12-1 CHAPTER 12 Other Topics in Capital Budgeting  Evaluating projects with unequal lives  Identifying embedded options  Valuing real options in projects 12-2 Evaluating projects with unequal lives Projects S and L are mutually exclusive, and will be repeated. If k = 10%, which is better? Expected Net CFs Year Project S Project L 0 ($100,000) ($100,000) 1 59,000 33,500 2 59,000 33,500 3 - 33,500 4 - 33,500 12-3 Solving for NPV, with no repetition  Enter CFs into calculator CFLO register for both projects, and enter I/YR = 10%.  NPV S = $2,397  NPV L = $6,190  Is Project L better?  Need replacement chain analysis. 12-4 -100,000 59,000 59,000 59,000 59,000 -100,000 -41,000 Replacement chain  Use the replacement chain to calculate an extended NPV S to a common life.  Since Project S has a 2-year life and L has a 4-year life, the common life is 4 years. 0 1 2 3 10% 4 NPV S = $4,377 (on extended basis) 12-5 What is real option analysis?  Real options exist when managers can influence the size and riskiness of a project’s cash flows by taking different actions during the project’s life.  Real option analysis incorporates typical NPV budgeting analysis with an analysis for opportunities resulting from managers’ decisions. 12-6 What are some examples of real options?  Investment timing options  Abandonment/shutdown options  Growth/expansion options  Flexibility options 12-7 Illustrating an investment timing option  If we proceed with Project L, its annual cash flows are $33,500, and its NPV is $6,190.  However, if we wait one year, we will find out some additional information regarding output prices and the cash flows from Project L.  If we wait, the up-front cost will remain at $100,000 and there is a 50% chance the subsequent CFs will be $43,500 a year, and a 50% chance the subsequent CFs will be $23,500 a year. 12-8 Investment timing decision tree  At k = 10%, the NPV at t = 1 is:  $37,889, if CF’s are $43,500 per year, or  -$25,508, if CF’s are $23,500 per year, in which case the firm would not proceed with the project. 50% prob. 50% prob. 01234 5 Years -$100,000 43,500 43,500 43,500 43,500 -$100,000 23,500 23,500 23,500 23,500 12-9 Should we wait or proceed?  If we proceed today, NPV = $6,190.  If we wait one year, Expected NPV at t = 1 is 0.5($37,889) + 0.5(0) = $18,944.57, which is worth $18,944.57 / (1.10) = $17,222.34 in today’s dollars (assuming a 10% discount rate).  Therefore, it makes sense to wait. 12-10 Issues to consider with investment timing options  What’s the appropriate discount rate?  Note that increased volatility makes the option to delay more attractive.  If instead, there was a 50% chance the subsequent CFs will be $53,500 a year, and a 50% chance the subsequent CFs will be $13,500 a year, expected NPV next year (if we delay) would be: 0.5($69,588) + 0.5(0) = $34,794 > $18,944.57 [...]... and produce A-T net CFs of $150,000, and a 40% chance it will produce annual A-T net CFs of -$ 25,000 1 2-1 3 Abandonment decision tree 150,000 60% prob -$ 200,000 40% prob 0 150,000 150,000 -2 5,000 -2 5,000 -2 5,000 1 2 3 Years If the customer uses the product, NPV is $173,027.80 If the customer does not use the product, NPV is -$ 262,171.30 E(NPV) = 0.6(173,027.8) + 0.4 (-2 62,171.3) = -1 ,051.84 1 2-1 4 Issues... advantage of changing conditions 1 2-1 1 Abandonment/shutdown option Project Y has an initial, up-front cost of $200,000, at t = 0 The project is expected to produce after-tax net cash flows of $80,000 for the next three years At a 10% discount rate, what is Project Y’s NPV? 0 k = 10% -$ 200,000 1 2 3 80,000 80,000 80,000 NPV = -$ 1,051.84 1 2-1 2 Abandonment option Project Y’s A-T net cash flows depend critically... costs incurred nor cash inflows received after the first year 1 2-1 5 NPV with abandonment option 150,000 60% prob -$ 200,000 40% prob 0 150,000 150,000 2 3 -2 5,000 1 Years If the customer uses the product, NPV is $173,027.80 If the customer does not use the product, NPV is -$ 222,727.27 E(NPV) = 0.6(173,027.8) + 0.4 (-2 22,727.27) = 14,725.77 1 2-1 6 Is it reasonable to assume that the abandonment option does... t = 5, and a 90% chance of an NPV of -$ 1,000,000 at t = 5 1 2-1 8 NPV with the growth option 100,000 10% prob -$ 500,000 90% prob 0 100,000 100,000 100,000 1 100,000 $3,000,000 100,000 100,000 100,000 -$ 1,000,000 100,000 100,000 2 3 4 5 Years At k = 12% , NPV of top branch (10% prob) = $1,562,758.19 NPV of lower branch (90% prob) = -$ 139,522.38 1 2-1 9 NPV with the growth option If it turns out that the project... branch should include only the -$ 500,000 initial outlay and the $100,000 annual cash flows, which lead to an NPV of -$ 139,522.38 Thus, the expected value of this project should be: NPV = 0.1($1,562,758) + 0.9 (-$ 139,522) = $30,706 1 2-2 0 Flexibility options Flexibility options exist when it’s worth spending money today, which enables you to maintain flexibility down the road 1 2-2 1 ... capital 1 2-1 7 Growth option Project Z has an initial up-front cost of $500,000 The project is expected to produce A-T cash inflows of $100,000 at the end of each of the next five years Since the project carries a 12% cost of capital, it clearly has a negative NPV There is a 10% chance the project will lead to subsequent opportunities that have an NPV of $3,000,000 at t = 5, and a 90% chance of an NPV of -$ 1,000,000 . product, NPV is -$ 262,171.30.  E(NPV) = 0.6(173,027.8) + 0.4 (-2 62,171.3) = -1 ,051.84 -$ 200,000 60% prob. 40% prob. 1 2 3 Years 0 150,000 150,000 150,000 -2 5,000 -2 5,000 -2 5,000 1 2-1 5 Issues with. analysis. 1 2-4 -1 00,000 59,000 59,000 59,000 59,000 -1 00,000 -4 1,000 Replacement chain  Use the replacement chain to calculate an extended NPV S to a common life.  Since Project S has a 2-year. 1 2-1 CHAPTER 12 Other Topics in Capital Budgeting  Evaluating projects with unequal lives  Identifying embedded options  Valuing real options in projects 1 2-2 Evaluating projects