June 2003

Using Breakeven Formulas to Analyze Tax Planning Strategies

By John O. Everett, Roxanne Spindle, and Thomas Turman

The combination of declining regular tax rates and the variety of capital gains rates has created a degree of uncertainty in planning for capital gains income. Nevertheless, significant tax saving opportunity can be identified by using simple breakeven analysis tools. Five different tax planning issues are described below, along with the appropriate breakeven formulas and examples that illustrate their use.

Each formula is derived by developing algebraic expressions for alternative tax options and then setting the two expressions equal to one another. Present-value analysis is incorporated in those cases that involve more than one tax year. The resulting formula is then solved for the necessary breakeven amount between the two options.

Long-Term Capital Gains Treatment

If the stock market should recover quickly, investors might realize significant stock gains in relatively short periods of time. This may induce taxpayers to sell in the short run to avoid potential price declines in the near future. Given the recent significant reductions in tax rates for long-term capital gains, some investors may be tempted to defer the sale until the stock has been held longer than one year. Thus, the question for investors sometimes becomes whether they should realize a certain gain today as short-term capital gain and pay the additional tax at ordinary income tax rates, or hold the stock until they have met the long-term holding period and pay the lower capital gains tax rates. What sales price would equate the two options on an after-tax basis?

Breakeven analysis can be used to determine how much loss in stock value a taxpayer can afford in chasing a lower tax rate. The breakeven formula developed below reflects the following equality:

After-tax proceeds from selling after achieving long-term status = After-tax proceeds from selling at the present time

The breakeven formula may be expressed as follows:

BSP - [(BSP - AB) x CGR] = CSP - [(CSP - AB) x OTR]

Where BSP is the breakeven sales price of the stock (a sales price exceeding this amount favors waiting for long-term status), AB is the adjusted basis of the stock, CGR is the capital gains tax rate, CSP is the current sales price of stock, and OTR is the ordinary income marginal tax rate.

Example 1. Tina, who is in the 38.6% marginal tax bracket, holds a stock with an adjusted basis of $80,000 that she bought eight months ago and would sell today for $140,000. How much decline in value can Tina afford to absorb while waiting to qualify for the 20% long-term rate? The answer may be determined by using the formula:

BSP - [(BSP - AB) x CGR] = CSP - [(CSP - AB) x OTR]
BSP - [(BSP - $80,000) x .20] = $140,000 - [($140,000 - $80,000) x .386]
BSP - .20 BSP + $16,000 = $140,000 - $54,040 + $30,880
.80 BSP = $100,840
BSP = $126,050

Thus, the stock could decline in value as much as $13,950 ($140,000 - $126,050) and Tina would realize the same after-tax proceeds from the sale. Note that the preceding calculation does not consider potential time value of money issues, since the time differential between the two options is only four months. If the stock did not achieve long-term status until the following tax year, then the left side of the equation would be discounted one year on a present-value basis to reflect this. (For even more precision, the discounting could be done on a quarterly basis.)

Election for Investment Interest Expense

In general, IRC section 163 limits the annual deduction for investment interest expense to the taxpayer’s net investment income for the year. (Any excess may be carried forward indefinitely to future years.) For these purposes, net investment income does not include any long-term capital gains on sales or exchanges of investment properties. IRC section 163(d)(4)(B)(iii), however, permits a special election whereby the taxpayer may treat a net long-term capital gain as investment income during the year if the taxpayer agrees to treat such elected gain as ordinary income taxed at the normal rates. The decision to make this election hinges on when the taxpayer believes that any investment interest otherwise disallowed in the current year will be deducted if the special election is not made.

Any analysis of the two options must consider the time value of money, because postponed interest expense would be deducted in future years. In this case, the breakeven number represents the rate of return generated by the tax savings from the election in the current year (created by offsetting income that would otherwise have been taxed at 20%) that would equal the tax savings from using the expense to offset ordinary income in the future. This can be expressed as follows:

Tax savings in current year with special capital gains election (20% of capital gain) = Present value of tax savings with deduction in Year 2 only (38.6% of ordinary income)

The number of present value factors incorporated in the formula depends upon the number of years the taxpayer believes will be necessary to fully recover the carryover interest deductions. If the taxpayer believes that postponed deductions will be utilized in the next taxable year, the comparison would appear as follows:


Where DED is the investment interest expense deduction, OTR is the ordinary income marginal tax rate, CGR is the capital gains marginal tax rate, and R = (1+ r)n, where r is the breakeven interest rate and n is the number of years in the future.

Example 2. Jim, a taxpayer in the 38.6% bracket, has $100,000 of net investment interest expenses and $80,000 of net investment incomes in 2003. Jim also has a $20,000 long-term capital gain on the sale of investments that qualifies for the 20% rate. Jim believes that any interest expense disallowed during the current year will be deducted in the next tax year (2004). Thus, Jim’s two tax choices are to save 20% tax on capital gain otherwise taxed in Year 1, or save 38.6% on ordinary income in Year 2.

The comparison would be calculated as follows:

20,000 x .20 = (20,000 x .386) / (1 + R)
4,000 = 7,720 / (1 + R)
4,000 (1 + R) = 7,720
4,000R = 3,720
R = .93

Thus, the additional tax savings generated by the election in Year 1 must be invested at an annual rate of return of 93% (an unlikely possibility) to equal the tax savings available by waiting one year. Clearly, the election does not make much sense in this example, because merely deferring the deduction one year yields $3,720 in tax savings.

Changes in the underlying assumptions can change this clearcut analysis. For example, if the taxpayer’s ordinary income tax rate is only 27%, the breakeven opportunity cost interest rate would be 25%, still unrealistic but much lower than the previous example. Additionally, the above analysis makes the assumption that any nondeductible investment interest in Year 1 can be deducted in Year 2. But if the taxpayer expects that it will be three years before the interest expense carryover can be deducted, the right side of the above equations could be modified to solve for a present value factor that could be used to determine the required interest rate. In such cases, the breakeven interest rate would decrease, since a longer period is required to fully recoup the deductions. For instance, a taxpayer who expects to defer the deduction until Year 3 when a 25% marginal tax rate applies would have to invest the tax savings at only about 8% to break even.

Sale vs. Abandonment of Business Assets

In some cases, it may make economic sense to abandon a business asset rather than sell it at a loss. If the loss on the sale and the abandonment loss would both be deductible against income taxed at the same rate, then the sale option is always preferable, since some cash is received. If, however, the decision must be made in a year in which the taxpayer has already recognized IRC section 1231 gains, any loss on the sale of the additional asset might offset gain that would be taxed at the lower capital gains rate. The abandonment might then result in greater after-tax savings, because the abandonment is not considered a sale or exchange [Treasury Regulations section 1.165-2(b)], and any recognized loss bypasses the IRC section 1231 netting process and is reported as an ordinary loss. (This situation would occur only if the taxpayer has a net section 1231 gain that is not recharacterized as ordinary income through the special five-year look-back rule.)

Breakeven analysis can be used under these circumstances to determine the price at which it becomes more profitable to sell the asset than abandon it. This can be expressed as follows:

Savings generated by a sale at a loss (tax savings at ordinary rates) = Savings generated by an abandonment (selling price + tax savings at capital gain rates)

The relevant equation is as follows:

BSP + [(AB – BSP) x CGR] = AB x OTR

Where BSP is the breakeven sales price (sales prices exceeding this amount favor sales), AB is the adjusted basis of the business asset, CGR is the capital gains tax rate, and OTR is the ordinary income marginal tax rate.

Example 3. Talbot has a greatly depreciated business asset with an adjusted basis of $100,000. Talbot has already recognized a net IRC section 1231 gain in the current year of $130,000 that qualifies for the 20% capital gains rate. Talbot’s marginal ordinary income tax rate is 38.6%. The equation determines the scrap value at which it will be more beneficial to sell the asset than abandon it.

BSP + [(AB - BSP) x CGR] = [AB x OTR]
BSP + [(100,000 - BSP) x .20] = [100,000 x .386]
BSP + 20,000 - .20BSP = 38,600
.80BSP = 18,600
BSP = $23,250

Thus, Talbot should sell the asset if he can receive at least $23,250 for it. If the sales price is less than $23,250, the tax savings from the abandonment will exceed the sum of the cash received plus the tax savings generated by the sale at a loss.

Investment or Inventory in Subdivided Realty

A longstanding controversy between taxpayers and the IRS is the tax treatment of sales of subdivided realty at a gain. Taxpayers generally contend that such properties are investment properties qualifying for capital gains treatment, while the IRS generally contends that the taxpayer in fact has the characteristics of a real estate dealer, and such gains should be treated as ordinary income sales of inventory. Generally, the courts examine a number of factors when classifying such sales, and they often note that each case is unique and must be decided on the basis of its particular facts. A classic and often-cited case that describes the appropriate factors to consider is Winthrop v. Comm’r [417 F.2d. 905 (CA-5, 1969)].

IRC section 1237 was enacted to make it easier for noncorporate taxpayers holding realty as an investment to do limited subdividing and yet still receive capital gains treatment. IRC section 1237 offers three different classifications for such taxpayers: (1) “investors,” for whom capital gains treatment is available for the first five lot sales (contiguous lots sold to the same purchaser count as one lot sale); (2) “brokers” for whom, in the year of the sixth lot sale and all future years, 5% of the sales price (less applicable selling expenses) is treated as ordinary income, and the balance of the gain is capital gain; and (3) “dealers,” for whom, if significant improvements are made to the lots, all gain must be reported as ordinary income. For these purposes, Treasury Regulations section 1.1237-1(c)(3) defines a “significant improvement” as one that increases the value of the lot more than 10%.

Taxpayers not meeting the safe harbor of IRC section 1237 may nonetheless contest the IRS position that they are in fact dealers by stressing the factors indicating an investment motive. A wealth of judicial decisions on both sides of the issue is available for these purposes.

Despite the lower marginal tax rates on ordinary income, the distinction between ordinary and capital gains treatment on subdivided realty can still be a significant tax issue. Sometimes taxpayers may decide that significant improvements will lead to a significant increase in the sales price of the subdivided lots that will compensate for forgoing capital gains treatment. Once again, this decision can be portrayed by means of a breakeven formula:

After-tax proceeds – dealer status (ordinary income for realized gains) = After-tax proceeds – investor status (capital gains for realized gains)

The breakeven formula is expressed as follows:

BSP - IMP - [(BSP - IMP - AB) x OTR] = CSP - [(CSP - AB) x CGR]

Where BSP is the breakeven sales price to equate dealer and investor options, IMP is the cost of the improvements to the realty, AB is the current adjusted basis of the property (without the improvements), OTR is the ordinary income marginal tax rate, CSP is the current sales price without the improvements, and CGR is the capital gains tax rate.

Example 4. Tracey purchased 10 acres of land 10 years ago for $40,000. Her real estate adviser has estimated that she could sell the 10 acres for a total of $100,000 by dividing the land into five two-acre plots. The potential selling price would increase substantially if she made $20,000 worth of improvements to the property (clearing, grading, and adding water and sewage). Tracey’s marginal ordinary income tax rate is 38.6%, and her marginal capital gains rate is 20%. The estimated sales price that she would have to receive to justify incurring the additional cost of the improvements and the additional taxes associated with ordinary income tax rates can be determined with the following equation:

BSP - IMP - [(BSP - IMP - AB) x OTR] = CSP - [(CSP - AB) x CGR]
BSP - 20,000 - [(BSP - 20,000 - 40,000) x .386] = 100,000 - [(100,000 - 40,000) x .20]
BSP - 20,000 - .386BSP + 23,160 = 100,000 - 12,000
.614BSP = 84,840
BSP = $138,176

Thus, Tracey would have to realize an additional $138,176 in the sale to cover the $20,000 cost of the improvements and the additional taxes caused by ordinary income treatment. If her ordinary income tax rate was less than 38.6%, the required breakeven sales price would decrease.

“Deemed Sale” Election 2001 Returns and Later

For properties acquired after 2000, the maximum capital gains rate for properties held more than five years is reduced from 20% to 18%, as prescribed in IRC section 1(h). Taxpayers holding capital assets on January 1, 2001, however, could elect to mark to market the asset on that date (i.e., treat the asset as having been sold for its fair market value and then immediately reacquired on that date for the same value). Any resulting gain (but not loss) is reportable as a taxable gain on the 2001 tax return, and the asset will then qualify for the new 18% rate, if held more than the required five years.

Given that this election must be made on the 2001 return, the window for considering this election has closed. However, it is instructive to see how breakeven
analysis could have been applied to this election. Such “opportunities” to accelerate tax liability (and accelerate total tax collections) will undoubtedly be considered by Congress again.

In essence, a taxpayer making this election would pay a 20% tax rate now on unrealized appreciation on a capital asset for the privilege of paying an 18% tax rate five years from now on any additional appreciation on the same asset. In making this decision, it would have been helpful for the taxpayer to know how much the property would have to appreciate in five years (generating tax savings on the 2% capital gains rate differential) to justify the current payment of tax at a 20% rate.

The breakeven formula can be stated as follows:

Present value of total taxes paid with a deemed election in the current year = Present value of total taxes paid without a deemed election

The breakeven equation is as follows:

[(BSP - AB) x .20] - {[(BSP - SP) x.18] x PV} = {[(BSP - AB) x .20] x PV}

Where BSP is the necessary breakeven sales price of the stock, PV is the present value factor of cost of capital for five years, SP is the current selling price of the stock, and AB is the adjusted basis of the stock.

The left side of the equation is the cost of paying a 20% tax on the current appreciation (SP - AB) now and an 18% tax on the future appreciation (BSP - SP) in Year 5.

The right side of the equation is the cost of paying all of the tax in Year 5 at the 20% rate.

Example 5. Sam owns stock with an adjusted basis of $40,000 and a current value of $100,000. A gain on the sale of such stock would qualify for the 20% rate. Using the discount factor of 5% for amounts received in Year 5 (.783526), what is the breakeven sales price of the stock necessary to justify making the deemed sale election?

The cost of paying a 20% tax on the current appreciation (SP -AB) and an 18% tax on the future appreciation (BSP - SP) in Year 5 is

[($100,000 - $40,000) x .20] + {[(BSP - $100,000) x .18] x .783526
141035BSP - $2,103.

The cost of paying all of the tax in Year 5 at the 20% rate is

{[(BSP - $40,000) x .20] x .783526}
.1567052BSP - $6,268.

Setting the two equations equal and solving yields the following:

.141035BSP - $2,103 = .1567052BSP - $6,268
.0156702BSP = $4,165
BSP = $265,791

The price of the stock would have to almost triple to justify the deemed sale election, which accelerates the payment of some tax for five years. If the adjusted basis of the stock were $80,000, the computed breakeven sales price would fall to $155,298.

John O. Everett, PhD, is a professor of accounting at Virginia Commonwealth University.
Roxanne Spindle, PhD, is an associate professor of accounting at Virginia Commonwealth University.
Thomas Turman, PhD, is an assistant professor of accounting at the University of Wisconsin in Oshkosh.

William Bregman, CFP, CPA/PFS

Contributing Editors:
Theodore J. Sarenski, CPA
Dermody Burke & Brown P.C.

David R. Marcus, JD, CPA
Marks, Paneth & Shron LLP

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