Small Business Taxes & ManagementTM--Copyright 2008, A/N Group, Inc.
We've compiled a number of formulas, ratios, etc. used in business, tax and accounting. We'll be adding to the list on a regular basis. Feel free to e-mail us at question@smbiz.com with any suggestions.
Contents
Back-End Ratio--Mortgage credit ratio.
Front-End Ratio--Mortgage credit ratio.
Breakeven Holding Period for Long-Term Capital Gains--Should you hold investment to get long-term capital gain rate?
Social Security Tax Threshold--Will you pay tax on social security payments?
Grossup--Calculating the gross to get to an after-tax amount.
Months' Supply--How long will it take to bring rental space to equilibrium?
Wilcox's Gambler's-Ruin Formula--Computing the liquidation value of a company in trouble.
Altman Z-Score--A relatively painless way to compute the likelihood a company will fail.
Taxable Amount of Repayment of Loans to S Corporation--Loan repayments to shareholders can create taxable income.
Cash-on-Cash Return
Used by mortgage lenders and other creditors to determine the percentage of a person's income that is used to pay debts. The formula is:
Back-End Ratio = Monthly Debt Payments/Monthly Income
Example: Fred's monthly income is $6,000; his monthly debt payments (service) is $2,400. His back-end ratio is 0.4 or 40%.
Notes:
Monthly debt payments include credit-card payments, auto loans, child support, house payments (mortgage principal, interest, taxes, and insurance), etc. Most lenders look for a back-end ratio of 36% or less, but higher ratios may be accepted if other credit factors are offsetting.
Used by mortgage lenders and other creditors to determine the percentage of a person's income that is used to pay debts. The formula is:
Front-End Ratio = Monthly Housing Expenses/Monthly Income
Example: Sue's monthly housing costs total $1,800; her monthly income is $6,000. Her front-end ratio is 0.3 or 30%.
Notes:
Housing costs include mortgage principal, interest, real estate taxes and insurance (often called PITI). The threshold front-end ratio most lenders look for is about 30% (0.30). The higher the ratio, the riskier the loan from a creditor's standpoint.
Breakeven Holding Period for Long-Term Capital Gains
Hold a stock for 11 months and your gain is short-term; hold it for even one day more than a year and your gain is long-term and taxed at 5% (if you're in the 10% or 15% bracket) or 15% (if you're in the higher brackets). How much of your gain can you lose and come out even by holding for the extra time?
You can figure your breakeven by using this formula:
BE = G1(1-TR)/(1-CGR)Where:
BE = Breakeven gain
G1 = Current gain
TR = Marginal tax rate
CGR = Capital gain tax rate
Example: Fred has a $20,000 gain in Madison Inc. If he holds the stock another 15 days the gain would be long-term. Fred's marginal tax rate is 33%; the rate on long-term capital gains is 15%. Plugging into the formula:What the formula does is help quantify the risk. The closer you are to the one-year threshold and the less volatile the stock, the more sense it makes to take that risk.
BE= 20,000(1-.33)/(1-.15) = 20,000(.67)/.85 = $15,764.71If Fred sells the stock today, his after tax gain will be $13,400 ($20,000 gain less taxes at 33%). If he holds the stock for the required one-year plus period and his gain at that time is more than $15,764.71 he'll end up with a larger net gain; if the stock drops below that, he would have been better off not to wait.
You don't have to work through the formula each time. We've run the formula for the various tax rates and developed a factor for each:
Marginal Tax Rate Factor
35% 0.7647
33% 0.7882
28% 0.8471
25% 0.8824
15% 0.8947
10% 0.9474
For example, if you're in the 25% bracket your gain can decrease to 88.24% of the original amount (a $10,000 gain can drop to $8,824) and you'll break even if you hold for the requisite one-year plus.
A portion of social security benefits is taxable to individuals whose modified adjusted gross income exceeds a threshold. You can determine if a taxpayer is taxable on his or her social security benefits by plugging into the formula:
AGI + TE + (1/2*SSI) - TH
Where:
AGI = Adjusted Gross Income
TE = Tax exempt income (line 8b of Form 1040)
SSI = Social Security Income
TH = Threshold amount $25,000 or $32,000, see Notes, below
If the result, sometimes called provisional income, is greater than zero, a portion of the benefits are taxable.
Example: Sue and Fred have AGI of $27,000, $2,500 in tax exempt income (municipal bonds), and social security benefits of $12,000. Plugging into the formula:Notes:
27,000 + 2,500 + (1/2*12,000) - 32,000 = 3,500Thus, a portion of their social security benefits are taxable.
It's not unusual for a company to agree to pay the tax on an employee's taxable fringe benefit, bonus, etc. or to pay some other charge that has to be included in the price. For example, Madison Inc. has agreed to pay Fred, an employee, a bonus of $20,000 after taxes. That means Madison will have to write a check for something more than $20,000 and withhold taxes on the gross (higher) amount so that Fred's check is $20,000. You could do this by trail and error, but you can set up a simple algebraic formula.
G = N/(1-TR)
Where:
G = Gross amountThe tax rate should include all amounts to be withheld--federal, state, FICA, etc. at the recipient's marginal tax rate.
N = Net amount
TR = Tax rate
Example: Madison will pay Fred $20,000 after taxes. Fred's in the 33% bracket for federal purposes; 10% for state and 1.45% for social security (Medicare only). Adding all three together gives a tax rate of 44.45%. Plugging into the formula:Caution. This won't work cleanly if the payment will take you through a tax bracket. There can be other factors that will create inaccuracies. For example, if the recipient becomes subject to the alternative minimum tax, etc.
G = 20,000/(1-.4445) = 20,000/.5555 = $36,003.60
Real estate investors and developers are interested in knowing the number of months' supply of apartments, office space, etc. on the market. The problem is that the amount of space is always changing--existing space is being leased, new space is becoming vacant. Fortunately, the formula isn't that complex. Moreover, it can be useful for other business and investment analysis.
Months' Supply = Vacant Space/Net Absorption or MS = VS/NAWhere:
VS = total amount of vacant space
NA = space leased during the month less space going vacant
Notes.
Example: In the Madison, NY market there's 30,000 square feet of vacant space. Space is being leased up at the rate of 15,000 square feet per month, but space is becoming vacant at the rate of 6,000 square feet per month and 4,000 square feet of new construction is coming onto the market.
MS = 30,000/(15,000 - 6,000 - 4,000) = 30,000/5,000 = 6 Months's Supply
If the denominator is negative, (more space is coming onto the market than is being leased) the result is meaningless.
Wilcox's Gambler's-Ruin Formula
This model can be used to estimate the liquidation value of a company. It's likely to be significantly less than the book value because of the "fire sale" nature. Most current assets are valued at 70% of their balance sheet values; fixed and other assets at 50% of book value. Real estate should generally be valued separately.
Cash plus marketable securities at market value + Inventory, accounts receivable, prepaid expenses, at 70% of book value + Fixed and other assets at 50% of book value - Current liabilities - Long-term liabilities = Liquidation Value
Example: Madison Inc. has assets with the following book values:The liquidation value of $74,500 is considerably less than the company's net book value of $181,000.
Cash on hand = $26,000 Accounts receivable = $80,000 Inventory = $20,000 Prepaid insurance = $5,000 Equipment, office furniture, and trucks = $150,000 Accounts payable and accrued expenses = $40,000 Long-term liabilites = $60,000 Here's the computation: Cash $26,000 Accounts receivable $80,000 x .7 56,000 Inventory $20,000 x .7 14,000 Prepaid insurance $5,000 x .7 3,500 Equipment, etc. $150,000 X .5 75,000 Accounts payable and accruals -40,000 Long-term liabilities -60,000 Liquidation Value $74,500
Notes.
The formula shouldn't be applied to a company in good financial shape unless there's some sort of a risk on the horizon. For example, assume Madison's financials are as shown above. The company has substantial working capital, good current and quick ratios, etc. Moreover, the company's profit margins are strong and sales are rising. If you're looking at the creditworthiness of the company the formula has little value. A creditor should be looking at the company's cash flow. On the other hand, there may be an outside risk, for example, the company may be in danger of losing a critical patent, that could warrant using the formula.
The Altman Z-Score is a formula that can be used as a forecaster of bankruptcy of a business. The model has held up very well over the years and uses 7 pieces of financial information arranged in 5 ratios that are weighted to produce a number. The simplicity, ease of computation, and availability of raw data in addition to its accuracy make it particularly attractive. While you can use it to check on the creditworthiness of customers, it can be used on potential acquisition targets and as an additional measure in determining the health of your business. Here's the formula:
Z = 1.2X + 1.4Y + 3.3Z + 0.6A + 0.999B
Where:
X = working capital/total assets
Y = retained earnings/total assets
Z = earnings before income taxes/total assets
A = market value of equity/book value of debt
B = sales/total assets
Z score Probability of Failure
1.8 or less Very High
1.81-2.99 Not Sure
3.0 or higher Unlikely
You can tell by the weighting of the formula that earnings before interest and taxes (EBIT) divided by total assets is the most important factor (it's weight is 3.3). The greater a company's earnings, the larger that factor will be. The second most important factor is retained earnings. It's weight is 1.4.The formula above is the general formula developed by Edward Altman. It works very well on publicly held manufacturing companies. The formula has been modified slightly for nonpublic companies and an additional variation is designed for use with nonmanufacturing companies.
Nonpublic Companies
Z = 0.717X + 0.847Y + 3.107Z + 0.42A + 0.998B
Where:
X = working capital/total assets
Y = retained earnings/total assets
Z = earnings before income taxes/total assets
A = book value of equity/book value of debt
B = sales/total assets
Z score Probability of Failure
1.23 or less Very High
1.23-2.90 Not Sure
2.9 or higher Unlikely
Notice the change in the coefficients and the replacement of book value of equity for market value of equity. But while the coefficients have changed, their relative importance remains the same.
Nonmanufacturing Companies
Z = 6.56X + 3.26Y + 6.72Z + 1.05A
Where:
X = working capital/total assets
Y = retained earnings/total assets
Z = earnings before income taxes/total assets
A = market value of equity/book value of debt
Z score Probability of Failure
1.0 or less Very High
1.1-2.6 Not Sure
2.6 or higher Unlikely
The Z-score formula for nonmanufacturing companies eliminates the last factor, sales divided by total assets.
Example: Madison Inc. is a nonpublic manufacturing company with the following information:Because even the nonpublicly held formula was not specifically designed for small businesses, simply plugging into the formula and comparing the result with the score table is not the final answer. However, the results can still be useful. First, they provide a relative measure--if the score is less than 1.0, you should be concerned; if more than 3.0, not very concerned. The middle ground is likely to provide little guidance. Second, you can use the formula on your own or other businesses to watch trends. If the number is going up, financial strength is improving; going down and it's getting worse. Third, you can use the formula to gauge relative strength of customers or others. For example, if you have 10 customers and the Z-scores are generally clustered near 3.0 with one at 1.2, consider dropping that customer or at least monitoring him closely and/or cutting back on his credit line.
We're using the formula:working capital = $600,000 total assets = $3,000,000 retained earnings = $585,000 earnings before income taxes = $225,000 book value of equity = $600,000 book value of debt = $2,400,000 sales = $6,500,000
Z = 0.717X + 0.847Y + 3.107Z + 0.42A + 0.998B Here:The result is 2.809, slightly higher than the 2.6 threshold for an unlikely chance of bankruptcy.X = $600,000/$3,000,000 = 0.2 Y = $585,000/$3,000,000 = 0.195 Z = $225,000/$3,000,000 = 0.075 A = $600,000/$2,400,000 = 0.25 B = $6,500,000/$3,000,000 = 2.166Z = (0.717 * 0.2) + (0.847 * 0.195) + (3.107 * 0.075) + (0.42 * 0.25) + (0.998 * 2.166)
Taxable Amount of Repayment of Loans to S Corporation
You can take losses up to your basis in an S corporation. Once your stock basis is exhausted by losses and distributions, additional losses go to reduce any loan basis. There's a trap. Repayment of loans (in whole or part) that have been reduced by losses can create taxable income. The formula is:
Where:Gain = P x (1 - DB/FA)
P = Principal Payment
DB = Basis of Debt
FA = Face Amount of Debt
Example: Fred has a signed note from Madison Inc. for $75,000. Losses have reduced the basis of the note to $30,000. In 2008 Madison repays Fred $15,000 of the note. The gain would be:If the note was held for more than a year, the gain should be long-term. If less than a year or the debt is open account, the gain would be ordinary income. There is some controversy about this issue. In some cases it has been held that no gain is reportable until basis is recovered. We suggest you check with a tax professional for your particular situation.
Gain = $15,000 x (1 - $30,000/$75,000) Gain = $15,000 x (1 - .4) Gain = $9,000Thus, only $9,000 of the $15,000 principal payment constitutes gain.
This is a quick, albeit not very accurate, way to compute a return on your investment. The computation is simply the annual cash flow from the property, equipment, etc. divided by your invested cash.
Cash-on-Cash Return = Before-Tax Cash Flow/Invested Cash
Example: Fred is considering purchasing a rental property. He believes he has to put $200,000 down and spend about $50,000 of his own cash to fix up the property. Annual rental income less expenses and debt service (loan payments) is projected to be about $30,000. His cash-on-cash return would be 12% ($30,000/$250,000).
The cash-on-cash return calculation is often used in real estate as an initial filter. If the property doesn't pass a predetermined hurdle rate, some investors won't go further. This approach has merit for risky properties where current income and cash flow is more important than appreciation (which is difficult to project), but fails to take into account additional, future investments, increasing (or decreasing) rents and expenses, vacancies, and appreciation or depreciation in property value. The calculation can also be misleading if your cash investment in the property is very small.
Copyright 2007-2008 by A/N Group, Inc. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is distributed with the understanding that the publisher is not engaged in rendering legal, accounting, or other professional service. If legal advice or other expert assistance is required, the services of a competent professional should be sought. The information is not necessarily a complete summary of all materials on the subject.--ISSN 1089-1536
--Last Update 04/22/08