18.31 (a) The subscripts identify the series by probability.
PW0.5 = –5000 + 1000(P/A,20%,3)
= –5000 + 1000(2.1065)
= $–2894
18.32 Certificate of Deposit
Stocks
Stock 1: – 6000 + 250(P/A,i*,4) + 6800(P/F,i*,5) = 0
Stock 2: –6000 + 600(P/A,i*,4) + 4000(P/F,i*,5) = 0
Real Estate
Prob. = 0.3
Prob. 0.5
Prob. 0.2
Decision Trees
18.33 Compute the expected value for each outcome and select the maximum at D3.
18.34 Maximize the value at each decision node
D1: Top: 0.9(D3 value) + 0.1(final value)
D2: Top: E(value) = 0.3(150 – 30) + 0.4(75) = $66
Middle: E(value) = 0.5(200 – 100) = $50
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Conclusion: Select D2 path and choose top branch ($25 investment)
18.35 Calculate the E(PW) in year 3 and select the largest expected value. In $1000 units,
18.36 (a) Select the minimum E(cost) alternative. Monetary values are in $1000 units
Make: E(plant cost) = 0.3(-250) + 0.5(-400) + 0.2(-350)
290)
Use Goal Seek to set the function = $–312.5 and change cell A2. Display is 0.0088.
New probabilities are:
18.37 (a) Construct the decision tree
(b) At D2, compute PW of cash flows and E(PW) using probability values.
Expansion option
No expansion option
Conclusion at D2: Select no expansion option
(c) Complete rollback to D1 considering 3 year cash flow estimates.
Produce option, D1
Buy option, D1
E(PW for buy) = cost + E(PW of sales cash flows)
Conclusion: E(PW for produce) is larger than E(PW for buy); select
produce option.
Note: Both returns are less than 15%, but the return is larger for
produce option.
(d) The return on the initial investment would increase, but it would increase faster
for the produce option.
Real Options
18.38 In $ billion units,
18.39 In $ million units,
Conclusion: Company should implement the pilot option and delay the full-scale
decision for 1 year
PW1 year = -100,000 – 1,900,000(P/F,15%,1) + 1,000,000(0.70)(P/A,15%,5)(P/F,15%,1)
Clearly, Dupont should purchase the license now
18.41 (a) Find E(PW) after determining E(Rt), the expected repair costs for each year t
Without considering noneconomic factors, the warranty is worth an expected $2045, or
$455 less than the $2500 extended warranty cost.
Additional Problems and FE Exam Review Questions
18.42 Answer is (c)
18.47 Answer is (b)
Solution to Case Study 1, Chapter 18
Sometimes, there is not a definitive answer to a case study exercise. Here are example responses.
SENSITIVITY TO THE ECONOMIC ENVIRONMENT
1. Spreadsheet analysis used for changes in MARR. PW is not very sensitive; plan A is
selected for all three MARR values.
2. Sensitivity to changes in life is performed by hand. Not very sensitive; plan A has the best
PW for all life estimates.
Expanding economy
PWB = –30,000 + 5000(P/F,10%,32) – 100(P/A,10%,32) – 5000
Expected economy
PWA = –10,000 + 1000(P/F,10%,40) – 500(P/A,10%,40)
Receding economy
PWA = –10,000 + 1000(P/F,10%,44) – 500(P/A,10%,44)
PWB = –30,000 + 5000(P/F,10%,44) – 100(P/A,10%,44) – 5000
3. Use Goal Seek to find breakeven values of PA for the three MARR values of 4%, 7%, and
10% per year. For MARR = 4%, the Goal Seek screen is below. Breakeven values are:
MARR, % Breakeven PA, $
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of McGraw–Hill Education.
23
Solution to Case Study 2, Chapter 18
Sometimes, there is not a definitive answer to a case study exercise. Here are example responses.
SENSITIVITY ANALYSIS OF PUBLIC SECTOR PROJECTS —
WATER SUPPLY PLANS
1. Let x = weighting per factor
Since there are 6 factors and one (environmental considerations) is to have a weighting that is
double the others, its weighting is 2x. Thus,
Therefore, the environmental weighting is 2(14.3), or 28.6%
2.
Alt Ability to Relative Engineering Institutional Environmental Lead–Time
ID Supply Area Cost Feasibility Issues Considerations Requirement Total
The top three are the same as before: 1A, 3, and 4
3. For alternative 4 to be as economically attractive as alternative 3, its total annual cost would
have to be the same as that of alternative 3, which is $3,881,879. Thus, if P4 is the capital
investment,
4. Household cost at 100% = 3,952,959(1/12)(1/4980)(1/1)
5. (a) Sensitivity analysis of M&O and number of households.
Alternative
Estimate
M&O,
$/year
Number of
households
Total
annual
cost, $/year
Household
cost,
$/month
Pessimistic
4980
3,925,235
69.40
Pessimistic
1,071,023
4980
3,963,563
69.82