No Free Lunch: Economics for a Fallen World: Third Edition, Revised

Chapter Sixteen: Valuing the Future - Concepts in Capital & Finance 404 interest rate; therefore, it will have a lower present value, as seen in Figure 16.4 . For a firm to accept a higher risk investment project, the project must be expected to provide higher returns, or higher CFs. This leads to a fundamental conclusion of finance: risk equals return. For investors wanting higher returns, they must be willing to accept a higher risk level. Just as the fundamental tradeoff in economics is comparing costs vs. benefits, the fundamental tradeoff in finance is risk vs. return. FINANCIAL ASSETS: STOCKS & BONDS Our present value calculation process is equally valid in assessing the value of an investment within a firm, or valuing an entire firm, or valuing any debt or loan in a market. Much of the financial news you hear on television or see on the Internet will report on the value of various stock market indexes. So what is the stock market, and why is it important? Let’s first think about a small firm, say a bakery owned by Anne that makes $50,000 per year after all expenses. If we expect that to continue forever and the interest rate is 5%, we can calculate the present value of this bakery. You may ask, how do we calculate income streams forever? It turns out that because each additional cash flow contributes less to the net present value than the previous cash flow, CFs well into the future have very small net present value and lead to a very simple calculation for a constant stream of cash flows into the future. While constant returns forever may not be a good assumption for a bakery, there are some bonds of this type and are called perpetuities . The formula for Anne’s bakery (or any perpetuity) is… [Equation 8] PV = CF/i Figure 16.4, Present Value comparison of Five $100 payments for two different interest rates. If investment B is expected to yield the same cash flow as investment A, but has a higher risk preimium, then B’s interest rate will be higher and present value is therefore lower. If a firm is considering the two investments, it will always pick investment A, since it has a higher expected return in present value terms. For B to be chosen with a higher risk premium, it must have higher cash flows; it must provide higher returns. CF/(1+i ) CF/(1+i ) 2 CF/(1+i ) 3 CF/(1+i ) 4 CF/(1+i ) 5 Present Value $83.33 $69.44 $57.87 $48.22 $40.18 $299.02 A) i=10% PV for N=5, CF=$100 B) 1=20% $90.91 $82.64 $75.13 $68.30 $62.09 $379.07 Perpetuity: an investment that promises a constant return forever into the future Just as the fundamental tradeoff in economics is comparing costs vs. benefits, the fundamental tradeoff in finance is risk vs. return.