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Chapter 8: Strategy and Analysis Using NPV

Chapter 8: Strategy and Analysis Using NPV. Where are the sources of positive NPV Introduction to real options and decisions trees. Introduction to Real Options.

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Chapter 8: Strategy and Analysis Using NPV

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  1. Chapter 8: Strategy and Analysis Using NPV • Where are the sources of positive NPV • Introduction to real options and decisions trees

  2. Introduction to Real Options • Traditional NPV analysis (Chapters 4, 6, and 7) usually does not address the decisions that managers have after a project has been accepted. • In reality, capital budgeting and project management is typically dynamic, rather than static in nature. • 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 and also incorporates opportunities resulting from managers’ decisions.

  3. Real options and decision trees, an example • A new proposed project would cost $500 now (t=0) in order to explore the project’s feasibility. • Next year, it will cost an additional $1500 at t=1 upon final acceptance, and is expected to produce cash flows in years 2 through 6 (from t=2 to t=6). • Our current (t=0) forecast for cash flows CF2 through CF6 is: • 70% probability of $1000 per year • 30% probability of $400 per year • Next year (t=1), we will know cash flows CF2 through CF6 with certainty; they will be either $1000 or $400 per year.

  4. Traditional or static NPV • Calculate the expected cash flows CF2 through CF6 • E(CF) = (0.70)(1000) + (0.30)(400) = $820 per year • A time line of expected cash flows is shown below.

  5. Traditional or static NPV • Now calculate the NPV of the project’s timeline. • This project’s NPV consists of the following items: • $500 spent today • $1500 spent at t=1 • Five expected cash flows of $820 each from t=2 to t=6 (a n=5 year annuity). The PV annuity formula produces a value for t=1, which must be discounted by n=1 years from t=1 to t=0.

  6. Traditional or static NPV • This estimated NPV of $585.884 is incomplete. It assumes the continuation of the project from t=0 to termination at t=6 if the project is accepted today. • All we have is the NPV of expected future cash flows, ignoring the option to abandon the project. • In reality, if $500 is spent today, then next year at t=1, the firm has the option to either spend $1500 to continue, or abandon the project. • The decision at t=1 to continue or abandon depends on whether CF2 to CF6 are then known to be $1000 or $400 per year. If the project is believed to be negative NPV at t=1, then it will be cancelled at that time.

  7. NPV including the option to abandon • When the $1500 expenditure is made at t=1, we know if CF2 through CF6 is either $1000 or $400 per year. • We first calculate the project’s NPV1, for CF1 through CF6 being $1000 per year. We deem this as the success NPV. • From today’s (t=1) perspective, this success NPV has a p=70% chance of occurring.

  8. NPV including the option to abandon • Next we calculate the project’s NPV1, for CF1 through CF6 being $400 per year. We deem this as the failure NPV. • From today’s (t=1) perspective, this failure NPV has a p=30% chance of occurring.

  9. NPV including the option to abandon • What is today’s (t=0) decision, based on this new scenario analysis of next year’s likelihood of p=70% success and p=30% failure? • NPV0 = -500 + (0.7)[success NPV1/(1+r)] + (0.3)[failure NPV1/(1+r)] • We will not go forward next year with negative NPV1, therefore the failure NPV1 is ZERO, as the project will just be cancelled at t=1 if CF2 through CF6 are then known to be $400 per year. • PV0 = -500 + (0.7)[1852/(1+0.15)] + (0.3)[0] = $627.399

  10. NPV including the option to abandon • Note that this dynamic NPV=$627.399 is greater than the earlier static NPV=$585.884. The $41.52 difference is the value of the option to abandon. • A decision tree of the project is shown below.

  11. Second example of incorporating the option to abandon • A project has a k=10% cost of capital. If accepted, the project costs $1100 today at t=0. • Next year, at t=1, we will know whether or not the project is actually a success or failure. Today at t=0, all we know are the probabilities of future success or failure. • Success: probability=50%, and the project will generate cash flows of $180 per year forever (perpetuity) if a success. • Failure: probability=50%, and the project will generate cash flows of $30 per year forever (perpetuity) if a failure. • Project X can be abandoned at t=1 for $500 salvage value. • CFs here are perpetuities. The PV of a perpetuity is always PV=CF/r

  12. Second example, NPV while ignoring the option to abandon • Expected annual CF = (p success)(180) + (p failure)(30) = (0.5)(180) + (0.5)(30) = $105 • The expected cash flow is $105 per year forever. • NPV0 = -1100 + 105/0.1 = -1100 + 1050 = -$50 • If treated as a project that is allowed to continue forever after t=0 acceptance, the expected NPV is negative. • Under this type of analysis (ignoring the abandonment option), the project should be rejected.

  13. Second example • A tree diagram of the project is shown below. There are really two NPVs for this project; one for success and one for failure, each with a probability of 50%. CF = $180/year, forever, PV0 = 180/0.1 = $1800 Success, p=50% Investment costs $1100 today CF = $30/year, forever, PV0 = 30/0.1 = $300 Or abandon at t=1 for $500 Failure, p=50%

  14. Second example • The first timeline shows the project, if successful and, of course, never abandoned. • The second timeline shows the project, if an eventual failure and not abandoned. • The third timeline shows the project, if known to be a failure at t=1 and abandoned at t=1 for $500 (the project’s t=1 cash flow will be earned). t=0 t=1 t=2 CF2 = 180 CF0 = -1100 CF1 = 180 t=0 t=1 t=2 CF2 = 30 CF0 = -1100 CF1 = 30 t=0 t=1 CF0 = -1100 CF1 = 30 + 500 salvage

  15. Second example • NPV0 (if success) = -1100 + 180/0.1 = -1100 + 1800 = $700 • NPV0 (if failure): this issue must be further addressed in detail. Either the project can be continued at t=1 or it can be abandoned and the assets sold for $500 salvage value. • First, calculate the NPV0 if as though the project is continued in operation as a failure with the $30 annual cash flows: • Failure NPV0 = -1100 + 30/0.1 = -1100 + 300 = -$800

  16. Second example • Now investigate abandoning the project at t=1 if we realize it is a failure. At t=1 one cash flow (the only project cash flow since the project is then cancelled) of $30 is received and then the assets are sold for $500. This abandon upon failure NPV0 is thus: • NPV0 = -1100 + 30/(1+0.1) + 500/(1+0.1) = -1100 + 481.18 = -$618.18 if abandoned at t=1. • If a failure at t=1, the abandonment NPV is higher than the NPV if allowed to continue.

  17. Second example • If accepted today, at t=0, there is a 50% chance that the project will be allowed to operate forever, and a 50% chance that it will be abandoned for a $500 salvage value. • Dynamic NPV0 = (0.5)[success NPV0] + (0.5)[failure NPV0] • Dynamic NPV0 = (0.5)[700] + (0.5)[-618.18] = $40.91. • The project should now be accepted since the NPV becomes positive when we allow for project abandonment.

  18. Second example • The NPV0 = –$50 if the project is treated as continuing forever after acceptance. • The NPV0 = $40.91 when we include the decision to abandon at t=1 when the project becomes a failure. • The difference between these two NPVs is called the value of the option to abandon. • Value of option = 40.91 – (–50) = $90.91

  19. Types of Real Options • Investment timing options • Often, the option to delay investment is valuable if market or technology conditions are expected to improve. • Abandonment/shutdown options • Two example were previously shown • Growth/expansion options • May be valuable if the demand turns out to be greater than expected • Flexibility options • Projects may be more valuable if an allowance is made for greater future modifications.

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