Required: 1. Holding everything else constant, what is the expected NPV of the decision if the probabilities for the three scenarios are as follows: high (20%), medium (47%), and low (33%)? 2. Holding everything else constant, what is the expected NPV of the decision if the probabilities for the three scenarios are as follows: high (24%), medium (43%), and low (33%)? 3. Prepare a 5 × 3 table containing the estimated NPV of the decision to delay for each combination of the following: risk-free rate of interest (7%, 8%, 9%) and weighted-average cost of capital (10%, 11%, 12%, 13%, and 14%). For example, one cell in your table would be the estimated NPV of the project if the risk-free rate of interest is 7% and the weighted-average cost of capital is 10%.
Refer to the XYZ Company example in the chapter and the results in Panels A and B of Exhibit 12.7. On the basis of this information, management of the company has decided to delay the implementation of the project for 1 year. Those managers are now interested in knowing how sensitive this decision is with respect to the assumptions they’ve made regarding the basic analysis. Therefore, they have asked you to prepare some supplementary analyses regarding Panel B of Exhibit 12.7.
Required:
1. Holding everything else constant, what is the expected
2. Holding everything else constant, what is the expected NPV of the decision if the probabilities for the three scenarios are as follows: high (24%), medium (43%), and low (33%)?
3. Prepare a 5 × 3 table containing the estimated NPV of the decision to delay for each combination of the following: risk-free rate of interest (7%, 8%, 9%) and weighted-average cost of capital (10%, 11%, 12%, 13%, and 14%). For example, one cell in your table would be the estimated NPV of the project if the risk-free rate of interest is 7% and the weighted-average cost of capital is 10%.
 alt="EXHIBIT 12.7
Decision Trees: Real-Options Analysis (Investment-Timing Option)
A
C
H
1 Panel A: Expected NPV--Invest in Project Today (time 0); amounts in $ millions
3 Discount rate (WACC) =
15.00%
5
Cash Outflow
Market Demand
End-of-Period Cash Inflows
NPV of Weighted
6.
@ time 0
(Scenario)
Probability
1
$70
2
$70
3
$70
Scenario
NPV
$14.956
7
High
0.25
$59.826
8.
$100
Medium
0.50
$50
$50
$50
$14.161
$7.081
Low
0.25
$5
$5
$5
($88.584)
($22.146)
10
1.00
Expected NPV =
($0.109)
11
12 Panel B: Expected NPV--Delay Investment by One Year, Only if NPV is increased, amounts in $ millions
13
14 Discount rate (WACC)=
15.00%
15 Risk-free rate =
5.00%
16 Cash outflow one year from the presenet (?) =
$100
17
End-of-Period Cash Flows
PV of Cash PV of Cash
Outflows Inflows** NPV @ time 0***
($95.24)
($95.24)
18
Market Demand
Weighted
(Scenario)
High
Probability
3
$70
19
2
$70
4
$70
$10.94
($100)
($100)
$0
20
0.25
$138.979
21
Medium
0.50
$50
$50
$50
$99.271
$2.016
22
Low
0.25
$0
$0
$0
$0.00
$0.000
$0.000
23
1.00
Expected NPV =
$12.951
24
*discounted at risk-free rate of interest
25
**discounted at WACC (weighted-average cost of capital); formula for cell 120: =PV(B14,1,(PV(B14,3,E20)))
***formula for cell J20: =C20* (120+H20)
26
27
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