Consider the illustration in Section 7.3 where you are choosing between two investments, fully taxable bonds yielding 10% pretax per year and tax-exempt bonds yielding 7% per year. Both investments have 3-year maturities. At the time of investment, you are unsure—because of the uncertain profitability of your other investments already in place—as to whether your tax rate will be 40% over the 3 years or 0%. You assess a 70% chance of the former. This makes your expected marginal tax rate 28% or .7 × 40% + .3 × 0%.
If you are risk-neutral and if you must choose one investment or the other and hold it for the entire 3-year period, you would be better off choosing taxable bonds. At an expected tax rate of 28%, taxable bonds yield 7.2% after tax, whereas tax-exempt bonds yield only 7%. Now let us consider what your optimal strategy would be if you could sell your asset and purchase the other at the end of the first year. At the end of the first year you will find out whether your tax rate for the next 2 years (as well as for the year just ended) will be 40% or 0%. At the end of the subsection, it is stated, “We leave it as an Exercise for the reader to verify that in the absence of transaction costs, taxable bonds would be the investment of choice in the first period. Over the 3-year period, they would yield 7.7% per year after tax, versus 7.6% for tax-exempt bonds.” Show that this statement is correct.