The Container Pier Investment Is Economically Equivalent to a Bank Account Paying 15 Percent Annual Interest To confirm that an investment's IRA is equivalent to the interest rate on a bank account, suppose that instead of building the pier, Pacific Rim Resources puts the S40 million cost of the pier in a bank account earning 15 percent annual interest. The table below demon-strates that Pacific can then use this bank account to replicate precisely the cash flows from the pier and that. just like the investment. the account will run dry in 10 years. In other words, ignoring any differences in risk, the fact that the pier's IRR is 15 percent means the investment is economically equivalent to a bank savings account yielding this rate. ($ millions} Beginning-Interest End-of-Withdrawals = of-Period Earned Period Investment Year Principal at15% Principal Cash Flows S40.0 $6.0 $46.0 $ 7.5 2 38.5 5.8 44.3 7.5 3 36.8 5.5 42.3 7.5 4 34.8 5.2 40.0 7.5 5 32.5 4.9 37.4 7.5 6 29.9 4.5 34.4 7.5 7 26.9 4.0 30.9 7.5 8 23,4 3.5 26.9 7.5 9 19.4 2.9 22.3 7.5 10 14.8 2.2 17.0 17.0 T he IRR function calculates the internal rate of return of the numbers ap-pearing in cells 83 through L3. To aid in the iterative search for the IRR, the function requests an initial guess of what the IRR might be. I have used 12 percent. Chapter 7 Durounrrd Cash Filli!• Ttrbmqurs 245 TABLE 7.3 calculating Container Pier's Estimated NPV with a Computer Spreadsheet ' IRR, and BCR 1 1 1 4 A I B I C I D I E L F ESTIMATED ANNUAL CASH FLOWS($ millions) Year O I 2 3 Cash flow ($40) 7.5 7.5 7.5 j 7.5 I] Discount rate 10% .§ 1 ! _!! .!Q 11 12 Net present value (NPV) Benefit-Cost Ratio (BCR) Internal Rate of Return (IRA) Eguation = NPV (CS, C3:L3) + B3 = NPV (C5, C3:L3)/-B3 = IRA (83: L3, 0.12) K L 9 10 7.5 17 ~ $9.75 1.24 15% A common mistake to avoid: The NPV function calculates the net present value o f an indicated range of numbers as of 011e period before the first cash flow occ11rs. Consequently, if I had entered -npv(C5,B3:L3), the computer would have calculated the NPV as of time -1. Because I want the NPV at time 0, 1 added the time O cash flow of ($40) to the net present value, at time 0, of the annual cash flows in years I through 10. Bond Valuation: An Example of NPV and IRR Calculations Investors regularly use discounted cash flow techniques to value bonds. Here is an example. Suppose ABC Corporation bonds have an 8 percent coupon rate paid annually, a par value of $1,000, and nine years to ma-turity. What is the most an investor should pay for an ABC bond if she wants a return of at least 14 percent on her investment? The cash flow diagram is as follows: $80 2 3 4 6 8 9 p The IRR of a Perpetuity An a · · • • nnwty1s a stream of cash flows having the same value each year. A perpeturty1s an annuity that lasts forever. Many preferred stocks are perpetuities, as are some British and French government bonds. They have no maturity date and promise the holder a \'
246 Part Four £:·11/11,11i11g /11,·tstmelll Opport1111i1ies constant annual dividend or
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- Winter '16