1. 9-0 Appendix A – The Modified Internal Rate of Return The MIRR is used on projects with non- conventional cash flows The cash flows are modified first and then the IRR is calculated using the modified cash flows There are three MIRR methods that are used: The Discounting Approach The Reinvestment Approach The Combination Approach LO6 © 2013 McGraw-Hill Ryerson Limited

2. 9-1 MIRR Method #1 The Discounting Approach All negative cash flows are discounted back to the present at the required return and added to the initial cost. From the previous non-conventional cash flow example, we had a required return of 15% and: Year 0-$90,000 Year 1$132,000 Year 2$100,000 Year 3-$150,000 LO6 © 2013 McGraw-Hill Ryerson Limited

3. 9-2 MIRR Example - Continued Using Method #1, the cash flow at year 3 would be discounted back to year 0 at 15% The cash flows would look like this: Year 0: -$90,000 - $150,000/(1.15 3 ) = -$188,627.43 Year 1: $132,000 Year 2: $100,000 Year 3: $0 MIRR using Method #1 is 15.77% LO6 © 2013 McGraw-Hill Ryerson Limited

4. 9-3 MIRR Method #2 The Reinvestment Approach All cash flows (positive and negative) except the first are compounded out to the end of the project’s life and then the IRR is calculated The cash flows would look like this: Year 0: -$90,000 Year 1: $0 Year 2: $0 Year 3: $-$150,000 + $100,000(1.15) + $132,000(1.15 2 ) MIRR using Method #2 is 15.75% LO6 © 2013 McGraw-Hill Ryerson Limited

5. 9-4 MIRR Method #3 The Combination Approach All negative cash flows are discounted back to the present and all positive cash flows are compounded out to the end of the project’s life The cash flows would look like this: Year 0: -$90,000 - $150,000/(1.15 3 ) = -$188,627.43 Year 1: $0 Year 2: $0 Year 3: $100,000(1.15) + $132,000(1.15 2 ) = $289,570 MIRR using Method #2 is 15.36% LO6 © 2013 McGraw-Hill Ryerson Limited

6. 9-5 MIRR vs. IRR MIRR can handle non-conventional cash flows, where as the IRR can’t But there are problems with MIRR: There are three methods, and three different MIRRs. Which MIRR is correct? The differences could be larger on a more complex project MIRR is a rate of return on a modified set of cash flows, not the project’s actual cash flows Since the MIRR depends on an externally supplied discount rate, the result is not truly an “internal” rate of return LO6 © 2013 McGraw-Hill Ryerson Limited