Comparison of IRR and MIRR The evaluation of an investment’s IRR assumes that any future cash flows are reinvested at the same rate as

the IRR at the end of the analysis period. This can result in reinvestment rates that are unrealistically high. Assume, for example, the situation shown in the spreadsheet of Figure 12-1. An investment of $100,000 (Cell B5) generates after-tax cash flows of $35,000 at the ends of years 1 to 4 and $50,000 at the end of year 5. If the discount rate is 10 percent (Cell B2), the IRR at the end of year 5 is 24.55% (Cell G7, computed by the entry = IRR(B5:G5,guess)). This result assumes that the $35,000 cash inflows at the ends of years 1 to 4 are reinvested at the calculated IRR rate of 24.55 percent and are allowed to accumulate to the end of year 5, when the accumulated values would be added to the $50,000 inflow at the end of year 5.

Figure฀12-1

Comparison of IRR and MIRR

1 COMPARISON OF IRR AND MIRR

2 Discount Rate

3 Reinvest Rate

5 Year-End Cash Flow

9 Analysis of value at end of year 5 of the year-end cash flows reinvested at 24.55%

10 Year-5 Value of Year-1 Cash Flow

$84,231 11 Year-5 Value of Year-2 Cash Flow

$67,627 12 Year-5 Value of Year-3 Cash Flow

$54,296 13 Year-5 Value of Year-4 Cash Flow

$35,000 $43,593 14 Year-5 Value of Year-5 Cash Flow

Total = $299,748 16

24.55% 17 Analysis of value at end of year 5 of the year-end cash flows reinvested at 12.00%

Fifth root of $299,748/$100,000 – 1 =

18 Year-5 Value of Year-1 Cash Flow

$55,073 19 Year-5 Value of Year-2 Cash Flow

$49,172 20 Year-5 Value of Year-3 Cash Flow

$43,904 21 Year-5 Value of Year-4 Cash Flow

$35,000 $39,200 22 Year-5 Value of Year-5 Cash Flow

Total = $237,350 24

Fifth root of $237,350/$100,000 – 1 =

370 ❧ Corporate Financial Analysis with Microsoft Excel ®

The total at the end of year 5 would be $299,748, as shown by the calculations in Rows 10 to 15. Thus, for example, the $35,000 received at the end of year 1 would be reinvested for four years at 24.55 percent, which would provide a total of

The result of this calculation is shown in Cell G10. Similar calculations are made for reinvesting the cash inflows for years 2, 3, and 4, with the results at the end of 5 years shown in Cells G11:G13. Their sum is then added to the year-end $50,000 inflow for year 5 (Cell G14) to give a total of $299,748 at the end of year 5 (Cell G15). The rate of return would then be calculated as

A reinvestment rate of 24.55 percent is probably too high to be realistic. We might assume a more reasonable rate of 12 percent, as indicated in Cell B3. In this case, the value of the modified rate of return, or the rate of return adjusted for the reinvestment rate, as calculated in Cell G8 by the entry =MIRR(B5:G5,B2,B3), is only 18.87 percent.

Rows 18 to 24 show the analysis for reinvesting the cash flows for years 1 to 4 at a rate of 12 percent. In this case, the $35,000 received at the end of year 1 would be reinvested for four years at 12 percent, which would provide a total at year 5

as indicated in Cell G18. Repeating this calculation for the other years (Cells G19:G21) and adding the cash flow for year 5 (Cell G22) gives a total of $237,350 at the end of year 5 (Cell G23). The rate of return would then be

In other words, if the discount rate is 10 percent and the reinvest rate is 12 percent, the investment’s actual rate of return is 18.87 percent rather than 24.55 percent. The bottom line of this comparison is that the modified internal rate of return generally provides a more realistic assessment of an investment’s financial merit than the internal rate of return.

Break-Even Point When time is money, speed is profit! The race today is to reach pay dirt before the competition. Companies

must recoup their investments for developing new products and installing production facilities while there is still a market for their output. Beyond reaching a break-even point quickly, companies hope to earn a positive amount on their investments so long as the products continue to sell well.

Capital Budgeting: The Basics ❧ 371 The time for an investment to pay back its cost has become critical in high-technology industries.

Break-through products encounter competition sooner than ever before, and commercial lifetimes can be as short as one or two years. Patents no longer provide long-term market protection for many types of new products. The knowledge base for products in telecommunications and other information technology industries, as well as in pharmaceuticals and biotechnology firms, can become obsolete in 18 months, or less. (For example, Monsanto’s Celebrex, a medicine for treating arthritis, faced competition from a similar product from Merck within five months of its introduction.) The profit race is won by those who move new products from their research laboratories to markets quickly and reach the break-even point first.

Breaking-even means achieving a net present value of zero—that is, when the present value of the future cash inflows equals the value of the investment. Because money has a time value, the future cash inflows should be discounted back to the same time as making the investment. Some analysts emphasize this need by referring to it as the discounted payback period or break-even point. Failure to discount future cash flows to their present value results in shorter payback periods that are misleading because they fail to recognize the time value of money.

Figure 12-2 shows the change in NPV from a negative value at the end of period n to a positive value at the end of the following period, period n+1. The break-even point, when the NPV is zero, is at an intermediate point between n and n+1. Using linear interpolation between the two known points gives the following formula for the number of periods to break even:

− NPV

Periods to break even = n +

NPV n +1 − NPV n

Figure฀12-2

Interpolation of the Break-Even Point between a Negative and a Positive Net Present Value

NPVn+1

Break-Even Point = n + (–NPVn)/(NPVn+1 – NPVn)

Time, Year or Other Period

372 ❧ Corporate Financial Analysis with Microsoft Excel ®

Equation 12.1 simply indicates that the number of periods to break even is the last period at which the NPV is negative plus a fraction of the next period, where the fractional part of the next period is calculated by the second term on the right side of the equation.

Comparison of IRR and MIRR The evaluation of an investment’s IRR assumes that any future cash flows are reinvested at the same rate as