The chapter covered the following major points:

• If markets are perfect, everyone has the same information, and there are infinitely many buyers and sellers, no transaction costs, and no taxes.

• In perfect markets, promised borrowing and lending rates can be different. In imperfect markets, even expected borrowing and lending rates can be different.

• If markets are not perfect, capital budgeting decisions can then depend on the cash position of the project owner.

NPV and interest rate computations can still be used, although it then requires special care in working with correct and meaningful inputs (especially for the cost of capital). This is usually best done by thinking in terms of concrete examples first, and translating them into formula later.

• Transaction costs and taxes are market imperfections that reduce earned rates of return.

• Transaction costs can be direct (such as commissions) or indirect (such as search or waiting costs). It is often useful to think of round-trip transaction costs.

• Financial assets' transaction costs tend to be very low, so that it is reasonable in many (but not all) circumstances to just ignore them.

• In the real world, buyers often prefer more liquid investments. To induce them to purchase a less liquid investment may require offering them some additional expected rate of return.

• Many financial markets have such low transaction costs and are often so liquid that they are believed to be fairly efficient—there are so many buyers and so many sellers that it is unlikely that you would pay too much or too little for an asset. Such assets are likely to be worth what you pay for them.

• The tax code is complex. For the most part, individuals and corporations are taxed similarly. You must understand

1. how income taxes are computed (the principles, not the details);

2. that expenses that can be paid from before-tax income are better than expenses that must be paid from after-tax income;

3. how to compute the average tax rate;

4. how to obtain the marginal tax rate;

5. that capital gains enjoy preferential tax treatment;

6. why the average and marginal tax rates differ, and why the marginal tax rate is usually higher than the average tax rate.

• Taxable interest rates can be converted into equivalent tax-exempt interest rates, given the appropriate marginal tax-rate.

• Tax-exempt bonds are usually advantageous for investors in high-income tax brackets. You can compute the critical tax rate for the investor who is indifferent between the two.

• Long-term projects often suffer less interim taxation than short-term projects.

• You should do all transaction cost and tax NPV calculations with after-transaction cash flows and after-tax costs of capital.

• Like taxes and transaction costs, inflation can also cut into returns. However, in a perfect market, inflation can be neutralized through proper contracts.

• The relationship between nominal interest rates, real interest rates, and inflation rates is

Unlike nominal interest rates, real interest rates can and have been negative.

• In NPV, you can either discount real cash flows with real interest rates, or discount nominal cash flows with nominal interest rates. The latter is usually more convenient.

• TIPS are bonds whose payments are indexed to the future inflation rate, and which therefore offer protection against future inflation. Short-term bond buyers are also less exposed to inflation rate changes than long-term bond buyers.

• Empirically, inflation seems to be able to explain the level of the yield curve, but not its slope.

• The IRS taxes nominal returns, not real returns. This means that higher inflation rates disadvantage savers and advantage borrowers.

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