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Your company is considering an expansion of a current product that will operate for 5 years (with...

Question:

Your company is considering an expansion of a current product that will operate for 5 years (with the option to renew the project). There is concern among management that the economy will go into a recession next year, which will cause at least 2 or 3 years of low sales of the product. To help evaluate this project, you have put together the following estimates:

Time 0: An initial investment of $10 million in preparing for expansion
Time 1: A choice to spend $100 million on new equipment (depending on the economy). If the project is implemented in Time 1, the expected cash flows received in years 2-6 are $20 million each year
Time 6: A choice to extend the project if it has been more successful than expected. If the project is extended, the discounted value (as of time 6) of the project is $50 million The probability of a recession is 30% and the probability of extension in time 6 is 20%. The decision tree diagram is as follows:

Time 0 Time 1Time 2-6 Time 6
/.2 probability 50M
/.7 probability -100M20M
-10M \.8 probability 0
\.3 probability 0

If the annuity factor for 5 years at 8% is 3.9927, set up an equation to find the NPV.

Decision tree:

A decision tree is the tree-shaped pictorial format to understand the uncertainty of a business problem and related outcomes. The branches of the tree are different possible outcomes with different scenarios, generally attached with an estimated probability. The net outcome of a project or business decision can be assessed using the decision tree from the expected probable outcomes.

Answer and Explanation:

NPV at year 6 {eq}= 80\%*0+20\%*$50 ...............(1) {/eq}

PV of regular cash flows (time 2-6) at the end of year 1{eq}= 20*PVIFA( 8\%, 5 ~years) = $20*3.9927 = 79.854M {/eq}

NPV at year 1 (if success) {eq}= $79.854M - $100M + (80\%*0+20\%*$50M)(1+8\%)^{-5} ............(2) {/eq}

NPV at year 0 {eq}= (2)*70\%/(1+8\%) + 30\%*0 - $10M {/eq}

{eq}= [$79.854M - $100M + (80\%*0+20\%*$50M)(1+8\%)^{-5} ] *(1+8\%)^{-1} -$10M ..............(3) {/eq}

We found equation (3) is the required equation for finding the value of NPV

By solving the equation (3) we found, NPV = -$22.35M


Learn more about this topic:

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What Is a Decision Tree? - Examples, Advantages & Role in Management

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Chapter 2 / Lesson 12
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Clearly identifying all possible solutions for a given decision is an important part of successful management. In this lesson, you will learn how to use a decision tree to identify and select possible courses of action.


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