How the calculators work.

Purpose and scope

Rental Property Math is an educational underwriting tool for US rental property. The seller financing calculator adds the note payment, balloon balance, rental underwriting, refinance exit, bank comparison, installment-sale tax estimate, and compliance flags. The cap rate calculator estimates unleveraged operating yield, net operating income, implied value at a target cap rate, the value gap, and the monthly rent required to hit a target. The cash flow calculator adds financing, vacancy, reserves, cash-on-cash return, DSCR, a five-year outlook, and reverse solves for rent and price. The cash-on-cash calculator extends the same model with all-in cash invested, down-payment-only return, leverage spread, simple payback, a break-even interest rate, financing scenarios, and a cash-on-cash projection. The DSCR calculator adds lender qualifying rent, PITIA, coverage status, the max loan at a target DSCR, rent needed, amortizing vs. interest-only comparisons, reserves, prepayment, a rent and rate stress matrix, and investor DSCR. The hard money calculator adds short-term loan sizing, an initial advance and rehab holdback, drawn or commitment interest, points and fees, cash to close, exit profit, ROI, break-even, and hold sensitivity. The BRRRR calculator adds the acquisition loan, rehab and contingency, hold costs, refinance, cash left in the deal, post-refi DSCR and cash-on-cash return, ARV stress, and reverse solves for ARV, price, rent, and refinance rate.

None of the calculators is an appraisal, a broker opinion of value, a tax return, or a lending decision. They do not model income taxes, depreciation, sale costs, lease-up timing, or taxable refinance proceeds. Those require a separate after-tax or disposition model.

Shared operating model

The calculators use the same property-level operating model. The demo inputs are independent, but the math below is shared. Percentage expenses are applied to gross scheduled income. Fixed expenses are entered as annual or monthly dollar amounts.

Seller financing and tax

The seller financing calculator treats the purchase as three linked models: a seller note, a rental underwriting, and a seller tax event. The note amount is the purchase price minus the down payment. The payment is amortized at the note rate over the amortization term. If there is an interest-only period, the payment steps up afterward. If there is a balloon, the balance at the end of the balloon term is due then, even though the payment was based on the longer amortization.

Recapture is taxed in the closing year in the model. The down payment is treated as a principal payment at closing, so part of the closing-year gain is recognized then. Remaining gain follows principal as it is received. Interest is taxed as ordinary income. State tax is a flat user input, and the net investment income tax is an optional 3.8% toggle.

The compliance panel is educational. It identifies whether the occupancy is investment or owner-occupied, counts the properties financed in the last 12 months, checks the note rate against the AFR, and flags balloons, interest-only periods, thin down payments, and refinance shortfalls. It does not determine whether Reg Z applies or whether a seller qualifies for an exemption. That analysis depends on the facts and state law.

The bank comparison uses a separate amortizing loan at the bank rate, down payment, term, points, closing costs, and PMI inputs. It is a side-by-side estimate, not a lender preapproval. The refinance stress varies value and rate together but holds rent, expenses, taxes, insurance, HOA, and the balloon balance constant.

Cap rate and value

Cap rate compares annual NOI with the acquisition basis. The default basis is purchase price. The all-in option adds closing costs and immediate rehab.

Cap rate = NOI ÷ acquisition basis × 100

When a target cap rate is greater than zero, the calculator estimates the value the current NOI would support at that target:

Implied value = NOI ÷ (target cap rate ÷ 100)

The value gap is implied value minus the acquisition basis. A positive gap means the current NOI supports a value above the basis at the target cap rate. It does not mean the property will sell for that amount, and it does not include transaction costs or future capital needs.

The rent-needed output solves for the gross scheduled income that produces the required NOI after vacancy and percentage expenses:

Required GSI = (required NOI + fixed expenses) ÷ (1 − vacancy rate − percentage expense rate)

The calculator divides by 12 and subtracts other monthly income. If vacancy plus percentage expenses consume all gross income, the result is unavailable and the interface explains why.

Cash flow and returns

Cash flow is a cash measure. It subtracts annual debt service from NOI, so it includes mortgage principal, interest, and PMI.

Cash invested is the down payment plus closing costs, immediate rehab, and lender fees. For an all-cash purchase, cash invested is the purchase price plus those costs, cash flow equals NOI, and DSCR is unavailable because there is no debt service.

PMI is entered as a monthly amount and held constant through the projection. The model does not automatically remove PMI when the loan balance reaches 80% of the original value. If that matters, use a shorter projection or adjust the PMI assumption outside the calculator.

Cash-on-cash and leverage

Cash-on-cash return is a leveraged cash return. It divides first-year pre-tax cash flow by the cash invested. The dedicated calculator uses all-in cash invested for the headline result: down payment, closing costs, immediate rehab, lender fees, and any other upfront cash. It also shows the return on the down payment alone so the effect of the convention is visible.

The loan constant captures the full annual cost of the debt, including principal and interest, as a percentage of the loan. When the cap rate is above the loan constant, the spread is positive and leverage is adding to the property-level cash yield. When the loan constant is above the cap rate, the spread is negative and the calculator labels it as negative leverage.

The headline cash-on-cash return does not include principal paydown. Principal paydown is a real economic benefit, but it is not cash in hand during the year. The calculator reports it separately and shows a first-year total return that adds cash flow and principal paydown, divided by all-in cash invested. That total return still excludes appreciation, income taxes, depreciation, and sale costs.

The break-even interest rate is the loan rate that reduces annual cash flow to $0 while holding the other inputs constant. The calculator solves it by bisection on the same debt model. It is unavailable for an all-cash purchase because there is no loan rate to solve. Simple payback is all-in cash invested divided by annual cash flow, expressed in years, and is shown only when annual cash flow is positive.

The financing scenarios compare an all-cash purchase, a 20% down loan, and the current plan or a nearby down-payment alternative. Each scenario holds the property inputs constant and changes only the financing structure. The cash-on-cash projection uses the same rent and expense growth assumptions as the five-year cash flow projection, with cash-on-cash return calculated against the original all-in cash invested.

DSCR and lender coverage

The DSCR calculator separates the lender coverage test from the investor cash-flow test. Lender DSCR uses qualifying rent and PITIA. Investor DSCR uses net operating income and annual debt service. The two ratios can diverge because the lender does not include vacancy, management, maintenance, or capital reserves in PITIA.

The max-loan solve holds taxes, insurance, HOA, and other escrow constant. A real lender may use a different rent, expense, or reserve figure. The result is a negotiating range, not a loan commitment. The calculator uses the entered rent as market rent and applies the lender haircut to derive qualifying rent. It does not independently verify market rent.

Status bands are descriptive, not lender guidelines. A DSCR of 1.25 or higher is labeled strong, 1.00 to 1.249 qualifies, 0.75 to 0.999 is labeled buy-down, and below 0.75 is labeled ineligible. Actual lender minimums vary. The stress matrix multiplies rent by 80%, 90%, 100%, 110%, and 120% and shifts the note rate by −1, 0, +1, and +2 percentage points. It holds the loan amount and escrows constant.

Hard money and cash to close

The hard money calculator models a short-term, interest-only acquisition and rehab loan with a single payoff at the exit. The loan is sized from the lower of the lender’s loan-to-cost cap and its after-repair-value loan-to-value cap. The purchase price caps the initial advance. Any remaining commitment becomes the rehab holdback, which is drawn over the draw period rather than handed over at closing.

Points are charged on the loan commitment, not the initial advance, and are paid at closing. The model adds draw fees when a holdback exists, applies one extension fee when the hold exceeds the loan term, and extends the interest schedule to the minimum interest period when the lender requires one. The holdback is split into the entered number of draws and spread across the draw period, capped at the hold.

Interest can be charged on the drawn balance or on the full commitment. The drawn-balance method accrues interest only on the initial advance and the draws that have been released. Commitment interest, sometimes called Dutch interest, accrues on the entire commitment even while rehab funds remain undrawn. The two methods are identical only when the full commitment has been advanced.

The annualized cost is a comparison estimate, not a Reg Z APR. It divides every finance charge by the loan commitment and the planned hold, so fixed costs are spread over a short period. It does not account for the time value of money, and it is not a substitute for the disclosures in a loan estimate or a lender term sheet.

The hold sensitivity table varies only the hold period. The loan terms, the exit value, and the other inputs stay constant. Longer holds add interest and can trigger the extension fee, but the table does not model a delayed sale that also reduces the exit price.

BRRRR and refinance

The BRRRR calculator follows the buy, rehab, rent, refinance, repeat sequence. It models a short-term acquisition loan, a rehab budget with contingency, a holding period, and a single refinance at the end of that period. The acquisition loan is treated as interest-only during the hold. The refinance loan is a fully amortizing loan using the entered rate and term.

The acquisition loan is based on the purchase price plus the rehab budget, not the contingency. Contingency is treated as cash. Points and hold interest are charged on the acquisition loan, and holding costs are the monthly carry multiplied by the rehab plus lease-up months.

A positive cash-left result means cash is still in the deal after the refinance. A negative result means the refinance returned more than the cash invested, before income taxes and other costs outside the model. The capital-recycled percentage expresses the cash back as a share of the original cash invested, so 100% means the cash invested was fully returned.

Post-refinance cash-on-cash return uses the cash left in the deal as the denominator and is shown only when that number is positive. When the refinance returns all of the cash, the denominator is zero and the result is unavailable; the calculator still shows the return on the original cash invested for context. Neither result includes principal paydown, appreciation, income taxes, or sale proceeds.

The refinance LTV is a user input, not an automatic 75% rule. A 75% loan-to-value refinance is a common screen, but the actual loan depends on the appraisal, lender, property type, and borrower qualification. The ARV is also an assumption, not a verified value. The calculator shows the project cost and all-in cost as a percentage of ARV so an optimistic ARV is easier to spot.

Five-year projection

The projection is a straight-line scenario, not a forecast. Rent and other income grow at the rent growth rate. Fixed expenses grow at the expense growth rate. Percentage expenses remain a percentage of gross scheduled income. Debt service stays at the original payment; the loan balance is calculated from the amortization schedule.

Property value grows at the appreciation rate. Equity is property value minus loan balance. Cumulative cash flow adds each year's annual cash flow without reinvestment or interest. The cash-on-cash calculator applies the same projection and adds annual cash-on-cash return, cumulative cash-on-cash return, and annual principal paydown.

The projection excludes sale costs, capital-gains taxes, depreciation, refinance proceeds, lease-up, turnover timing, and changes in financing. It is a way to inspect the direction of the deal, not a substitute for a discounted cash-flow model.

Reverse solves

The cash flow, cash-on-cash, and BRRRR calculators include several reverse solves. All of them hold the other assumptions constant, which makes them useful for sensitivity, not for predicting a negotiated outcome.

• Break-even rent is the monthly rent that produces $0 monthly cash flow after debt service, fixed expenses, vacancy, and percentage expenses.
• Rent for target CoC adds the target annual cash flow to fixed expenses and debt service, then solves for rent. The cash-on-cash calculator uses all-in cash invested in this solve.
• Break-even occupancy is the occupancy level at which NOI covers debt service. It is calculated from annual debt service plus operating expenses divided by gross scheduled income.
• Max price at target CoC solves for the purchase price that produces the target cash-on-cash return at the current rent, expenses, loan terms, down payment percentage, and upfront costs.
• Max price at target DSCR solves for the purchase price that produces the target debt-service coverage ratio at the current loan terms and down payment percentage.
• Break-even interest rate is the loan rate at which annual cash flow reaches $0. It is available only when the deal has a loan and the other assumptions can produce a solution.
• ARV needed to recycle is (cash invested + acquisition payoff + refinance costs) ÷ refinance LTV. It is the ARV that returns the cash invested at the current refinance terms.
• ARV for target cash left uses the same equation, with the target cash left subtracted from the required refinance loan.
• Max price at target cash left re-solves the full cash-left equation for the purchase price, including points and hold interest on the acquisition loan. It is not a simple 75% screen.
• Rent for target DSCR solves for the monthly rent that produces the target coverage ratio after vacancy, percentage expenses, fixed expenses, and refinance debt service.
• Rent for target CoC solves for the monthly rent that produces the target cash-on-cash return on the cash left in the deal.
• Max refinance rate at target DSCR uses bisection on the amortizing refinance loan to find the highest rate that still meets the target DSCR.

The BRRRR stress table varies only the ARV in −10%, −5%, 0%, +5%, and +10% steps. Rent, expenses, the acquisition loan, and the refinance terms stay constant. That isolates the appraisal risk, but it does not capture a rent shortfall or a longer hold at the same time.

The max-price solves are not appraisals. They answer a narrow question: what price makes the current assumptions hit the target? If rent, expenses, or financing change, the answer changes.

Expense conventions

Management, maintenance, and capex are entered as percentages and applied to gross scheduled income, not effective gross income. This is a deliberate convention and is disclosed in the interface. Property taxes, insurance, HOA dues, utilities, reserves, and other costs are entered as annual or monthly dollar amounts.

A separate annual reserve can be included in NOI with a toggle. It is off by default because the conventional broker cap rate often excludes a separate reserve. When it is on, the reserve is added to fixed expenses. This gives the user an explicit choice rather than hiding a capital assumption inside the expense percentages.

Mortgage principal and interest, income taxes, depreciation, and capital improvements are excluded from NOI. Routine repairs are operating expenses; a roof replacement or major renovation is a capital item. The line can be judgmental, so the assumption should be documented outside the calculator when it matters.

Validation and rounding

The calculators validate that the purchase price is greater than zero, vacancy is between 0% and 100%, percentage expenses do not exceed 100% combined, units are between 1 and 100, the holding period is between 1 and 10 years, and financing assumptions are within the supported ranges. Negative dollar inputs are clamped to zero in the operating model.

The BRRRR calculator separately requires a purchase price and ARV greater than zero, refinance LTV from 0% to 100%, a refinance rate from 0% to 30%, a refinance term from 1 to 50 years, 1 to 100 units, vacancy from 0% to 100%, a target cash left from $0 to $100,000,000, target cash-on-cash from 0% to 100%, and target DSCR from 0 to 10. Rehab and lease-up periods can each run from 0 to 60 months, but the combined hold must be at least one month. Hard-money LTC must be 0% to 100%, the acquisition rate 0% to 30%, and points 0% to 20%. Negative purchase closing costs, rehab budget, other acquisition fees, refinance costs, or extra monthly holding costs produce an error rather than a silent adjustment.

The DSCR calculator requires a property value and monthly rent greater than zero; a down payment or equity from 0% to 100%; an interest rate from 0% to 30%; a loan term from 1 to 40 years; a target DSCR from 0.50 to 5.00; a lender rent haircut, vacancy, management, maintenance, capital reserves, and closing costs from 0% to 100%; points from 0% to 20%; reserves from 0 to 24 months; an exit year from 1 to 30; a credit score from 300 to 850; and 1 to 100 units. Negative taxes, insurance, HOA, escrow, utilities, other income, lender fees, available reserves, or existing loan payoff produce an error rather than a silent adjustment. A $0 PITIA returns an unavailable result.

The hard money calculator requires a purchase price, ARV, and exit value greater than zero; nonnegative closing costs, rehab, holding costs, lender fees, third-party costs, and draw fees; LTC and ARV LTV from 0% to 100%, with at least one limit above 0%; an interest rate from 0% to 30%; points from 0% to 20%; a term and hold from 1 to 60 months; a minimum interest period from 0 to 24 months; an extension fee from 0% to 20%; a draw count from 0 to 24; and a draw period from 1 to 60 months. Invalid combinations return an error and an unavailable result instead of silently changing the loan.

Displayed dollar values are rounded to the nearest dollar. Percentages are displayed to two decimal places unless the interface says otherwise. The underlying calculations use unrounded inputs. Copying a share link preserves the entered values, not just the rounded display.

Worked example

The seller financing calculator starts with a $285,000 rental, $57,000 down, a 7.00% seller note, a 30-year amortization, and a 5-year balloon. It produces:

• Seller note: $228,000
• Monthly payment: $1,517
• Balloon balance: $214,620
• NOI: $20,910
• Monthly cash flow: +$226
• DSCR: 1.15x
• Refinance cash out: $26,980
• Cash-sale tax: $12,468
• Closing-year installment tax: $7,494
• Tax deferred at closing: $4,974

The cap-rate calculator starts with a $300,000 purchase price, $2,600 monthly rent, 5% vacancy, $3,600 annual taxes, $1,800 annual insurance, and 18% combined management, maintenance, and capex. It produces:

• NOI: $18,624
• Cap rate: 6.21%
• Implied value at a 6% target: $310,400
• Value gap: $10,400
• Rent needed at a 6% target: $2,532/mo

The cash-flow calculator starts with a separate $200,000 property at $2,300 monthly rent, $2,400 annual taxes, and $1,200 annual insurance. With 25% down, a 7% loan, a 30-year term, and no PMI, it produces:

• Annual debt service: $11,975
• Monthly cash flow: +$473
• Cash invested: $50,000
• Cash-on-cash return: 11.35%
• DSCR: 1.47

The cash-on-cash calculator starts with the same cash-flow demo deal plus $6,000 closing costs and $0 other upfront cash. Its all-in cash invested is $56,000. It produces:

• Annual cash flow: +$5,677
• Cash-on-cash return: 10.14%
• Down-payment-only CoC: 11.35%
• Loan constant: 7.98%
• Leverage spread: +0.84 pp
• Break-even interest rate: 11.37%
• Simple payback: 9.9 years
• Rent for an 8% target CoC: $2,171/mo
• Max price at an 8% target CoC: $214,980

The DSCR calculator starts with a $250,000 property at $2,300 monthly rent, $3,000 annual taxes, $1,500 annual insurance, 25% down, a 7.50% rate for 30 years, and a 1.25 target DSCR. It produces:

• Loan amount: $187,500
• Monthly P&I: $1,311
• Monthly PITIA: $1,686
• Lender DSCR: 1.36
• Max loan at target: $209,521
• Max price at target: $279,361
• Rent needed: $2,108
• Investor DSCR: 1.06
• Monthly cash flow: +$85
• Cash to close: $73,375
• Reserves required: $10,116
• Prepayment penalty in exit year 3: $5,625

The BRRRR calculator starts with a $150,000 purchase, $4,000 closing costs, a $35,000 rehab budget with 10% contingency, a $260,000 ARV, 85% acquisition LTC at 11% plus 2% points, and a refinance at 75% LTV and 6.75% for 30 years. It produces:

• Project cost: $192,500
• Acquisition loan: $157,250
• Cash invested: $49,894
• Refinance loan: $195,000
• Cash back at refinance: $34,250
• Cash left in the deal: $15,644
• Capital recycled: 68.65%
• Post-refi annual cash flow: +$4,203
• Post-refi DSCR: 1.28
• ARV needed to recycle the cash: $280,858

The hard money calculator starts with a $150,000 purchase, $4,000 purchase closing costs, a $35,000 rehab budget, a $260,000 ARV, 85% LTC, 70% ARV LTV, a 11.00% interest rate, and 2% points. It produces:

• Loan commitment: $157,250
• Initial advance: $150,000
• Rehab holdback: $7,250
• Cash to close: $38,895
• Total finance charge: $16,194
• Total cash invested: $50,644
• Net profit at the exit: +$36,506
• ROI on cash invested: 72.08%
• Annualized cost: 20.60%
• Break-even sale price: $221,164

The calculators share the same operating model but not the same starting deal. Use the Cap-rate example preset on the cash-flow calculator to reproduce the shared cap-rate property and compare its thinner cash flow.

Known limitations

• The seller financing model assumes a standard seller-carried note. It does not model wraps, subject-to transactions, contract-for-deed, lease options, variable or escalating rates, negative amortization, late fees, servicing, or a default and foreclosure.
• The installment-sale tax estimate uses flat capital-gain, recapture, ordinary-income, state, and discount rates. It excludes AMT, passive-activity limits, at-risk rules, 1031 exchanges, principal-residence exclusions, state apportionment and withholding, and the buyer's income tax.
• The seller financing tax model assumes no assumed debt and no existing loan being wrapped. Debt relief can count as a payment and accelerate gain, so those structures need separate analysis.
• The seller financing refinance stress changes value by −10%, 0%, and +10% and the refinance rate by 0, +1, and +2 percentage points. It holds rent, expenses, taxes, insurance, HOA, and the balloon balance constant.
• Seller financing compliance flags are educational prompts. They do not decide whether Reg Z applies, whether a seller-financer exemption is available, or whether the loan satisfies state licensing, usury, disclosure, or foreclosure law.
• One year of stabilized operating income. The projection extends it, but the model does not simulate lease-up or month-to-month turnover.
• Cash flow and headline cash-on-cash return exclude income taxes, depreciation, principal paydown, appreciation, and sale proceeds. The first-year total return adds principal paydown only.
• Cash-on-cash conventions differ. The headline uses all-in cash invested, while the down-payment-only result is shown separately. A broker or lender may quote the down-payment-only version.
• PMI is held constant and is not automatically removed at 80% loan-to-value.
• The cash flow and cash-on-cash models do not include a capital expenditure schedule, refinance, variable-rate loan, or balloon payment. The break-even interest-rate solve assumes the same amortizing loan structure.
• The financing scenarios change only the loan structure. They do not test lender qualification, reserve requirements, or rate locks.
• No local market data. Rent, taxes, insurance, and expenses are user inputs.
• The sensitivity table is a simple two-variable grid, not a probability-weighted scenario model.
• The DSCR max-loan solve holds taxes, insurance, HOA, and other escrow constant. It does not re-underwrite those expenses at a different purchase price or loan amount.
• DSCR qualifying rent is the entered market rent after the entered lender haircut. The calculator does not verify the rent with a lease, appraisal, or market-rent data source.
• The DSCR status bands and stress matrix are descriptive. They are not lender guidelines, and the stress matrix holds the loan amount and escrows constant while rent and rate change.
• The DSCR model does not include lender overlays, state-specific prepayment rules, income taxes, depreciation, lease-up timing, or a failed refinance or sale. It compares interest-only and amortizing payments but does not model an interest-only reset.
• The DSCR reserve and prepayment results are simplified. Reserves are months of PITIA, and the prepayment penalty is the original loan times the scheduled percentage for the exit year.
• The BRRRR model assumes one interest-only acquisition loan and one refinance at the end of the hold. It does not model construction draws, holdbacks, minimum-interest rules, extension fees, prepayment penalties, or a failed refinance.
• The BRRRR refinance uses the entered ARV and LTV. It does not verify the appraisal, seasoning requirements, borrower qualification, reserves, or lender caps on cash-out.
• BRRRR holding costs are a simple monthly carry. The model does not schedule property taxes, insurance, utilities, or HOA changes month by month, and it does not tax the refinance proceeds.
• The BRRRR rent is stabilized at lease-up. It does not model vacancy during the hold, tenant turnover, or a rent that differs from the post-refinance assumption.
• The hard money model assumes an interest-only loan with a single payoff. It does not include amortization, a balloon payment, prepayment penalties, late fees, default interest, or a refinance of the short-term loan.
• Hard money draws are split into the entered count and spread across the draw period. The model does not schedule inspections, retainage, change orders, failed draws, or a construction timeline that differs from the input.
• The hard money model does not include rent received during the hold, lease-up income, income taxes, entity costs, state-specific fee schedules, or a failed exit. Holding costs are a simple monthly carry.

Review and correction policy

The methodology and calculators are reviewed when a formula, convention, or source changes. Corrections are welcome. Email [email protected] with the page, the issue, and a supporting reference if available.

This page is maintained by the Rental Property Math editorial team. It is educational information, not professional advice.