term), we measure return with the Internal Rate of Return (IRR) — the single rate that discounts all the investment's future cash flows back to a present value equal to its purchase price.
Deeper dive — price, return, and the two components
The single idea to carry through the course: price and return are opposite sides of the same coin. As the price you pay rises, your return falls — so an investor who demands a higher return must offer a lower price. From this comes the maxim money is made when you buy, not when you sell: once your purchase price is fixed, so is your expected return. But your realized return is never fully in your control, because future cash flows are dictated by the market — so always underwrite for volatility.
Total return splits into two additive pieces: income return (yield) = CFₜ / Vₜ₋₁ (matters to income-focused investors) and appreciation (growth) return = (Vₜ − Vₜ₋₁) / Vₜ₋₁ (matters to growth-focused investors). The cap rate is essentially the income-return piece; the discount rate is the total return. One classification habit that trips students: separate operating cash flows (rent, lease income) from capital transactions (a unit sale, building a new wing) — the first belongs in NOI, the second in the reversion.
Worked example — decomposing a 6% return
Buy at €200,000; collect €7,000 rent; sell at €205,000 one year later.
- Income return = 7,000 / 200,000 = 3.5%
- Appreciation = (205,000 − 200,000) / 200,000 = 2.5%
- Total = 6.0%, i.e. (7,000 + 5,000) / 200,000.