1. Copyright: M. S. Humayun Financial Management Lecture No. 11 Capital Budgeting - Special Cases Batch 3-4

2. Copyright: M. S. Humayun Capital Budgeting Real Asset Projects Evaluating profitable projects and investments in Real Fixed Assets (and affiliated working capital) Importance of good Cash Flow forecasts and accurate Proforma Cash Flow Statement: –Cover the entire Life of the Project (3 Time Periods) –Net After-tax Cash Flows = Net Operating Income + Depreciation + Tax Savings from Depreciation + Net Working Capital + Other Cash Flows –Other Cash Flows: Include Opportunity Costs and Externalities but Exclude Sunken Costs.

3. Copyright: M. S. Humayun Major Capital Budgeting Criteria 2 Major Criteria: NPV (the best) & IRR –Combined View: NPV Profile (NPV vs i Graph) Multiple IRR: –Standard NPV Equation gives wrong multiple answers –Use the MIRR Equation: Separate the Incoming and Outgoing Cash Flows at each period in time. Discount all the Outflows to the present and Compound all the Inflows to the termination date. Assume reinvestment at a Cost of Capital or Discount Factor (or Required Return) such as the risk free interest rate.

4. Copyright: M. S. Humayun Multiple IRR - Example Numerical Example: A project with the following cash flows: Initial Investment = -Rs100, Year 1 = +Rs500, Year 2 = -Rs500 IRR Equation: NPV = 0 = -100 + 500/(1+IRR) - 500/(1+IRR) 2. From Iteration, IRR = 38% and 260% MIRR Approach (Assume Cost of Capital k = 10%): (1+MIRR) n = CFin * (1+k) n-t CFout / (1+k) t (1+MIRR) 2 = 500 * (1+0.1) 2-1 (100 / 1) + ( 500 / (1+0.1) 2 ) (1+MIRR) 2 = 550 / 504 = 1.091 MIRR = 0.0446 = 4.46%

5. Copyright: M. S. Humayun NPV - Ranking Projects with Different Lives NPV of Projects with Different Lives –Common Life Approach: Find least common multiple for common life. Repeat the cash flow pattern of the project back to back to cover common life. Compute the NPV of each project over the common life and choose the project with the highest NPV. –Equivalent Annual ANNUITY (EAA) Approach: Find out what yearly annuity gives the same NPV. Compare annual annuity of each project and choose the highest. Note: Equivalent perpetuities can also be compared since life spans are identically infinite.

6. Copyright: M. S. Humayun Different Lives NPV - Example 2 Projects with following Cash Flows: –Project A: Io= - Rs100, Yr 1 = +Rs200 –Project B: Io= - Rs200, Yr1= +Rs200, Yr2= +Rs200 Simple NPV Computation (assume i=10%): –NPV Project A = -100 + 200/1.1 = +Rs 82 –NPV Project B = -200 + 200/1.1 + 200/(1.1) 2 = + Rs 147 Conclusion from Simple (or Normal) NPV Calculation is that Project B is better. BUT Project Lives are different !

7. Copyright: M. S. Humayun Different Lives NPV - Example Common Life Approach Common Life Approach –Common Life = 2 Years (because this is the shortest cycle in which both project lives can exactly be replicated back to back). –Project A: –Project B: Yr 0Yr 1Yr 2 Yr 0Yr 1Yr 2 -100 -200 -100 +200 Cash Flow Pattern of A is repeated exactly 2 times to cover the life of the longer Project B.

8. Copyright: M. S. Humayun Different Lives NPV - Example Common Life Approach Common Life (C.L.) NPV’s –Project A C.L. NPV = -100 + [(200-100)/1.1] + 200/(1.1) 2 = +Rs 156 –Project B C.L. NPV = Same as before = +Rs 147 Now our conclusion has changed ! After doing the Common Life NPV, Project A looks better. The Simple NPV of Project A was + Rs 82 but after increasing its life to match Project B’s, the NPV of Project A increased.

9. Copyright: M. S. Humayun Different Lives NPV - Example Equivalent Annual Annuity Approach Start with the Simple (or Normal) NPV’s calculated earlier (at i = 10%): –Project A Simple NPV = + Rs 82 –Project B Simple NPV = + Rs 147 Multiply the Simple NPV of each project by the EAA FACTOR = (1+ i) n / [(1+i) n -1] where n = life of project & i=discount rate –Project A’s EAA Factor = 1.1 / (1.1-1) = 11 –Project B’s EAA Factor = 1.1 2 / (1.1 2 -1) = 5.76 Final step is to compute the EAA for each project: –Project A’s EAA = Simple NPV * Factor = 82*11= + Rs 902 –Project B’s EAA = 147*5.76 = + Rs 847 Conclusion: Project A is Better. Same conclusion as Common Life Approach but of course the numbers for EAA and NPV are different.

10. Copyright: M. S. Humayun Different Lives & Budget Constraint In comparing two projects or assets (ie. Sewing or Printing Machines) with different lives: –Disadvantage of project with very long life: Does not give you the opportunity (or option) to replace the equipment quickly in order to keep pace with technology, better quality, lower costs –Disadvantage of project with very short life: Your money will have to be reinvested in some other project with an uncertain NPV and return so it is risky. If a good project is not available, the money will earn only a minimal return at the risk free interest rate. Use Common Life and EAA Techniques to quantitatively compare such Projects Ideal Case: So far our Capital Budgeting Criteria have assumed NO Budget Constraints Budget Constraint: In practical life, individuals and companies have a limited amount of money and limited human resources. This prevents them from undertaking projects with high positive NPV’s that would have added value and maximized shareholder wealth !!