In a Wall Street Journal piece this morning, a man named Clifford Asness says that Warren Buffet is wrong when he says the impact of taxes on investment decisions is very small. His argument:
Here is the problem with this argument--it focuses on the numerator of the discounted cash flow calculation, but not the denominator. The denominator contains the discount rate, which is the opportunity cost of capital. One can do an analysis based on before tax cash flows, in which case the denominator is the before tax OCC. The formula for before tax cash flow valuation is
Where CF is cash flow subscripted by time t, r is the discount rate, and E is the expectations operator.
But if one is going to take taxes out of the denominator, he must also take it out of the numerator. This means the ATDCF formula needs to be
The greek letter τ is the marginal income tax rate. If we examine this formula, we see that for small t, value does in fact decline with an increase in taxes. But now let us approximate a long term investment by looking at the perpetual annuity formula--one that has a constant cash flow for infinite t.
Now the formula for before tax valuation becomes:
Analogously, the formula for after tax valuation becomes:
Of course, the (1-τ) divides through, so the after tax and before tax values are the same.
But here is where I will add a kicker of my own: if it is really true that fiscal issues as creating uncertainty, resolving those issues should reduce the discount rate, and thus encourage investment. People such as Mr. Asness should welcome greater certainty, and the investment opportunities it will doubtless induce.
Consider how every business-school student, investment banker and investment analyst on Earth has been taught to choose whether to invest in a specific project or company. You make a spreadsheet (a napkin will do sometimes). You put in your best guess of the future cash flows, and you discount those cash flows back to the present at some required rate of return you believe reflects the risk entailed. Of course, opinions about the future cash flows and the proper discount rate can vary widely, but the essential methodology is ubiquitous.
Now here's the kicker: Nobody who pays taxes and has ever done this exercise has failed (while sober) to use after-tax cash flows in this calculation. Somewhere in the spreadsheet there is a number, say 20%, or 28%, or a Gallic 75%, representing the taxes you'll pay on the assumed cash flow—and you only count the amount you'll get after paying this tax. If you turn the tax rate up high enough, projects or companies that looked like good investments become much less attractive and vice versa.
Here is the problem with this argument--it focuses on the numerator of the discounted cash flow calculation, but not the denominator. The denominator contains the discount rate, which is the opportunity cost of capital. One can do an analysis based on before tax cash flows, in which case the denominator is the before tax OCC. The formula for before tax cash flow valuation is
Where CF is cash flow subscripted by time t, r is the discount rate, and E is the expectations operator.
But if one is going to take taxes out of the denominator, he must also take it out of the numerator. This means the ATDCF formula needs to be
The greek letter τ is the marginal income tax rate. If we examine this formula, we see that for small t, value does in fact decline with an increase in taxes. But now let us approximate a long term investment by looking at the perpetual annuity formula--one that has a constant cash flow for infinite t.
Now the formula for before tax valuation becomes:
Analogously, the formula for after tax valuation becomes:
Of course, the (1-τ) divides through, so the after tax and before tax values are the same.
But here is where I will add a kicker of my own: if it is really true that fiscal issues as creating uncertainty, resolving those issues should reduce the discount rate, and thus encourage investment. People such as Mr. Asness should welcome greater certainty, and the investment opportunities it will doubtless induce.
4 comments:
Under this theory, if gross-of-tax discount rates are 10% and an investment promises $10 per year, I'll plunk down $100 for it if tax rates are zero, and $100 if tax rates are 50% and I get only $5 per year. "To be tested." Recall also, if tax rates are on nominal returns, with even moderate inflation, the tax falls on what is a compensation for inflation. The effect of higher taxes seems like an empirical question, with all due respect to both Buffett & Asness, and Richard.
I believe you left out a consideration. The discount rate does not exclusively represent the opportunity cost of capital. It also represents the estimated risk premium of the investment. This is why investments such as venture capital have discount rates in the 30-50% range.
The reason why this is an important distinction is that the tax rate should only be included into the opportunity cost portion, since that represents alternative cash flows. The risk premium portion of the equation represents the expected probability of loss, which may, in some circumstances, actually be a tax benefit.
Richard's point is a valid one when the cost of financing is fully tax deductible. But not all forms of financing are, in fact, so deductible. If the project is to be entirely financed by debt, then sure, the tax terms in the numerator and denominator cancel out. But equity financing is not tax deductible and so the discount rate should be weighted according to the proportion of financing taking the form of debt and the proportion taking the form of equity with the tax term only being applied to the former.
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