What is it?

1. What is it? • An analytical method of comparison is an objective way to assess the relative risks and potential rewards from alternative investments. • The assessment should initially be based on both factual and measurable information. • However, the ultimate decision as to which (if any) investment should be made may be subjective,

2. How does it work? • Chapter 32 focuses on five comparative techniques commonly used to evaluate alternative investments. • They are all designed to measure the return on an investor’s principal, which is the concept of return on investment (ROI). • Net Present Value (NPV): The difference between the present value of all future benefits of an investment and the present value of all capital contributions. • Measures the tradeoff between the cash invested (outflows) and the benefits projected (inflows)

3. How does it work? • Internal Rate of Return: The discount rate at which the present value of all future benefits an investor will receive from an investment exactly equals the present value of all the capital contributions the investor will be required to make. • Compares the effective interest rates • Modified Internal Rates of Return: IRR methods that adjust cash flows for realistic assumptions regarding reinvestment rates, borrowing rates, etc.

4. How does it work? • Pay Back Period: Measures the relative periods of time needed to recover the investor’s capital. • Income received after the pay back period will be considered gain • Cash on Cash: Analyzes an investment by dividing the annual cash flow by the amount of the cash investment in order to determine the cash return on the cash invested.

5. Advantages • These methods of comparison offer a way to measure the potential return on alternative investment choices in a logical and consistent manner. • The use of mathematics balances an investor’s natural inclination to play a hunch by introducing objectivity into the decision-making process. • Assuming the accuracy of the input • The use of more than one comparative method will help the investor more effectively recognize and evaluate risk/reward parameters.

6. Disadvantages • There are a number of unknowns in the measurement process. • There is no way to completely guarantee either the amount or timing of cash flows. • These uncertainties, although drawbacks, should not preclude the use of analytical techniques. • There is no single technique that can be applied to every case, • The method that most closely reflects the investor’s perception of how return should be measured is the one that should be used. • It is important that the chosen method by used consistently. • In many cases, more than one analytical technique should be used in order to corroborate the results of the other approaches.

7. Disadvantages • Undue reliance on mathematical quantitative evaluation techniques may create a false sense of security. Such excessive reliance can: • Hinder the investor’s ability to utilize appropriate subjective analytical skills • Inhibit the consideration of external factors that may affect the viability of the investment. • It is possible that a particular investment may not be adequately or properly quantified by any of the evaluation techniques described. • An investor may not have objective tools available.

8. Disadvantages • It is often difficult to know which measuring device to select. • The use of an inappropriate technique will often result in drawing an inappropriate conclusion. • In practice, it is difficult to obtain accurate and comprehensive data.

9. When is the use of this technique indicated? • The techniques are all useful when: • An investor wants to compare alternative investments that are seemingly similar with respect to risk • It is desirable to distinguish the investments by their relative rewards in terms of: • Timing: When and/or how often must cash be invested in and/or may be taken out of the investment) • Quantity: The rate of interest the investment will earn or the rate at which it will grow

10. When is the use of this technique indicated? • The techniques can also be used to evaluate one particular investment in comparison with a safe alternative • The safe alternative serves as a benchmark to determine whether the potential reward from the investment under consideration is sufficient relative to the associated risks.

11. Rate of Return Concepts • Rate of return means different things in different contexts. • Depending on a host of factors. • Financial economists and investors use a wide variety of terms to describe returns in these different contexts, such as: • Total return, holding-period return, annualized return, simple return, compound return, arithmetic average return, geometric average return, time-weighted return, dollar-weighted return, nominal return, real return, risk-adjusted return, after-tax return, taxable-equivalent return, internal rate of return, and various modified rate of return measures.

12. Rate of Return Concepts • Although financial professionals do not always define and use these terms in exactly the same way, there are some commonly accepted definitions for various measures. • Total Return: The total gain or loss over a specified period relative to an initial dollar investment at the beginning of the period.

13. Rate of Return Concepts • All investments potentially have some combination of six components or sources of return for which a proper analysis must account: • Cash inflows from the investment (outflows to the investment); plus (minus) • Price or capital appreciation (price or capital depreciation); plus (minus) • Debt amortization (negative amortization); plus (minus) • Tax shelter (tax payments); plus (minus) • Other tangible property or boot received (paid); plus (minus) • Intangible but measurable benefits or services received (paid), if any.

14. Rate of Return Concepts • Investors must consider the potential erosion of their future purchasing power as a result of inflation. • To computer the rate of return on investment for any period, one simply divides the total return by the investor’s equity in the investment at the beginning of the period. • An investor’s equity in an investment at any point in time is the sum of all cash contributions, plus debt amortization, plus price appreciation or less price depreciation.

15. Rate of Return Concepts • Holding Period Return: The total return for a specified period over which an investment is held. • Annualized Returns: Since comparing returns over different holding periods is difficult, the standard practice is to express returns in annualized terms. • Annualized return may be expressed in one of two ways: • Simple • Compound • Two closely related terms also applicable are: • Arithmetic average annual return • Geometric average annual return

16. Rate of Return Concepts • Simple and Arithmetic Average Annual Returns: • Investors compute the simple annual return by dividing the holding-period return by the number of years in the holding period. • The simple annual return is the rate of return computed by stretching or shrinking the holding period to be equal to just one year and stretching or shrinking the holding-period return proportionately. • The annual rate is computed as if the holding period were actually one year without assuming any reinvestment of principal and interest. • The arithmetic average return corresponds conceptually to the simple return, only applied to a series of holding period returns.\ • If investors want to find the arithmetic average annual return of a series of 1-year holding period returns, they simply sum the returns and divide by the number of years of returns.

17. Rate of Return Concepts • Compound and Geometric Average Annual Returns: • One computes the compound annual return by assuming earnings and principal are being reinvested. • Investors calculate the compound annual return of an n-year holding-period rate of return by adding one to the holding-period return, taking the nth root of the sum, and subtracting one. • The geometric average return is related to the compound return in the same manner as the arithmetic average return is related to the simple return. • To calculate the geometric average annual return for a series of 1-year holding-period returns, add one to each period’s return, compute the product of these sums over all periods, extrapolate the nth root of the product, where n is the number of years, and subtract one.

18. Rate of Return Concepts • Simple Versus Compound and Arithmetic Versus Geometric: • For any investment providing a net positive return over a given holding period, the simple annual rate is always equal to or greater than the compound annual rate if the holding period is greater than one year and always equal to or less than the compound annual rate if the holding period is less than a year. • For any series of (on average, positive) annual holding-period returns, the arithmetic average annual return is always equal to or greater than the geometric average annual return. • The greater is the variability of the annual holding-period returns, the larger the difference will be.

19. Rate of Return Concepts • Simple Versus Compound and Arithmetic Versus Geometric: • Whether one measure is better than another depends upon how one intends to use it: • If the objective is to measure historical performance, the compound or geometric average returns are the better measures. • If one is looking to estimate future returns based on historical performance, the simple or arithmetic average returns are the better measures for estimating returns in any given future year. • In general, the simple or arithmetic average is an unbiased estimate of expected future returns for a single year. • However, if investors are attempting to estimate the average annual rate at which they could expect their money to grow over a period of years in the future, the compound or geometric average returns are the ideal measures.

20. Rate of Return Concepts • Nominal and Real (Inflation-Adjusted) Returns: • Nominal returns are the actual returns earned over a given period computed without accounting for changes in the purchasing power of the dollar (inflation). • The inflation-adjusted or real rate of return representsthe return adjusted for changes in the general level of prices of goods and services that investors could purchase if they liquidated their investments.

21. Rate of Return Concepts • Real Rate of Return (Nominal Rate of Return - Inflation Rate) / (1 + Inflation Rate) • Note: For the sake of consistency and simplicity in calculating the simple annual real rate of return, it is advisable to calculate first the real holding-period rate of return and then to derive the simple annual real rate of return.

22. Rate of Return Concepts • Internal Rate of Return and Net Present Value: • Net present value is the current value of a stream of cash flows discounted at some appropriate rate of return representing the investor’s opportunity cost rate (best alternative rate). • The key aspect of evaluating an investment in terms of NPV is whether it is positive or negative (whether it earns more or less than the investor’s required rate of return). • The magnitude of the NPA is not necessarily a valid way to select between two different investment choices. • The internal rate of return is the rate of return that equates the NPV to zero, which is the annual rate of return earned by the investment.

23. Rate of Return Concepts • Time-Weighted and Dollar-Weighted Annual Returns: • The time-weighted annual return is the geometric (compounded) annual return measured on the basis of periodic market valuations of assets. • This method eliminates the impact of cash contributions and disbursements (inflows and outflows). • In principle, it requires valuations to be made on the occasion of each cash flow. • Approximations to this measure can be obtained by: • Prorating cash flows to successive valuation points, or • Computing internal rates of return between valuation points. • If there are no interim cash flows, this return, compounded annually, determines the ending value of the investment.

24. Rate of Return Concepts • Time-Weighted and Dollar-Weighted Annual Returns: • The dollar-weighted annual return is the rate of return that discounts a portfolio’s terminal value and interim cash flows back to its initial value. • It is equivalent to a portfolio’s internal rate of return (IRR). • It is influenced by the timing and magnitude of contributions and disbursements that are beyond the control of a portfolio manager. • Can be misleading for purposes of comparative performance measurement • This method of return should be used if investors want to compute the average annual return they actually have earned on an investment over a given period where they have made cash withdrawals and/or contributions during that period.

25. Rate of Return Concepts • After-Tax Return and Taxable-Equivalent Return: • The real value of any financial planning strategy or tactic or investment choice relates to the real spendable dollars that each option provides relative to the alternatives. • What investors get to keep after paying taxes is what matters. • If it is assumed that the investment return is entirely currently taxable, the after-tax return (tax-free-equivalent return) is simply equal to the before-tax return less the taxes on the return: rat = r x (1-t) • Where, r = before-tax return, rat = after-tax return or tax-free equivalent return, t = tax rate. • The taxable-equivalent return is the reverse of the after-tax return: r = rat / (1 - t)

26. Rate of Return Concepts • After-Tax Return and Taxable-Equivalent Return: • Although these formulas are frequently used to compute after-tax returns, they are often not an accurate measure. • Only a relatively small class of investments are entirely currently taxable. • A whole host of investment vehicles provide unique tax incentives that cannot be accounted for using the simple formulas. • In many financial planning and investment situations, not only the level of taxation but also the timing of taxation is a critical factor. • Between two investments providing identical before-tax returns and identical total tax burdens, the one that defers some or all of the taxation to a later date is generally preferable.

27. Rate of Return Concepts • Risk-Adjusted Returns: • These measures were developed to help investors gauge how much return they were getting per unit of risk. • Both volatility (level of risk) and return are combined in one measure, permitting a rank ordering of investments. • Investments ranking high on a risk-adjusted scale demonstrated a favorable trade-off between risk and reward. Either: • The returns were high enough to compensate for the additional risk taken, or • The returns may not have been extraordinarily high, but the risk taken was much lower than expected. • Some risk-adjusted return measures use standard deviation, while others use beta.

28. How is it implemented? • Net Present Value: • Present value is the amount that must be invested now to produce a given future value. • It is affected by: • The interest (discount) rate • The length of the investment period • Present value is a simple means of comparing two investments. • Net present value is the net difference between: • The present value of all future benefits to be realized from an investment • The present value of all capital contributions into the investment • A negative net present value should result in an almost automatic rejection of the investment.

29. How is it implemented? • Net Present Value: • A positive net present value indicates that the investment is worth further consideration • The present value of the stream of dollars that will be recovered exceeds the present value of the stream of dollars that will be paid out. • The difficulty is determining what discount rate should be used in computing the present values of the cash inflows and cash outflows. • Usually this discount rate will be the minimal acceptable rate of return, found by determining: • The cost of capital • The rate an alternative investment of similar quality/risk can earn

30. How is it implemented? • Internal Rate of Return: • In computing the internal rate of return, the interest rate sought is that rate at which inflows of cash, discounted to present value, will equal the original (and subsequent, if applicable) principal contributions. • It is a method of determining what percentage rate of return estimated cash inflows would provide based on a known investment (cash outflow). • Even the cash outflow must sometimes be estimated. • IRR is really the same as a present value computation except that the discount rate is either not known or not given.

31. How is it implemented? • Shortcomings of the Internal Rate of Return Method: • A common misconception is that the IRR inherently assumes that the cash flows from an investment being evaluated are implicitly reinvested at the computed IRR of the investment itself. • The IRR assumes that the cash flows are not reinvested, at any rate. • The cash flows from an investment are assumed to be consumed when paid and never enter the analysis again. • When investors want to use the IRR to compare investments that involve different initial outlays, cash flow patterns, and/or investment terms, they must explicitly account for the differences in cash flows. • The investor, not the IRR method, is implicitly assuming cash flows are reinvested at the IRR. • When the reinvestment at the IRR is not realistic, the IRR method, improperly used, leads to poor choices among investments.

32. How is it implemented? • Shortcomings of the Internal Rate of Return Method: • Investors cannot use an IRR method (unless modified) to compare (directly) mutually exclusive investments, particularly when they have different time periods and cash flow timings. • The unmodified IRR method does not consider realistic reinvestment rates for positive cash flows or realistic borrowing rates for negative cash flows over the holding period. • An investment project may have multiple IRRs • Solving for the IRR often requires a series of iterative calculations to determine the IRR since, for many types or IRR calculations, there is no single, closed-end formula to compute the IRR.

33. How is it implemented? • Modified IRR Method: • Devised to circumvent the problems inherent in the use of the regular IRR method. • Modified IRR methods adjust the cash flows of the investment to account for reinvestment, borrowings, setting up sinking funds to cover later cash outflows, and the like. • The best method is that which most closely approximates how an investor is most likely to handle the cash flows of the investment. • None of the modified methods is the best approach all of the time and each of the modified methods is the best approach some of the time.

34. How is it implemented? • Modified IRR Methods: • IRR-reinvestment-rate method • Solves the problem of intermediate cash flows by making specific assumptions about how these cash flows will be reinvested. • IRR-safe-rate method • Solves the problem of additional cash outflows (or additional investments required after the initial investment) by assuming additional funds are set aside up-front as a sinking fund that is treated as part of initial year-0 investment to cover later cash outflows. • IRR-borrowing-rate method • Solves the problem of later cash outflows by assuming money will be borrowed to cover future cash outflows and will be repaid out of later cash inflows.

35. How is it implemented? • Adjusted Rate of Return (ARR) • Based on a “one-size-fits-all” approach • It is applied in the following manner: • Discount all cash flows into the project (negative cash flows or investments into the project) at a safe rate of return back to period 0 • Compound all cash flows out of the project (positive cash flows or returns of investment) at a safe rate to the end of the holding period (find the FV of the cash flows from the project) • The ARR is the discount rate that equates the PV of cash flows into the project with the discounted FV of cash flows out of the project. • IRR-Borrow/Reinvestment Rate Method • A combination of the IRR-Borrow and IRR-Reinvestment methods

36. How is it implemented? • Pay Back Period: • Pay back period analysis is a time value of money concept. • This method compares alternative investments by measuring the length of time required to recover the original investment. • From this perspective, the investment that returns the original capital in the shortest period of time is the best investment. • It fails to capture the potentially extremely favorable returns that may accrue under one investment beyond the end point of the pay back period of another investment choice.

37. How is it implemented? • Cash on Cash: • Cash on cash analysis focuses on the amount of cash generated by the investment. • It ignores both taxes and the potential gain from any sale. • To computer cash on cash return, divide the annual cash flow by the cash investment.

38. How is it implemented? • Using Analytical Methods to Compare Investments: • The NPV method or the unmodified IRR method should virtually always give the same accept or reject decision regarding an investment when the investment is evaluated independently of other investments.

39. How is it implemented? • Independent Versus Mutually Exclusive Investments: • As long as investments are evaluated independently, the NPV and unmodified IRR will work just fine in determining whether an investment is acceptable or unacceptable. • Two projects are considered independent if the acceptance or rejection of one project has no bearing on the acceptability or feasibility of investing in the other project. • If the investments cannot be evaluated independently and an investor cannot choose to invest in both alternatives at the same time, the NPV method and/or IRR method must be applied in a more involved manner to determine the better alternative. • Two investments that are not independent are said to be mutually exclusive.

40. How is it implemented? • Independent Versus Mutually Exclusive Investments: • The Discounted Accounting Return Ratio (DARR) is the ratio of discounted benefits to discounted costs. • It is a measure of the PV of benefits to the PV of the costs of an investment relative to each dollar of investment. • It is also called the Discounted Profitability Index (DPI), • Decision Rule: The project is acceptable when the ratio is greater than one. • It gives the same accept and reject decisions as the NPV method. • The Undiscounted Accounting Return Ratio (UARR) is a version of the payback method. • Also called the Undiscounted Profitability Index (UPI)

41. How is it implemented? • Incremental Analysis Methodology: • The NPV and IRR methods are up to the task of evaluating mutually exclusive investments or comparing any two or more investments to determine the better or best among the alternatives. • They must be applied incrementally.

42. How is it implemented? • Incremental Analysis Methodology: • According to three basic rules, the analysis must: • Take account of all costs and all sources of return; • Give more weight to early cash flows than later ones; • Standardize choices by accounting for differences in: • Initial outlays • Holding periods • Cash flow payouts • Risk levels • Time perspective

43. How is it implemented? • Incremental Analysis Methodology: • An incremental analysis is applied as follows when one is using the NPV method, the DPI method, or the IRR method: • Each of the investments must be evaluated as if they were independent by applying any of the traditional NPV, DPI, or unmodified methods. • Any investment that is unacceptable when evaluated as a completely independent investment can be disregarded from further consideration • The surviving investment alternatives are sorted by the size of the initial outlay, from smallest to largest. • Not necessary, but eases the analysis

44. How is it implemented? • The investments are compared head-to-head based upon the NPV, DPI, or IRR of the additional or incremental investment in the larger outlay investment over the smaller outlay investment. • Should start with the investments with the smallest and next to smallest initial outlays • The winner of the comparison goes on to challenge the next larger outlay project until all investments have been challenged and the winner determined. • At each step, apply the NPV, IRR, or DPI analysis to the incremental cash flows. • If, after applying the chosen methodology, the incremental project is an acceptable investment in its own right, then the larger outlay project is the better investment. • If the larger project is rejected, then the smaller outlay project is the better investment.