Chapter 12 – Strategy and the Analysis of Capital Investments
12-49 (Continued-4)
5. Modified internal rate of return (MIRR):
A summary table for Problem12-49 appears below.
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Chapter 12 – Strategy and the Analysis of Capital Investments
Problem 12-49: Summary Table
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Chapter 12 – Strategy and the Analysis of Capital Investments
12-50 Real Options (50-60 Minutes)
1. “Real Options” are options embedded in capital investment projects. These options
provide an opportunity for management to dynamically adjust to new information and as
such are analogous to financial options. There are two primary differences between
There are, in general, two types of real options: those that provide managerial
flexibility, and those that provide growth options. As noted in the excerpt regarding the
CMA exam, these two general types of options can be further subdivided into the
following categories:
A. Expansion Options (i.e., the opportunity to make follow-on investments of the
original investment goes well)
output, to reduce, but not eliminate, investment in a project)
2. The following two terms are associated with financial options:
A. “Put Option” provides the holder with the ability, but not the requirement, to sell a
given security (e.g., share of stock) at a specified price (called the “exercise price”
or “strike price”) on or before a given date, called the “exercise date”
B. “Call Option” provides the holder with the ability, but not the requirement, to buy a
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Education.
Chapter 12 – Strategy and the Analysis of Capital Investments
12-50 (Continued-1)
3. Part a:
Required Investment Outlay, t = 0, $100
Outcome
(Demand) pYear 1 Year 2 Year 3
NPV of
Outcome
Weighted
NPV
High 0.25 $70 $70 $70 $59.83 $14.96
Medium 0.50 $50 $50 $50 $14.16 $7.08
Part b:
Calculation 1
Calculation 2
4. As seen from Part 3 above, the NPV of the project if demand is “low” for each of the
three years would be negative. In Exhibit 12.10, Panel B, this negative amount
would be discounted back from t = 1 to t = 0. As such, at t = 1 (when the level of
5. In Panel B of Exhibit 12.10, show for each of the three scenarios the calculation for
present value (at t = 0) of cash inflows (cells H20:H22), present value of cash
outflows (cells I20:I22), and weighted net present value (cells J20:J22). What is the
interpretation of the expected NPV of the project (i.e., a positive $12.95 million)?
PV of Cash Inflows, at t = 0:
High: (=NPV(0.15,70,70,70)) ÷ (1 + 0.15) = $138.9789 million
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Education.
Chapter 12 – Strategy and the Analysis of Capital Investments
12-50 (Continued-2)
PV of Cash Outflows, at t = 0:
Low: $ 0 million
Weighted NPV, at t = 0:
High: ($138.9789 million − $95.2381 million) × 0.25 = $10.935 million
Interpretation: If the company delays the decision to invest (i.e., to time period 1 versus
time period 0), the NPV of the project, at t = 0, is expected to be $12.951 million.
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Education.
Chapter 12 – Strategy and the Analysis of Capital Investments
12-51 Real Options and Sensitivity Analysis (60 Minutes)
ORIGINAL ASSUMPTIONS:
WACC =0.15
Risk-Free Rate =0.05
Scenario pYear 1 Year 2 Year 3 Year 4
@ t = 0
PV of
Outflows
@ t = 0
PV of
Inflows
Weighted
NPV (@ t =0)
High
0.2
5
($100.00
) $70 $70 $70
($95.2381
)
$138.978
9 $10.935
Medium
0.5
0
($100.00
) $50 $50 $50
($95.2381
) $99.2707 $2.016
0.2
RE
1. DEMAND PROBABILITIES: 20%, 50%, 30%
Scenario pYear 1 Year 2 Year 3 Year 4
@ t = 0
PV of
Outflows
@ t = 0
PV of
Inflows
Weighted NPV
(@ t =0)
High 0.20 ($100.00) $70 $70 $70 ($95.24) $138.98 $8.748
Expected NPV = $10.764
Sample calculations:
1. ($95.2381) = ($100.00) ÷ (1 + 0.05)
Chapter 12 – Strategy and the Analysis of Capital Investments
12-51 (Continued-1)
2. Demand Probabilities: 30%, 40%, 30%
WACC =0.15
Risk-free rate = 0.05
Scenario pYear 1 Year 2 Year 3 Year 4
@ t = 0
PV of
Outflows
@ t = 0
PV of
Inflows
Estimated
NPV (@ t =0)
High 0.30 ($100.00) $70 $70 $70 ($95.2381) $138.9789 $13.122
Sample calculations:
1. ($95.2381) = ($100.00) ÷ (1 + 0.05)
3. Sensitivity Analysis: Assumptions Regarding Discount Rates
@ t = 0 @ t = 0 Weighted
Cash Flows PV of PV of NPV @
Scenario pYear 1 Year 2 Year 3 Year 4 Outflows Inflows t =0)
High 0.25 ($100.00) $70 $70 $70 ($95.2381) $138.9789 $10.935
Medium 0.50 ($100.00) $50 $50 $50 ($95.2381) $99.2707 $2.016
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Chapter 12 – Strategy and the Analysis of Capital Investments
12-51 (Continued-2)
PV of Outflows PV of Inflows
Expecte
d
Risk-Free Rate WACC High Medium High Medium NPV
5% 13% ($95.24) ($95.24) $146.27 $104.48 $17.38
5% 14% ($95.24) ($95.24) $142.56 $101.83 $15.12
5% 15% ($95.24) ($95.24) $138.98 $99.27 $12.95
5% 16% ($95.24) ($95.24) $135.53 $96.81 $10.86
5% 17% ($95.24) ($95.24) $132.20 $94.43 $8.83
Sample Calculations:
1. $16.69 = [($146.27 − $96.15) × 0.25] + [($104.48 − $96.15) × 0.50] + [$0 × 0.25]
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Chapter 12 – Strategy and the Analysis of Capital Investments
Chapter 12 – Strategy and the Analysis of Capital Investments
12-51 (Continued-3)
Sensitivity Analysis Summary: Estimated NPVs at Time t = 0
Risk-Free Rate
WACC 4% 5% 6%
13% $16.69 $17.38 $18.05
14% $14.44 $15.12 $15.80
15% $12.26 $12.95 $13.63
On the basis of the above summary results, we can conclude that the decision to delay
the project one year (to gain better information regarding the level of consumer
demand) is relatively insensitive to assumptions regarding the discounting rates—both
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