End of Chapter Exercises: Solutions



End of Chapter Exercises: Solutions

Chapter 9

1. The following table describes the projected costs and net benefits for two projects.

(All values in $ millions)

| |PROJECT A |PROJECT B |

| |Pessimistic |Best Guess |Optimistic |Pessimistic |Best Guess |Optimistic |

|Year 0 |-80 |-75 |-70 |-100 |-75 |-50 |

|Year 1 |-110 |-100 |-90 |-150 |-100 |-50 |

|Year 2 |18 |20 |22 |12 |20 |28 |

|Year 3 |28 |30 |32 |20 |30 |40 |

|Year 4 |28 |30 |32 |25 |45 |65 |

|Year 5 |40 |45 |50 |25 |45 |65 |

|Year 6 |40 |45 |50 |25 |45 |65 |

|Year 7 |40 |45 |50 |25 |45 |65 |

|Year 8 |40 |45 |50 |25 |45 |65 |

|Year 9 |40 |45 |50 |25 |45 |65 |

|Year 10 |55 |65 |75 |35 |65 |95 |

a) Using the NPV decision rule and assuming a 10% discount rate, which of the two projects would you prefer using the “best guess” estimate of cash flow?

b) Using the available range of estimates apply an @RISK simulation with a triangular distribution (1000 iterations) to derive the following:

i) the mean, minimum, and maximum NPVs for each project;

ii) a graph of the probability distribution of NPVs for each project

iii) a graph of the cumulative (ascending) distribution of NPVs for each project.

c) Which project would a risk-averse decision-maker favour, and why? (Assume a 90% confidence level.)

d) Which project would a risk-taking decision-maker favour, and why? (Assume a 20% confidence level.)

e) Would your answers to questions (a), (c) and (d) be any different if the discount rate was set at: (i) 5%; and (ii) 15%?

Answer:

(a) NPV(A) = $27.51; NPV(B) = $37.76. Therefore select B.

(b) (i)

|Output |Statistics |

|Name |Minimum |Mean |Maximum |

|NPV (A)= |$11.88 |$27.51 |$43.00 |

|NPV (B)= |-$22.29 |$37.76 |$111.80 |

(ii)

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(c) The risk averter will choose A (at 90% confidence NPV(A) = $21.3 and NPV (B) = $5.97.

(d) The risk taker will prefer B (at 20% confidence NPV(B) = $58.34 and NPV(A) = $31.65)

(e) At a 5% discount rate B is still preferred to A; at 15% neither project has a positive NPV but project B is less negative than A. Changing the discount rate will not affect the comparative variance of the results from the risk analysis.

2. Nicole leads an exciting life. Her wealth is a risky prospect which will take the value $100 with probability 0.5, or $36 with probability 0.5. Her utility of wealth function is: U = W0.5.

a) What is the expected value of her wealth?

b) What is the expected utility of her wealth?

c) What level of wealth with certainty will give her the same utility as the risky prospect?

d) What is the cost of the risk associated with the risky prospect?

Answer:

(a)$68

(b)8 utils

(c)$64

(d)$4

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