***Show calculations ADVANCED CAPITAL BUDGETING TOOLS Now, on to advanced capital budgeting tools MIRR = modified internal rate of return (this is not in the text), and DPB = discounted payback. Remember the problems inherent with IRR and PB? IRR sometimes can give conflicting answers when compared to NPV; and, PB does not take into account the time value of money. Well, someone solved the problem with MIRR and DPB respectively. Let's discuss DPB first. Since you are all masters of computing PB (Payback) and PV (present value), you will be able to easily understand the calculation of DPB (discounted payback). Discount Rate = 10% Projected Cash Flow Years 0 1 2 3 4 5 6 Project A (500) 45 55 65 175 185 300 PV - YR1 = 40.91 PV - YR2 = 45.45 PV - YR3 = 48.84 PV - YR4 =119.52 PV - YR5 =114.87 PV - YR6 =169.34 I gave you the answer for payback for project A as 4.86 years. DPB is figured in a similar fashion, but with a different cash flow -- a discounted cash flow -- I have shown each years' discounted cash flow above. Now you compute payback with this new cash flow discount adjustment -- see if you can mimic my calculations. Your answer should be = 5.77 years. DPB will always be more conservative than PB. Now, lets look at MIRR (without the year 6 from the prior example) Discount Rate = 10% Projected Cash Flow Years 0 1 2 3 4 5 Project A (500) 45 55 65 175 185 FV - YR5 = 185.00 FV - YR4 = 192.50 FV - YR3 = 78.65 FV - YR2 = 73.21 FV - YR1 = 65.88 ------ Terminal Value = 595.24 MIRR (modified internal rate of return) takes everything out to the future first before discounting it back to the present. Let us take year 1 for an example -- to get this year's value out to year five, we must use the FV (future value) function: PV = 45 i = 10 n = 4 because it is 4 years to get to year 5. Solving for FV = 65.68 Once this process has been done for each year, you add them up to get what is called the terminal value. Now you have all of the numbers to calculate MIRR: FV = 595.24 PV = (500.00) n = 5 Solving for i = 3.55% MIRR is 3.55%, which will almost always be more conservative than IRR. Of course since MIRR is below our required rate of return, it is thumbs down on this project. Make sure that you go through the above answer to see if you can come up with the same solution. Remember, always make sure your PV is entered as a negative, or you will get an error when solving for "i". ************The second discussion item for the week -- calculate DPB and MIRR for the following projects YEAR 0 1 2 3 4 5 Project B (250) 85 65 55 45 100 Project C (400) 175 75 75 175 25