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Canvas Example MCQ — Q5

• A) Higher property income-growth expectations have no effect on cap rates.
• B) Higher property income-growth expectations result in lower cap rates.
• C) Higher Treasury / risk-free bond yields have no impact on cap rates.
• D) A higher property risk premium results in a lower cap rate.

Using the standard growth intuition, cap rate ≈ required return - expected growth. If expected growth rises while required return is unchanged, the cap rate falls.

Rule: Growth up -> cap rate down, ceteris paribus.

Old Exam — Oct 2023, Q7 · adapted

Given: Severe recession: p = 10%, IRR = −4.75% Moderate recession: p = 30%, IRR = 0.55% Baseline: p = 35%, IRR = 6.53% Moderate expansion: p = 20%, IRR = 9.80% Strong boom: p = 5%, IRR = 18.94%

• A) 6.22%
• B) 4.53 %
• C) 4.88%
• D) 3.55 %
• E) None of the above (A, B, C, D) is close to be correct.

E[IRR] = 0.10(−4.75) + 0.30(0.55) + 0.35(6.53) + 0.20(9.80) + 0.05(18.94) = −0.475 + 0.165 + 2.286 + 1.960 + 0.947 ≈ 4.88% → C.

Rule: Probabilities sum to 1. Expected value is probability-weighted; variance uses squared deviations around the expected value.

Old Exam — Dec 2022, Q6

Given: Scenario setup: purchase price $45m; 15-year holding period; Year-1 NOI $2.5m; growth rates -0.5%, +1.5%, +2.5%; exit value at Year 15 uses Year-16 NOI / scenario exit cap (6%, 5.5%, 5%); probabilities 28%,45%,27%.

• A) 6.79 %
• B) 6.83 %
• C) 7.05 %
• D) 7.10 %
• E) None of the above (A, B, C, D) is close to be correct.

Method: compute the return/NPV separately in every scenario, then E[X]=sum p_s X_s. Risk: SD=sqrt(sum p_s(X_s-E[X])^2). Source correct answer: B) 6.83 %.

Rule: Probabilities sum to 1. Expected value is probability-weighted; variance uses squared deviations around the expected value.

Computer Lab 1 — Exercise 1, Base Case

• A) $1,111,111.11
• B) $1,288,082.30
• C) $1,000,000.00
• D) $833,333.33
• E) $1,400,633.19

NOI grows at 3%/yr: NOI1=100,000...NOI6=115,927.41. Reversion value = NOI6/0.09 = 1,288,082.30. Year5 total CF = NOI5+RV5 = 1,400,633.19. Discounting all CFs at 12% and summing PVs gives Property Value = $1,111,111.11.

Rule: DCF property value = sum of PV(NOI1..5) + PV(reversion), where reversion uses NOI of the year AFTER sale divided by terminal cap rate.

Computer Lab 1 — Exercise 1, Base Case

• A) 12.00%
• B) 9.00%
• C) 9.48%
• D) 8.57%

Going-in cap rate = NOI1 / Property Value = 100,000 / 1,111,111.11 = 9.00%.

Rule: Going-in cap rate = Year 1 NOI ÷ Property Value.

Computer Lab 1 — Exercise 1, Case A

• A) $1,054,776.08
• B) $1,111,111.11
• C) $1,214,141.11
• D) $1,166,992.19

RV5 = NOI6/0.09 = 109,272.70/0.09 = 1,214,141.11. Year5 total CF = 106,090+1,214,141.11=1,320,231.11. Discount all years 1-5 at 12%: PVs are 89,285.71+79,719.39+71,178.02+65,458.36+749,134.59 = $1,054,776.08.

Rule: Flat short-term NOI growth before resuming long-term growth lowers both NOI and reversion value, reducing property value versus the Base Case.

Computer Lab 1 — Exercise 1, Case B

• A) 8.57%, lower than Case A because higher growth raises property value
• B) 9.48%, same as Case A
• C) 10.48%, higher than Case A
• D) 9.00%, equal to the Base Case

Going-in cap rate = 100,000/1,166,992.19 = 8.57%. Since Case B has higher expected NOI growth, its property value is higher than Case A's, and with the same Year-1 NOI, a higher value implies a lower going-in cap rate.

Rule: With equal current income, higher expected growth → higher value → lower going-in cap rate.

Computer Lab 1 — Exercise 1 concept

• A) Year 6 NOI (the NOI expected in the year after sale)
• B) Year 5 NOI (the NOI in the year of sale)
• C) Year 1 NOI (initial NOI)
• D) The average NOI over Years 1-5

Reversion value = NOI_(T+1)/terminal cap rate, because the buyer at the end of Year 5 is purchasing rights to future (Year 6 onward) income.

Rule: Terminal/reversion value always capitalizes the NEXT year's NOI (forward-looking), not the NOI in the sale year.

Computer Lab 1 — Exercise 2A, Question 2

• A) $974,613.20
• B) $1,032,913.20
• C) $891,000.00
• D) $1,091,213.20

Sale Price = NOI6/0.10 = 103,291.32/0.10 = 1,032,913.20. NSP = Sale Price − Selling Expenses = 1,032,913.20 − 58,300 = $974,613.20.

Rule: NSP = Sale Price − Selling Expenses, and Sale Price = NOI_(T+1) / terminal cap rate.

Computer Lab 2 — Exercise 1(b)(c)

• A) Property value ≈ $1,745,458.48; cap rate ≈ 8.59%
• B) Property value ≈ $1,745,458.48; cap rate ≈ 12.00%
• C) Property value ≈ $1,079,423.11; cap rate ≈ 13.90%
• D) Property value ≈ $413,387.74; cap rate ≈ 36.29%

Property Value = PV(equity)+PV(mortgage) = 666,035.37+1,079,423.11 = $1,745,458.48. Going-in cap rate = NOI1/Property Value = 150,000/1,745,458.48 ≈ 8.59%.

Rule: Total property value = PV of debt claim + PV of equity claim. Going-in cap rate = Year-1 NOI ÷ total property value.

Computer Lab 2 — Exercise 3, Problem 12.15

• A) ≈21.25%
• B) ≈28.83%
• C) ≈4.55%
• D) ≈12.75%

Debt CAPM: r_d = 3.0%+0.31×5.0% = 4.55%. Default probability: p = (YTM−r_d)/L = (17.3%−4.55%)/60% = 12.75%/60% = 21.25%.

Rule: When YTM and the CAPM-implied expected return are known, solve for p via p = (YTM − r_d)/L.

Computer Lab 2 — Exercise 3, Problem 12.16

• A) ≈3.70% (default-adjustment) and ≈3.85% (debt CAPM) — both far below the 8.5% promised YTM
• B) 8.5% under both methods, since YTM is a market-determined fair rate
• C) ≈4.8% default-loss amount is itself the expected return
• D) ≈11.5%, since recession risk should raise expected return

Method 1: r_d = 8.5%−8.0%×60% = 8.5%−4.8% = 3.70%. Method 2 (CAPM): r_d = 3.0%+0.17×5.0% = 3.85%. Both are far below the promised 8.5% YTM, reflecting significant recession default risk.

Rule: Under recession-level default risk, promised YTM substantially overstates the investor's true expected return; two independent methods (default-adjustment, debt CAPM) should roughly agree.

Computer Lab 2 — Exercise 3, Problem 12.17

• A) YTM≈4.80%; spread≈0.80%
• B) YTM≈4.50%; spread≈0.50%
• C) YTM≈4.00%; spread≈0.00%
• D) YTM≈6.90%; spread≈2.90%

Required expected return via CAPM: r_d = 4.0%+0.10×5.0% = 4.50%. YTM = r_d + p×L = 4.50%+0.5%×60% = 4.50%+0.30% = 4.80%. Spread over AAA = 4.80%−4.00% = 0.80%.

Rule: Set promised YTM = required expected return (from debt CAPM) plus the expected default-loss compensation (p×L).

Computer Lab 3 — Problem 3 (Most likely)

• A) Because annual NOI (10% of price) plus an unchanged resale price means a 10% discount rate makes NPV exactly zero
• B) Because IRR always equals NOI/Purchase price regardless of other cash flows
• C) Because the sale price must always equal the purchase price for any IRR to exist
• D) Because flat NOI implies zero IRR

NOI/Purchase price = 200,000/2,000,000 = 10%, exactly matching a constant 'coupon-like' yield, and with the exit value unchanged, the investment behaves like a perpetual-income bond returning exactly 10% — so NPV(10%)=0 trivially.

Rule: When periodic income is a constant percentage of invested capital and the capital value is returned unchanged at the end, the IRR equals that constant income yield.

Computer Lab 4 — Exercise 1, Task 5

• A) The property should offer a higher expected return/cap rate than the Treasury yield to compensate for added risk
• B) They should offer identical returns since both are low-risk
• C) The Treasury should offer a higher return because it is less liquid
• D) Property risk is irrelevant once a cap rate is quoted

Real estate carries vacancy, operating, regulatory, liquidity and asset-specific risks beyond those of government bonds, so investors typically require a risk premium—i.e., a cap rate/expected return above the Treasury yield.

Rule: Riskier assets require a return premium above the risk-free (Treasury) rate.

Computer Lab 4 — Exercise 1, Task 6

• A) 200 bps
• B) 20 bps
• C) 2 bps
• D) 1.5 bps (ratio of the two rates)

Spread = Cap Rate − Government Bond Yield = 6.0% − 4.0% = 2.0 percentage points = 200 basis points.

Rule: Cap rate spread = Cap Rate − Government Bond Yield; 1 percentage point = 100 bps.

Computer Lab 4 — Exercise 1, Task 7

• A) Spread = Cap Rate − Government Bond Yield
• B) Spread = Cap Rate + Government Bond Yield
• C) Spread = Government Bond Yield − Cap Rate
• D) Spread = Cap Rate × Government Bond Yield

Simple algebra: subtract Government Bond Yield from both sides of Cap Rate = Government Bond Yield + Spread.

Rule: Always isolate the unknown term via basic algebraic rearrangement.

Computer Lab 4 — Exercise 1, Task 8

• A) 75 bps; a relatively small premium given office property's additional risks
• B) 675 bps; an unusually large premium
• C) 75 bps; abnormally large for office property
• D) 0.75 bps; essentially no premium

Spread = 5.75% − 5.00% = 0.75 percentage points = 75 basis points, which is a comparatively modest premium relative to the vacancy, leasing, operating and liquidity risks of office property, making Treasuries relatively attractive by comparison.

Rule: Compare the computed spread's economic magnitude to the asset's risk profile, not just its sign.

Computer Lab 4 — Exercise 1, Task 9a

• A) Property values fall
• B) Property values rise
• C) Property values stay constant
• D) NOI automatically rises to offset the higher cap rate

With V = NOI/Cap Rate and NOI held fixed, an increase in the cap rate (the denominator) decreases V.

Rule: Cap rate expansion (↑cap rate) → ↓value, all else equal.

Computer Lab 4 — Exercise 1, Task 9b

• A) Property values rise
• B) Property values fall
• C) Property values stay constant
• D) Values fall only if interest rates also fall

With V = NOI/Cap Rate and NOI fixed, a lower cap rate (smaller denominator) increases V.

Rule: Cap rate compression (↓cap rate) → ↑value, all else equal.

Computer Lab 4 — Exercise 1, Task 10

• A) False — cap rates compressed roughly 2010-2022, then expanded materially 2022-2024 before stabilizing
• B) True — cap rates fell continuously over the whole period
• C) True, but only for industrial property
• D) False — cap rates expanded continuously the whole period

The lab source indicates general compression from about 2010 to 2022, followed by material expansion from 2022 to 2024, then stabilization — so no single continuous trend describes the whole period.

Rule: Check whether a described trend holds for the entire stated period or only part of it.

Computer Lab 4 — Exercise 1, Task 11

• A) Narrowed, mainly because the 10-year Treasury yield rose while average cap rates stayed broadly stable
• B) Widened, mainly because cap rates fell sharply
• C) Narrowed, mainly because cap rates fell sharply
• D) Widened, mainly because the Treasury yield fell

Since Spread = Cap Rate − Treasury Yield, and the Treasury yield rose while the average cap rate stayed roughly stable, the spread shrank (narrowed).

Rule: To determine spread direction, track Cap Rate and Treasury Yield separately, then take the difference.

Computer Lab 4 — Exercise 1, Task 12

• A) Industrial — expectations shifted from compression toward no change
• B) Multifamily
• C) Retail
• D) Office

The lab identifies industrial property as having the most pronounced shift, moving away from expectations of cap rate compression toward expectations of no change.

Rule: Sector-specific expectations can shift independently of the broad market trend.

Computer Lab 4 — Exercise 1, Task 13

• A) Lower inflation expectations, weaker growth, expected Fed cuts, and a lower term premium
• B) Persistent inflation and heavy Treasury issuance
• C) Higher-for-longer policy rate expectations and strong private capital demand
• D) Stronger economic growth and rising inflation expectations

A major decline in the long yield generally requires a lower expected path of future short-term rates (driven by lower inflation/growth expectations and anticipated rate cuts) and/or a lower term premium.

Rule: Long yield = expected average future short rates + term premium; both components must fall for a substantial yield decline.

Formula Battle — method recognition (built from the Formula Book)

• A) NOI5 / cap rate
• B) NOI6 / cap rate
• C) Price × cap rate
• D) NOI1 / cap rate

Sale at end of year T uses next year's NOI. Correct method: NOI6 / cap rate.

Rule: TV5 = NOI6 / exit cap