Practice Problems – Chapter 10

1)    A five year project requires a capital investment of $6,000,000.   The project department has generated the following estimates for the first year of the project.

Depreciation will be $1,815,000 the first year, $1,375,000 the second year, $1,100,000 the third year, $880,000 the fourth year and $330,000 the last year.  Revenue and variable cost will increase by 30% in the second year, 20% in the third year and 15% each in the last two years.  Fixed costs will increase by 5% each year.  The working capital required for each year will be 10% of that year's revenue.  The fixed assets will be sold at the end of the project; the expected salvage value is $1,200,000. The company's tax rate is 35%, and the required return for the project is 12%.

a) Set up a spreadsheet to compute the project's expected cashflows each year.

b) Compute the project's expected NPV.

c) Perform a sensitivity analysis, and report the results in a table.  Which are the key variables you would consider re-estimating?

2)    Time Will Tell Inc. is evaluating whether it should invest in a new plant that will cost $395,000.  After investing today, demand for the product will be known at time 1.  With a probability of 0.5 demand will be high and the plant will generate cashflows of $55,000 per year forever, starting at time 2.  With a probability of 0.5 demand will be low and the plant will generate cashflows of $20,000 per year forever, starting at time 2.   If demand turns out to be high, the plant can be sold at time 1 for $475,000.  If demand turns out to be low, the plant can be sold at time 1 for $350,000.  

a) If the required return is 10%, what is the NPV of the project?

b) For a cost of $25,000 the firm can determine for sure at time 0 whether demand will be high or low.  Is it worth buying this information?

c) What is the value of the information?

3)    A farmer is deciding whether to drill a well for water.  He currently buys water at a cost of $3,750 per year.  It will cost $15,000 to drill up to 150’.  The probability of striking water at 150’ is 0.65.  If he doesn’t strike water at 150’, it will cost an additional $7,000 to drill to 200’.  If there’s no water at 150’ the probability he will find it at 200’ is only 0.3. If water is found, the operating/maintenance costs for the well will be $1,125 per year.  

a) If the discount rate is 10%, should he drill the well or not?

b) The drilling contractor informs him that before they start to drill the well, a small test well can be drilled for $6,000 to find out for sure if there is water at 150'.  Should they do so? 

c) What is the maximum amount the farmer should be prepared to pay for drilling the test well?

4)   At time 0, the Asimov Robot Corp. must decide whether to invest in a R&D project to develop surgical robots, which requires an initial investment of $1,250,000.  At time 1, preliminary progress results will be available.  With a probability of 0.7, a working prototype will result.  If a working prototype does not result at time 1, ARC will can either abandon the project or invest an additional $500,000 to develop the prototype.  If this additional investment is made, there is a probability of .2 that a working prototype will result at time 2.  If it doesn't, ARC will abandon this project.

      Whenever a working prototype is developed, the company will rush into production by immediately investing $10,000,000.  The investment will generate constant cashflows forever, starting from the following year.  With a probability of 0.6, demand for the robot will turn out to be high and cashflows will be $1,500,000 a year.   With a probability of 0.4, demand will be low and cashflows will be $800,000 a year. 

      The required return is 10%.  If the project is abandoned at any time, the R&D expenses incurred till then are sunk costs that will not be recovered.

a) Should ARC invest in the R&D project today?

b) Now assume that if a working prototype does not result at time 1, the company can spend $175,000 to find out for certain whether the additional investment (of $500,000) will produce a working prototype at time 2.  How does the availability of this information affect the NPV of the project?

5)    The Sub-Atomic Yo-Yo Corporation faces potential competition from a new Japanese firm that is trying to develop radically new technology for the firm's main product.  If they are successful in developing their technology, the cashflows from SAYY's operations will be adversely affected.  SAYY has come up with the following forecasts:

a) Should SAYY liquidate today or stay in business?

b) For a payment of $5,000,000, the internationally renowned consulting firm of Miss Cleo can tell SAYY for sure today whether the Japanese firm's development efforts will succeed or not.  What is the NPV to SAYY of buying this information?

6) At time 0, the North Career Corp. must decide whether to invest $6,666,666 in a R&D project to develop nuclear powered bicycles.  If the investment is made today, there is a 0.4 probability that NCC will be ready to start production at time 1, and a 0.6 probability that they will find defects in their containment shield technology.  If this happens, they can either abandon the project or make an additional investment of $4,000,000 at time 1 to try and solve the problems.  With a probability of 0.25, the containment shield problems will get solved, and NCC will be ready to start production at time 2.  With a probability of 0.75, the containment shield problems will turn out to be insurmountable, and NCC will have to abandon the project at time 2.  If the project is abandoned at any time, none of the R&D expenses will be recoverable.

Whenever NCC starts production of their nuclear powered bicycles, the initial investment required will be $125,000,000.  Cashflows will start from the following year.  The first cashflow is expected to be $10,000,000 and the cashflows are expected to grow at 6% forever.  The required return is 13%. 

a) What is the NPV of the R&D project today?  Should NCC invest in it?

b) Now assume that if the containment shield technology is found to be defective at time 1, they can spend $2,500,000 to find out for certain whether the additional investment of $4,000,000 will solve the problem.  How does the availability of this information affect the NPV of the project?  

7) Mark the following statements with a T or a F to indicate whether they are true or false (no explanations required):

a)    When we perform a sensitivity analysis, we compute three different versions of the NPV: pessimistic NPV (where all variables are set to their pessimistic value), expected NPV (where all variables are set to their expected value), and optimistic NPV (where all variables are set to their optimistic value).

b)    Sensitivity analysis considers the impact of different variables on the NPV estimate, taking each variable one at a time.

c)    A decision tree typically involves an alternating sequence of decisions you make followed by learning the random outcome of those decisions followed by future decisions, etc. 

d)    If the NPV of a project without information is $3,000 and information is available at a cost of $5,000 we will not consider buying the information, since the NPV of the project after buying the information would be negative.

e)    Decision trees provide a simple way to take the value of real options into account when computing a project's NPV, but it yields only an approximate estimate of the NPV.

f)    When a project has real options, the options may either increase or decrease the NPV of the project.

g)    A decision tree problem always has to be solved backwards, starting with the last decision to be made.

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