13.3 Yield Capitalization and Discounted Cash Flow

Beyond One-Year Income: Yield Capitalization

Direct capitalization (13.1–13.2) uses a single income estimate and a cap rate or multiplier. ECO VI.f Yield capitalization addresses situations where value is the present worth of future benefits over time—explicitly.

Yield capitalization discounts future cash flows (and often a terminal value) at a yield rate (discount rate) that reflects the time value of money and risk. The workhorse application is discounted cash flow (DCF) analysis.

ECO VI.h requires indicating value through yield capitalization for fee simple, leased fee, and leasehold—the rights applications appear in Section 13.4; here you learn the engine.

Yield Rates vs Cap Rates (Do Not Swap Labels)

Rule of thumb relationships (conceptual, not always exact):
If income and value grow, Ro is often below YO because part of the total yield comes from growth/appreciation (the classic “cap rate = yield − growth” intuition in level-growth models: Ro ≈ YO − g under simplifying assumptions).

Example intuition: YO = 10%, perpetual growth g = 2% → Ro ≈ 8%. Direct cap at 8% can match a growing perpetuity DCF at 10% discount—why stable properties can still use direct cap.

Present Value Building Blocks

PV of a single future amount:
PV = FV ÷ (1 + Y)^n
(or FV × 1/(1+Y)^n)

PV of a level annuity (optional if stem gives factors): sum of each period’s PV, or annuity factor × payment.

On the National Exam, expect either:

• Simple 2–5 year discrete discounting with given rates, or
• Use of tabulated PV factors in the stem, or
• Conceptual questions on what DCF includes

Bring calculator fluency (HP-12C-style TVM is common in appraisal education).

Mini Discount Drill

$10,000 received in 3 years; yield 9%:
PV = 10,000 / (1.09)^3 = 10,000 / 1.295029 ≈ $7,722

Property Models in Yield Capitalization

A property model is a structured forecast of how the property will produce benefits over a holding period. Typical elements:

Fee simple property model often uses market rent paths. Leased fee models may use contract rent until rollover, then market. Leasehold models focus on the tenant’s advantage (below-market rent) over time.

Common Model Patterns (Recognition)

Modern exam emphasis is on understanding DCF logic and simple multi-year discounting, not obscure table names.

Estimating the Reversion (Resale)

At the end of year n, the investor sells. Teaching method:

1. Forecast NOI in year n+1 (first year new buyer owns), or use year n NOI with growth.
2. Apply a terminal capitalization rate RT (going-out cap rate):
   Resale price ≈ NOI_{n+1} ÷ RT
3. Deduct selling costs if the stem requires (brokerage, etc.):
   Net reversion = Resale × (1 − cost %)
4. Discount net reversion n periods at YO.

Terminal cap rates are often equal to or slightly higher than going-in Ro when aging, risk, or slower growth is expected—follow the stem.

Simplified Exam-Ready DCF Example (Overall Property)

Facts

Investor holds 3 years. Discount rate YO = 10%. Selling costs 0% for simplicity. Terminal cap rate RT = 9% on Year-4 NOI.

Step 1 — Reversion at end of Year 3
Resale = NOI₄ ÷ RT = $115,000 ÷ 0.09 = $1,277,778

Step 2 — Benefits by year (cash flow + reversion in year 3)

Step 3 — Discount at 10%

Indicated value by yield capitalization ≈ $1,220,000 (rounded).

Cross-Check with Direct Cap (Stabilized Shortcut)

If someone naively caps Year-1 NOI at 9%: $100,000 ÷ 0.09 ≈ $1,111,000—different because cash flows grow and terminal RT/YO relationship differs. If the market were a level perpetuity of $100,000 at YO 10% with g = 1% roughly Ro ≈ 9%, values align more closely. The point: DCF earns its keep when the path matters.

Second Compact DCF (Two-Year, Clean Numbers)

YO = 12%. CF₁ = $50,000; CF₂ = $50,000 + reversion $600,000.

PV = 50,000/1.12 + (650,000)/(1.12)^2
= 44,643 + 650,000/1.2544
= 44,643 + 518,176
= $562,819

Equity DCF vs Property DCF (Concept)

Value property from overall DCF, or Value equity + loan balance from equity DCF + mortgage—ideally consistent. Exam items usually stay at overall NOI DCF unless financing is introduced.

Selecting a Yield Rate (Support Ideas)

Yield rates are supported by:

• Investor surveys and interviews
• Built-up risk analysis (recognition)
• Band-of-investment style thinking for YE with mortgage yield
• Comparison to alternative investments adjusted for real estate risk/illiquidity
• Extraction from sales when full forecasts can be reverse-engineered (advanced)

Higher risk → higher YO → lower PV. Lease-up risk, credit risk, and market volatility raise yields.

When to Use Yield Cap on the Exam

CG candidates face more income complexity; LR/CR still need conceptual DCF and simple PV math when tested.

Common Exam Traps — Yield Cap

• Discounting with Ro instead of YO
• Capitalizing Year-1 NOI with YO (mixing tools)
• Forgetting to add reversion in the final year
• Capitalizing Year-3 NOI for resale instead of Year-4 when RT is a going-out rate on forward NOI (follow stem convention)
• Using RE as the property discount rate
• Double-counting growth in both cash flows and an already growth-loaded low YO without thought
• Treating DCF output as automatic market value when inputs are investor-specific investment value

Formula Card

1. PV = Σ [CFt ÷ (1+Y)^t] + [Reversion_n ÷ (1+Y)^n] (reversion may be inside CF_n)
2. Resale ≈ NOI_{n+1} ÷ RT (common teaching form)
3. Ro ≈ YO − g (level-growth intuition; not universal law)
4. YO ≠ Ro; YE ≠ RE
5. Property DCF → discount NOI path + net resale at YO

Bridge

You can contrast direct vs yield capitalization, assemble a simple property model, and complete a multi-year DCF with reversion. Section 13.4 applies direct and yield techniques to fee simple, leased fee, and leasehold interests and finishes ECO VI.i with reconciliation to the indicated value by the income approach.