To start with, notice that over the first 2 years the company receives $120k in cash flows. With the original outlay of $100k you know that it will take less than 2 years.
After one year: 100,000 - 60,000 = 40,000 remains
40,000 / 60,000 = 0.67 (or, about 2/3 of a year), so total payback period is 1.67 years, or about 1 year and (12 * 0.67) = 8 months
NPV is the sum of the discounted cash flows, discounted at the required return
NPV: (100,000) + 60,000/1.12 + 60,000/1.12^2 + 65,000/1.12^3 + 80,000/1.12^4
NPV: $98,510.22
IRR is the discount rate that "makes NPV = 0", you'll need a financial calculator or spreadsheet to solve.
Cash flows: enter the outlay as a negative number, and the inflows as positive (as above in NPV)
IRR: 51.22789%
If you were to use the IRR (in decimal form) in the NPV equation above (e.g. 1.5122789^n) the NPV would equal 0.
IRR assumes that the positive cash flows are reinvested at the IRR - which is not always realistic, especially in this case where the IRR is over 51%!
Modified IRR (MIRR) "assumes that positive cash flows are reinvested at the firm's cost of capital, and the initial outlays are financed at the firm's financing cost. Therefore, MIRR more accurately reflects the cost and profitability of a project". (from: http://www.investopedia.com/terms/m/mirr... )
MIRR: geometric mean of: (the future value of the positive cash flows / original investment)
So, for MIRR you have to calculate the future value of the cash flows at the required rate of return.
Since the total time horizon is 4 years, the first cash flow, received at the end of year 1, can be invested for the remaining 3 years, and so on with the other cash flows.
FV CF1: 60,000(1.12^3) = 84,295.68
FV CF2: 60,000(1.12^2) = 75,264
FV CF3: 65,000(1.12) = 72,800
FV CF4: 80,000
Total FV: 312,359.60
total "n" = 4
MIRR: (FV cash inflows / PV investment)^1/n - 1 (see Note below)
MIRR: (312,359.60 / 100,000)^(1/4) - 1
= (3.1236^0.25) - 1
= 1.32942 - 1
= 0.32942, or 32.942%
Note: I don't want to get too far into the weeds here, but if you had had negative cash flows in year 1 or after, you would have to calculate the financing costs associated with "financing" those losses. See here if you want more info on this: http://en.wikipedia.org/wiki/Modified_in...
Profitability index: PV of future cash flows / initial investment
the PV of the future cash flows is the NPV you calculated above + the initial investment (e.g. the initial investment added back in)
NPV 98,510.22 + initial investment 100,000 = 198,510.22
PI: 198,510.22 / 100,000 = 1.9851
I hope this helps! Feel free to email me if you are confused about any of this.
Please help me UNDERSTAND, don't just give me the answers..try to walk me through it. I'm really stuck on this one. Thank you so much in advance.
Larry, Inc. is investing a 4-year investment that will yield total cash flows of $60,000 per year in Years 1 and 2, $65,000 in year 3, and $80,000 in year 4. The investment will cost the firm $100,000 today, and the required return is 12 percent. Calculate the payback period, the NPV, the IRR, and the profitability index for this investment.
Payback:
NPV =
IRR=
MIRR=
PI=
