## Equations Relating Inputs and Outputs

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The following documentation reflects the general structure of the calculations done in the Infinite Spreadsheet, which is designed to demonstrate the deterministic nature of the price with reasonable accuracy as compared to the actual market. This documentation is not guaranteed; users own judgment and discretion are strongly advised.
* PRICE: Price depends on the expected future investment return and is determined from all the factors affecting the price.
* Capitalization rate = net income / price
* where net income = gross income x ( 1 - vacancy factor ) - operating expenses
* Average return = Y-th root of [( cash from resale + cumulated cash flow )/(initial investment )] -1
* where Y = investment period, and
* cash from resale = resale price - broker's commission and termite work - remaining loan - prepayment penalty - resale gain tax + advanced deposit and rent + remaining tax deductions for the first and the second loans
* where the resale gain tax can be calculated as follows:
Let T1 = resale gain tax; Y = investment period
T2 = cumulated straight line depreciation
= Y x ( depreciable real property / recovery period of real property )
* T3 = profit from resale = resale price - price - closing cost - broker's commission and termite work,
and T4 = cumulated losses not claimed. For nonresidential properties using accelerated method of cost recovery:
* T1 = resale tax bracket x ( 0.4 x T3 + T4 )
For all other cases
* T1 = resale tax bracket x ( T2 + T3 - T4 )
* Accumulated cash flow = sum of all the cash flows plus their market interest ( see cash flow below )
* Initial investment = down payment - advanced deposit and rent + closing cost + loan points
* Down payment = price - first and second loans
* Before tax cash flow = net income - first and second yearly loan payments
* Tax shelter = depreciation allowance + interest payment + first loan points /term of first loan + second loan points / term of second loan - net income
* Deductible losses are limited to the lesser of: Tax shelter and L0+other passive losses (Cumulated losses are carried forward to future years),
where L0 is based on the adjusted gross income (AGI), the property type, filing status, etc. For example, L0=\$25,000 if AGI is less than the phase out threshold, \$100,000 (or \$200,000 for rehabilitation or low income housing). If AGI tops the phase out threshold, L0 is reduced by 50% of the amount that AGI exceeds the phase out threshold, until L0 is reduced to zero. For married couple filing separately, the phase out threshold is cut in half.
* where depreciation allowance = personal property value / useful life of personal property + recovery method x (depreciable real property - accumulated depreciation ) / (100 x recovery period of real property )
* where depreciable real property = price + closing cost - land value - personal property value, and
* accumulated depreciation = sum of K years of ( depreciation allowance - personal property depreciation ) where K is the K-th year from the year when the depreciation are calculated.
* After tax cash flow = before tax cash flow x ( 1 + market interest rate on cash flow x 0.5 ) + income bracket x tax shelter + \$ increase in advanced deposit and rent.
* Loan amount = price x loan as % of price or dollar amount or = dollar amount such as to satisfy (net income/loan pmt) ratio
* Monthly payment = loan amount x monthly payment for each \$100,000 / \$100,000
* RESALE PRICES satisfy the same relationships as does the price; they are determined the same way as the price is determined.