Sources of Positive Net Present Value

1
Sources of Positive Net Present Value

• Sources of Net Present Value Investment
  projects
• ?Analyst must recognize that the adoption of an
  investment project generates future investment
  opportunities that often are quite valuable
• ?Generating of new information
• ?Generating important new relationships

• Sources of Competitive Advantage
• ?Barriers to entry (patents)
• ?Economies of Scale (under proportional costs)
• ?Economies of Scope (Complementary production)

• Economies of Scope, Discounted Cash Flow, and
  Options

• Option Pricing Theory as a Tool for Quantifying
  Economies of Scope

2
Sources of Positive Net Present Value

• Economies of Scope, Discounted Cash Flow, and
  Options
• ?Economies of Scope seem to be the most important
  source for competitive advantage!
• ?Must be attributed to earlier investments
• ?The DCF methodology may be biased against
  long-term projects (aspects of long-term projects
  may not easily be quantified)!
• ?Derivatives Valuation methodology may at least
  provide rule of thumb about when subsequent
  opportunities are likely to significantly enhance
  a projects value

• Option Pricing Theory as a Tool for Quantifying
  Economies of Scope
• ? Subsequent investment opportunities will only
  be pursued if they prove to be valuable gt Option
  like components!

3
Valuing Strategic Options with Derivatives
Valuation Methodology

• Valuing a Mine with No Strategic Options

• Valuing a Mine with an Abandonment Option

• Valuing Vacant Land

• Valuing the Option to Delay the Start of a
  Manufacturing Project

• Valuing the Option to Expand Capacity

• Valuing Flexibility in Production Technology
  The Advantage of Being Different

4
Valuing a Mine with No Strategic Options
The date 1 and date 2 cash flows from the mine,
C1 and C2, respectively can be expressed as
Where p1is the date 1 copper price, p2 is the
date 2 copper price, Q1is the date 1 copper
quantity, Q2 is the date 2 copper quantity, K1is
the date 1 cost of extraction, K2 is the date 2
cost of extraction. p1 and p2 are assumed unknown
at decision time, date 0.
We apply the forward prices from forward
contracts maturing at date 1 and 2 to value the
copper mine. Note the following fact

• CF from operating the mine is p1Q1 K1 and
  p2Q2 K2, which is exactly the same as the
  future CF incurred by holding the following
  tracking portfolio
• A forward contract to purchase Q1 units of copper
  at date 1 at the current forward price of F1 per
  unit, and a second forward contract to purchase
  Q2 units of copper at date 2 at the current
  forward price of F2 per unit.
• A risk free zero-coupon bond paying F1Q1 K1 in
  year 1 and second bond paying F2Q2 K2 in year
  2.

5
Valuing a Mine with No Strategic Options
Since F1 and F2 represent current forward prices,
the forward contracts under 1) costs nothing. He
value of the mine therefore becomes
where rt is the yield to maturity of zero-coupon
bonds maturing at date t, and FtQt-Kt is the
future payment of the zero-coupon bond maturing
at date t.
Example X company will produce 75000 pounds of
copper 25000 at date 1 and 50000 at date 2.
Extraction costs are 0.10 per pound. Forward
prices F1 0.65 and F2 0.60. Risk-free rates
are 5 for one-year zero coupon bonds and 6 for
two-year zero coupon bonds. Present value?
6
Cash Flows of Forward Contracts to Exchange Qt
Units of Copper for Cash at Future Date t
7
Cash Flows of Copper Mine versus Portfolio of
Forward Contracts and Zero-Coupon Bonds
8
Valuing a Mine with an Abandonment Option

• Copper mine owners close down their mines when
  the price of copper becomes too low to make
  mining profitable and speed up production when
  copper prices recover to the point where mining
  is profitable
• ? A strategic option which enhances the value of
  the mine!
• ? Valuation by the Brennan Schwartz (1985)
  method, which can be approximated with the
  binomial approach.

Example X company will produce 75000000 pounds
of copper one year from now if economic
conditions are favourable. Two forecasts of
prices 0.50 if demand is low and 0.90 if demand
is high. The year 1 forward price is currently
0.60 per pound, implying that a forward contract
has a negative future cash flow of 0.10 per pound
if demand is low, and 0.30 if demand is high.
The risk free rate of interest is 5.Extraction
costs are 0.80. Present value?
Scenario 1 Copper mine closed down value zero
Scenario 2 Copper mine profitable CF is
750000075000000(0.90-0.80)
Simultaneous solving the equations x18750000
pounds received from a one-year forward contract
and y1785714 invested in zero-coupon bonds.?
Value 1785714.
9
Payoffs of a Copper Mine with a Shutdown Option
10
Valuing a Mine with an Abandonment Option
A Copper mine can be viewed as an option to
extract (or purchase) minerals at a strike price
equal to the cost of extraction. Like a stock
option, the option to extract the minerals has a
value that are increasing with both the
volatility of the mineral price and the
volatility of the extraction cost.
11
Valuing Vacant Land
Valuing Vacant Land (example) Six units
construction costs are 80000 per unit Nine
units construction costs are 90000 per
unit Market price is 100000. Rental income is
8000 per unit annually. Risk free interest rate
is 12. Sale good year 120000. Sale Bad year
90000
Vacant land can be viewed as an option to
purchase developed land where the exercise price
is the cost of developing a building on the land.
Like a stock option, this more complicated type
of option has a value that is increasing in the
degree of uncertainty about the land (and type)
of development.
12
Binomial Trees for Land Valuation
13
Valuing the Option to Expand Capacity

• The flexibility in the design of investment
  project.
• An option, and each option available enhances
  the projects value

Scaling down or scaling up the capacity of a
projects an example of option like investment
characteristics. Hence, the value of the option
to be flexible must be compared with the cost of
acquiring the flexibility. For valuation we apply
the binomial approach!
Example Global is considering building a plant
with a value in two years described in a figure
G1 below. The CF from the plant will be 200
million following two good years (D), 150 million
following one good and one bad year (E) and 100
million following two bad years (F). Initial
investment is 140 million (A). After one year,
Global, if the state of economy is good, the firm
has the option to double the pants capacity by
investing another 140 million. Figure G2
illustrate the situation. The risk free rate of
interest is 5. Furthermore, assume that 1
invested in the market portfolio today yields
future values as described in figure G3.
14
Cash Flows if There is No Capacity Change at Year
1 (G1)
15
Cash Flows if Plant Capacity Is Doubled at Good
Node in Year 1 (G2)
16
Market Portfolio Payoffs for Determining Risk
Neutral probabilities (G3)
17
Valuing the Option to Expand Capacity
Two scenarios 1. The option to expand is
ignored. 2. The option to expand is not ignored.
Scenario 1 At point B
Scenario 1 At point C
Scenario 1 At point A
Yields a Net Present Value of 133.30mill
140mill -6.67mill
18
Valuing the Option to Expand Capacity
Scenario 2 At point B
The 140mill in this state represent the
investment for doubling capacity!
Scenario 2 At point C
Scenario 2 At point A
Yields a Net Present Value of 146.71mill
140mill 6.71mill
Unless Global builds the factory at year 0, it
can never take advantage of the option to
increase capacity. The example show that the
flexibility the investment (option) enhances turn
an apparent negative NPV into a positive NPV
(approx. 13 mill.)
19
Valuing the Option to Expand Capacity (BS
Formula)
Example Global has six cutting machines for
fish. They are considering replacing each of the
old machines with new machines that cost 1000.
The new machines have a five-year life. The
anticipated cash flows for the new machines are
Cost of Capital 12 (Risk adjusted). The NPV
suggest that the project is unprofitable as shown
below.
The option twist (real options) The line manager
in charge of the cutting machines says I want to
try one of the machines for one year! At the end
of the year if the experiment is successful, I
want to replace the five other machines with new
ones.
20
Valuing the Option to Expand Capacity (BS
Formula)

• What we have is a package
• Replacing a single machine to day. The move has a
  negative NPV of 67.48.
• The Option to replace five more machines in one
  year from now. Suppose that the risk free rate is
  6. We view each such option as a call option on
  an asset that have the following current value

Which has an exercise price X 1000. Moreover,
these call options can be exercised only if we
purchase the first machine now! Apply Black and
Scholes formula!!
21
Valuing the Option to Expand Capacity (BS
FormulaExcel)
22
Valuing the Option to Expand Capacity (BS
FormulaExcel)
23
Valuing the Abandonment Option (Binomial Excel)
24
Valuing the Abandonment Option (Binomial Excel)
Abandonment option is active That is, we abandon
the project when the cash flow threatens to
become 50.
25
Exercise (Real Option)
Your Company is consider purchasing 10 new
machines, each of which has the following
expected cash flows and initial investment

• You estimate the appropriate cost of capital for
  the machines as 25.
• Would you recommend buying just one machine, if
  there are no options effects?
• Your purchase manager recommends buying one
  machine to day and then-after seeing how the
  machines operates-reconsidering the purchase of
  the other nine machines in six months. Assuming
  that the cash flow from the machines have a
  standard deviation of 30 and that the risk free
  rate is 10, value the strategy!

26
Exercise (Real Option)
Consider a project whose cash flows are as
follows
169
130
100
91
91
70
-90

• Using the state prices, value the project.
• Suppose that at date 2 the project can be
  abandoned at no cost. What does this fact do to
  its value?
• Suppose that at any time the project can be sold
  for 100. Show the tree of cash flows and value
  the project.