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**Chapter 8: Strategy and Analysis Using NPV**

Where are the sources of positive NPV Introduction to real options and decisions trees

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**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.

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**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.

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**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.

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**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.

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**Traditional or static NPV**

This estimated NPV of $ 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.

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**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.

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**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.

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**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 = (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 = (0.7)[1852/(1+0.15)] + (0.3)[0] = $

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**NPV including the option to abandon**

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

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**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

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**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 = /0.1 = = -$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.

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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 Failure, p=50% CF = $30/year, forever, PV0 = 30/0.1 = $300 Or abandon at t=1 for $500

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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 CF0 = -1100 CF1 = 180 CF2 = 180 t=0 t=1 t=2 CF0 = -1100 CF1 = 30 CF2 = 30 t=0 t=1 CF0 = -1100 CF1 = 30 + 500 salvage

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Second example NPV0 (if success) = /0.1 = = $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 = /0.1 = = -$800

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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 $500. This abandon upon failure NPV0 is thus: NPV0 = /(1+0.1) + 500/(1+0.1) = = -$ if abandoned at t=1. If a failure at t=1, the abandonment NPV is higher than the NPV if allowed to continue.

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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)[ ] = $40.91. The project should now be accepted since the NPV becomes positive when we allow for project abandonment.

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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 = – (–50) = $90.91

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**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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