Why present value leads to better investment decisions than other criteria Yes, there are two paths you can go by, but in the long run there’s still time to change the road you're on. And it makes me wonder. – Page, Plant

CFO Decision Tools Survey Data on CFO Use of Investment Evaluation Techniques SOURCE: Graham and Harvey, “The Theory and Practice of Finance: Evidence from the Field,” Journal of Financial Economics 61 (2001), pp

3 competitors of NPV Payback & Discounted Payback Average Return on Book Internal Rate of Return

Payback NPV Year: Payback At 10% A B Project A has shorter payback but lower NPV

Discounted Payback Discounted NPV Year: Payback At 10% A B Project A does not get paid back

Problems with Payback Payback does not recognize time value of money (discounted payback does). Payback & Dicounted Payback both ignore any cash flows after payback period.

Book Rate of Return Book Rate of Return - Average income divided by average book value over project life. Also called accounting rate of return.

Average return on book Year: Book Gross Profit (= cash flow) Depreciation Net Profit Average Return on Book = = 44% 2 4.5

Average return on book (continued) This project also has a 44% average return on book, but cash flows come later and NPV is less. Year: Book Gross Profit (= cash flow) Depreciation Net Profit Average Return on Book = = 44% 2 4.5

Problems with Average Return on Book Value It ignores time value of money. It is not based on project cash flows.

Rate of return rule Suppose you invest 350 in office building, which you expect to sell next year for 400. Cost of capital = 7%. Rate profit C1 + C of = = = = 14.3% return investment -C0 350 The project return is higher than equivalent investments. Note: 1. Project return is also the discount rate which gives zero NPV. 2. If the cost of capital is less than the return, NPV is positive. NPV Discount rate % Return = 14.3%

Internal rate of return rule (IRR) C 1 C 2 NPV = C = IRR (1 + IRR) 2 i.e., Find cost of capital at which project would be fair value (NPV=0). Accept project if actual cost of capital is less than this.

Internal Rate of Return Example You can purchase a turbo powered machine tool gadget for $4,000. The investment will generate $2,000 and $4,000 in cash flows for two years, respectively. What is the IRR on this investment?

Internal Rate of Return Example You can purchase a turbo powered machine tool gadget for $4,000. The investment will generate $2,000 and $4,000 in cash flows for two years, respectively. What is the IRR on this investment?

Internal Rate of Return IRR=28%

Internal Rate of Return Pitfall 3 - Mutually Exclusive Projects IRR ignores the magnitude of the project. The following two projects illustrate that problem.

But beware, there are potential problems with IRR---- Lending or Borrowing? Year: 0 1 IRR 10% A % B % Multiple Rates of Return Year: IRR 10% C % & 400% -1.9 Mutually Exclusive Projects Year: 0 1 IRR NPV AT 10% D % 1.8 E

Decisions Under Capital Rationing If capital is rationed in only one period: Profitability Index = NPV / PV of outlays If capital is rationed in more than one period or when there are other constraints, we may use: -Linear Programing Problem with fractional projects -Interger (zero-one) Programming

Profitability Index When resources are limited, the profitability index (PI) provides a tool for selecting among various project combinations and alternatives A set of limited resources and projects can yield various combinations. The highest weighted average PI can indicate which projects to select.