Costavon

Sensitivity Analysis

Economic Surface

Real Net Cost (Negative is Surplus)

SURPLUS

-$465,983

Break-Even Horizon

T* (YEARS)

7.0yrs

Sensitivity plot vs Net Cost

→

Surplus (Best)Break EvenHigh Cost (Worst)

-$755,131$0$49,694

10.0%7.5%5.0%2.5%0.0%

18162330

Continuous Time Model

\begin{aligned} C_n &= (P\phi + \Lambda) + \int_{0}^{T} \bigg[ \left( \frac{Pr}{1 - e^{-rT}} + (\tau + \iota + \kappa)e^{it} + (V_0 - P) r_m \right) \\ &\quad - \left( \frac{Pr e^{rt}}{e^{rT} - 1} + V_0 a e^{at} + R_0 e^{gt} + \theta \left( \frac{Pr}{1 - e^{-rT}} - \frac{Pr e^{rt}}{e^{rT} - 1} + \tau e^{it} \right) \right) \bigg] e^{-it} \,dt \\ &\quad + V_0 e^{(a-i)T} (\alpha + \beta + \gamma) \end{aligned}

Term 1Upfront Capital

Term 2Integrative Cashflow

Term 3Opportunity Cost

Term 4Terminal Friction

Variable	Definition	Economic Role
$C_n$	Real Net Cost	Total wealth change (Negative = Profit; Positive = Loss).
$P$	Loan Principal	The total amount of debt taken (impacts interest cost and equity speed).
$V_0$	Initial Value	The purchase price of the home at $t=0$, which yields the down payment ($V_0 - P$).
$R_0$	Initial Rent	Annualized market rent at the time of purchase.
$r$	Interest Rate	The continuous mortgage interest rate (the cost of debt).
$a$	Appreciation Rate	The continuous annual growth rate of the home's market value.
$g$	Rent Growth Rate	The continuous annual growth rate of market rental prices.
$i$	Inflation Rate	The continuous discount rate (CPI) used to bring future dollars to PV.
$T$	Time Horizon	The number of years the home is held.
$\tau$	Property Taxes	Annualized nominal cost of property taxes.
$\iota$	Insurance	Annualized nominal cost of homeowners insurance.
$\kappa$	Maintenance	Annualized nominal repair and upkeep costs.
$\phi$	Origination %	Points/fees expressed as a decimal of the loan amount.
$\Lambda$	Fixed Closing Fees	One-time fees for items such as appraisal, title, and escrow.
$\alpha, \beta, \gamma$	Selling Frictions	Percentages for agent commission, transfer taxes, and concessions.
$r_m$	Market Return Rate	The continuous benchmark return rate for forgone equity.
$\theta$	Marginal Tax Rate	Tax rate applied to combined deductible interest and property taxes.