The Blazingame Corporation is considering a three-year project that has an initi
ID: 2683061 • Letter: T
Question
The Blazingame Corporation is considering a three-year project that has an initial cash outflow (C0) of $175,000 and three cash inflows that are defined by the independent probability distributions shown below. All dollar figures are in thousands. Blazingame's cost of capital is 10%. C1 C2 C3 Probability $50 $40 $75 .25 $60 $80 $80 .50 $70 $120 $85 .25 a. Estimate the project's most likely NPV by using a point estimate of each cash flow. What is its probability? b. What are the best and worst possible NPVs? What are their probabilities? c. Choose a few outcomes at random, calculate their NPVs and the associated probabilities, and sketch the probability distribution of the project's NPV. [Hint: The project has 27 possible cash flow patterns (3?3?3) each of which is obtained by selecting one cash flow from each column and combining with the initial outflow. The probability of any pattern is the product of the probabilities of its three uncertain cash flows. For example, a particular pattern might be as follows. C0 C1 C2 C3 CI ($175) $50 $120 $80 Probability 1.0 .25 .25 .50 The probability of this pattern would be .25 ? .25 ? .50 = .03125.]Explanation / Answer
Although the problem asks for only a few outcomes, we'll list them all and identify the best, worst, and most likely. First restate the matrix of outcomes by multiplying each Ci by PVF10,i and rounding to the nearest $1,000:
C1 C2 C3 Probability
$45 $33 $56 .25
$55 $66 $60 .50
$64 $99 $64 .25
Next enumerate the possible cash flows and calculate their probabilities.
($000)
C0 C1 C2 C3 NPV Probability
-175 45 33 56 -41 .25×.25´.25 = .015625
Worst 60 -37 .25´.25´.50 = .031250
64 -33 .25´.25´.25 = .015625
-175 45 66 56 -8 .25´.50´.25 = .031250
60 -4 .25´.50´.50 = .062500
64 0 .25´.50´.25 = .031250
-175 45 99 56 25 .25´.25´.25 = .015625
60 29 .25´.25´.50 = .031250
64 33 .25´.25´.25 = .015625
-175 55 33 56 -31 .50´.25´.25 = .031250
60 -27 .50´.25´.50 = .062500
64 -23 .50´.25´.25 = .031250
-175 55 66 56 2 .50´.50´.25 = .062500
Most likely 60 6 .50´.50´.50 = .125000
64 10 .50´.50´.25 = .062500
-175 55 99 56 35 .50´.25´.25 = .031250
60 39 .50´.25´.50 = .062500
64 43 .50´.25´.25 = .031250
-175 64 33 56 -22 .25´.25´.25 = .015625
60 -18 .25´.25´.50 = .031250
64 -14 .25´.25´.25 = .015625
-175 64 66 56 11 .25´.50´.25 = .031250
60 15 .25´.50´.50 = .062500
64 19 .25´.50´.25 = .031250
-175 64 99 56 44 .25´.25´.25 = .015625
60 48 .25´.25´.50 = .031250
Best 64 52 .25´.25´.25 = .015625
1.000000
Finally, sorting the outcomes and grouping within NPV ranges yields the following probability distribution.
NPV Range ($000) Probability
NPV < -$40 .015625
-$40 < NPV < -$30 .078125
-$30 < NPV < -$20 .109375
-$20 < NPV < -$10 .046875
-$10 < NPV < $00 .125000
-$00 < NPV < $10 .250000
$10 < NPV < $20 .125000
$20 < NPV < $30 .046875
$30 < NPV < $40 .109375
$40 < NPV < $50 .078125
NPV > $50 .015625
1.000000
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