QUANT LAB
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3 questions · 1 formulas

LTV & DCR

LTV = Loan / Value DCR = NOI / Debt service

Mortgage & LeverageE-levelHigh priority

Centre Point purchase price = $885,000, LTV = 75%, up-front financing cost = 3% of the loan. What is the Initial Equity required?

→ A) $241,162.50

Computer Lab 1 — Exercise 2B, Step 1

  • A) $241,162.50
  • B) $221,250.00
  • C) $663,750.00
  • D) $259,912.50

Loan = 885,000×75% = 663,750. Financing cost = 663,750×3% = 19,912.50. Net loan proceeds = 663,750−19,912.50 = 643,837.50. Initial Equity = 885,000 − 643,837.50 = $241,162.50.

Rule: Initial Equity = Purchase Price − Net Loan Proceeds, where Net Loan Proceeds = Loan − up-front financing cost.

Scenario RiskD–A levelVery high priority

A two-way sensitivity table (PGI growth × LTV) gives, at 75% LTV, scenario IRRs of 5.89%, 13.74%, 20.25%, 25.95%, 33.50% with probabilities 5%, 20%, 50%, 20%, 5%. What is the Mean IRR at 75% LTV?

→ A) ≈20.03%

Computer Lab 1 — Exercise 2C

  • A) ≈20.03%
  • B) ≈19.86% (simple average)
  • C) ≈25.95%
  • D) ≈5.83%

E[IRR] = 0.05(5.89%)+0.20(13.74%)+0.50(20.25%)+0.20(25.95%)+0.05(33.50%) = 20.03%, a probability-weighted average, not a simple average.

Rule: Expected value under scenario analysis = Σ (probability × outcome), not a simple unweighted average.

Scenario RiskD–A levelVery high priority

In the Centre Point two-way sensitivity analysis, as LTV increases from 0% to 90%, Mean IRR rises from 12.25% to 29.71%, while the standard deviation rises from 1.98% to 10.21%, and Mean/Std.Dev. falls from 6.18x to 2.91x. What does this indicate about leverage?

→ A) Leverage increases expected return but increases risk proportionally even more, lowering the risk-adjusted return ratio

Computer Lab 1 — Exercise 2C

  • A) Leverage increases expected return but increases risk proportionally even more, lowering the risk-adjusted return ratio
  • B) Leverage increases expected return with no effect on risk
  • C) Leverage decreases both expected return and risk
  • D) Leverage has no effect on return or risk, only on cash flow timing

Both mean IRR and σ rise with LTV, but σ rises faster (1.98%→10.21%, a ~5.2x increase vs. mean IRR's ~2.4x increase), so the Mean/Std.Dev ratio falls from 6.18x to 2.91x — risk grows faster than return.

Rule: Financial leverage magnifies both expected equity returns and the variability (risk) of those returns; risk generally grows faster than return as leverage increases.