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  • Writer's pictureMike Brandly, Auctioneer

Calculations regarding real property at auction

What is that property worth? What will my payment be? What kind of return can I make by purchasing that property? Which property should I buy?

Lots of questions about real property values. Here’s some common ways real property is analyzed from the standpoint of investors, buyers, sellers, lenders, etc:

Loan amortizationBuyers often need to know what their monthly “mortgage” payment will be. Loan amortization is used to determine the uniform monthly payment of principal and interest for a certain period of time which pays off a debt completely.The formula involves the variables: A = payment; i = periodic interest rate; P = principal financed; n = number of payments. The formula is A = [P * ([i(1+i)^n]/[(1+i)^n – 1])].For example: A buyer wishes to buy a home for $250,000 putting 10% down and financing the remainder. A loan for $225,000 for 30 years with monthly payments at 4% interest would result in a monthly payment of $1,074.18.

Least seller can acceptSellers wishing to sell their real property often need to know the least amount they can accept and break even at closing. This number is calculated by backing in the auctioneer’s commission while considering all liens and other seller payouts to be paid at closing.The formula is [(total of liens or other seller payouts at closing)/(1-commission)] equals minimum sales price.For example: A seller has a first mortgage of $75,000 and a second secured line of credit of $11,000, plus desires another $5,000 out at closing for some other expenses; the seller’s auctioneer is charging 10% commission on the sale price. By taking $91,000/(1-0.10) = $101,111.11 we see the least the property can sell for without the seller bringing additional funds to closing.

Capitalization analysisInvestors use capitalization analysis to determine the most they can pay for an income producing property based upon the net income and a rate of return. The formula is I/R = V. Net income divided by a desired rate of return equals property value.For example: If a property would realize an annual gross income of $200,000 minus expected vacancy and collection loss of 10% and annual building expenses of $5,000, the net annual income is $175,000. If an investor wished a 25% rate of return on his investment, he could pay $175,000/.25 = $700,000.

Gross rent multiplier (GRM)Investors sometimes use gross rent multipliers to help determine real property values. The presumption is that there is a number which describes the relationship between gross rent per year and property value. The formula is gross rents per year * GRM = property value.For example: If area real property is generally renting for 1/8th of property value, then a property which would likely rent for $650 per month would be worth ($650*12*8) = $62,400.

Break even analysisLenders use the break even ratio to determine if financing a real property purchase is prudent. Generally, any break even ratio in excess of 85% is considered too high for underwriting. The formula is (total annual expenses + debt service)/total gross potential income = break even ratio.For example: A building potentially produces $32,000 in annual income. Annual expenses are $15,000 and annual debt service is $12,000. ($15,000 + $12,000)/$32,000 = 84.4% break even ratio.

Cash on cash analysisInvestors in real property use cash on cash analysis to determine their return on investment of a cash purchase. In these calculations, the formula is (single year net income)/(cash invested) to produce a return on cash investment.For example: A $1,000,000 building is purchased with all cash and earns $150,000 the first year in net income. By taking $150,000/$1,000,000 = 0.15 = 15% cash on cash return.

Return on investment (ROI)Investors use return on investment analysis to determine their return on investment of typically some cash and other financing. In these calculations, the formula is (single year net income)/(equity invested) — same as cash on cash calculation, except some sort of financing is used for part of the purchase — to produce return on equity investment.For example: A $1,000,000 building is purchased with 25% down and the remainder financed. The building earns $150,000 minus $59,000 in debt service the first year. By taking $91,000/$250,000 = 0.364 = 36.40% return on investment.

Debt service coverage ratio (DSCR)Lenders use the debt service coverage ratio to determine if financing a real property purchase (or refinancing) is prudent. The amount the debt service coverage ratio exceeds 1.0 denotes the excess profits left after paying debt obligations. The formula is net operating income (excluding debt service)/total debt service costs.For example: A building nets $200,000 in operating income per year and has annual debt service costs of $142,500. The debt service coverage ratio is $200,000/$142,500 = 1.40. The higher this number, the more income is available for expenses other than debt service.

Net present value (NPV)An investor of real property may want to know the net present value of periodic cash flows to determine if the purchase is prudent, or not.Discount rates are calculated in a variety of ways, and one way is to assess the rate of return the investor could earn in the marketplace on an investment of comparable size and risk.The formula is -initial investment + (cash flow first period/(1+discount rate) + cash flow second period/(1+discount rate)^2 + cash flow third period/(1+discount rate)^3 … + cash flow last period/(1+discount rate)^last period.For example: A warehouse will cost $500,000 and the first year cash flow is $200,000, the second year $300,000 and the third year $200,000. For a discount rate of 10%, the net present value would be -$500,000 + $200,000/(1.10) + $300,000/(1.21) + $200,000/(1.331) = $80,015.02.

Internal rate of return (IRR)An investor of real property may want to know the internal rate of return, which is simply the discount rate for which net present value of periodic cash flows equals the initial investment.Solving for the discount rate allows an investor to determine how the rate of discount compares to the desired rate of return. Generally, if the internal rate of return is greater than the cost of capital, the real property should be purchased.This calculation is the same as net present value, but solving for the discount rate, rather than the present value. The formula is 0 = initial investment – (cash flow first period/(1+discount rate) + cash flow second period/(1+discount rate)^2 + cash flow third period/(1+discount rate)^3 … + cash flow last period/(1+discount rate)^last period.For example: A warehouse will cost $300,000 and the first year cash flow is $120,000, the second year $95,000 and the third year $110,000. The rate which makes the initial investment equal the sum of all the discounted cash flows (net present value = 0) = 4.18%.

Payback periodInvestors sometimes use payback periods to determine if a purchase of real property is advisable. A (discounted) payback period is the amount of time, given discounted cash flows, for the initial investment to be paid back. The formula with uniform cash flows is simply the initial investment/periodic cash flows. For cash flows which are not uniform, they can be summed to determine the payback period.For example: If a real property would require $500,000 initial investment, and the discounted annual cash flows were $150,000, $125,000, $100,000, $90,000, $75,000, $65,000 … the payback period would be approximately five years (where the payback would be $540,000 (> $500,000.)

Profitability indexInvestors often look at net present value (NPV) in terms of the initial investment. A profitability index allows NPV to be expressed relative to that initial amount similar to how return on investment shows net income relative to equity. The formula is 1+(NPV/C) where NPV = net present value [see described earlier,] and C is initial investment.For example: Earlier here we discussed net present value and calculated a NPV of $80,015.02 on an initial investment of $500,000. The profitability index for that same circumstance would be 1+($80,015.02/$500,000) = 1.16. As long as the NPV > 0, the profitability index will be > 1. The higher the profitability index, the more advisable the investment.

Equivalent annuityWhen investors are comparing two different real property purchases, both having a net present value, discount rate and length of investment, the two can be compared/contrasted to find the better one. Equivalent annuities are used because net present value doesn’t reflect the length of return by itself; the equivalent annual annuity formula provides a way to factor in the length of an investment.The formula for equivalent annuity = r(NPV)/1-(1+r)^-n where r = discount rate, NPV = net present value [see described earlier] and n = number of years.For example: One real property prospect (#1) has a NPV of $150,000 over 4 years at a 10% discount rate and another real property project (#2) has a NPV of $225,000 over 16 years at a 12% discount rate. The equivalent annuity for #1 is $47,320.62 and the equivalent annuity for #2 is $32,262.75. Real property prospect #1 is preferred by the investor.

Investors, buyers, sellers and lenders indeed use these formulas to make decisions about real property every day. Auctioneers selling real property at auction should be familiar with these calculations to better serve their clients, customers and others involved in the real estate auction process.

Mike Brandly, Auctioneer, CAI, AARE has been an auctioneer and certified appraiser for over 30 years. His company’s auctions are located at: Mike Brandly, Auctioneer, Keller Williams Auctions and Goodwill Columbus Car Auction. He serves as Adjunct Faculty at Columbus State Community College, Executive Director of The Ohio Auction School and Faculty at the Certified Auctioneers Institute held at Indiana University.

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