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LECTURE 4
Investment under uncertainty, real options


Derivatives valuation approach. Example:
 Copper mine



Strategic options. Examples:
 Copper mine with shutdown option
 Valuing Vacant Land
 Valuation of an option to delay



Ratio comparison approach



Additional Definitions

ECOM051 Business Finance, Lecture 4 (Dr Giles Spungin, G.Spungin@qmul.ac.uk, www.excalibur24.com, QMUL©2010-11)

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Discounted cash flow methods ignore opportunities (strategic options, indirect cash flows) created by investment project. Strategic options exist whenever management has any flexibility regarding the implementation of a project. Options to change the scale of a project (downsize, expand), abandon it, or drastically change its implementation in the future are examples of strategic options. The existence of these options improves the value of an investment project and as such should be reflected on the price / investment cost.

Alternative methods of valuing such projects, with an additional advantage of yielding more accurate estimates of future cash flows are given by: 

Derivatives valuation approach (copper mine examples)



Strategic options (vacant land and option to delay examples)



Ratio comparison approach

ECOM051 Business Finance, Lecture 4 (Dr Giles Spungin, G.Spungin@qmul.ac.uk, www.excalibur24.com, QMUL©2010-11)

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Sources of positive NPV
There might be several sources of competitive advantage:


Barriers to entry



Economies of scale



Economies of scope

Derivatives valuation approach
DEFINITION: Financial derivative is a financial asset value of which is determined by some other underlying asset. For example, stock option’s value is determined by the price of the underlying stock.

DEFINITION: Call (put) option on a stock is a financial asset giving its owner right to buy (sell) an underlying stock at a given stock price and predetermined date. The owner can either exercise this right or not. ECOM051 Business Finance, Lecture 4 (Dr Giles Spungin, G.Spungin@qmul.ac.uk, www.excalibur24.com, QMUL©2010-11)

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Copper mine example
Suppose you are told that the cash flows of a project are

C 1  p 1Q 1  K 1 and C 2  p 2Q 2  K 2 ,
where i  1, 2 and

pi - date i copper price (unknown)
Qi - date i quantity of copper extracted

K i - date i cost of copper extraction
Our task is to value the copper mine with above cash flows. We cannot employ PV as we do not know future copper prices.
Trick: create the following tracking portfolio comprising



Risk-free assets



Forward contracts

In particular,



Forward contract to buy Q 1 at date 1 at price F1

ECOM051 Business Finance, Lecture 4 (Dr Giles Spungin, G.Spungin@qmul.ac.uk, www.excalibur24.com, QMUL©2010-11)

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Forward contract to buy Q 2 at date 2 at price F2



A risk-free zero-coupon bond paying F1Q1  K 1  at date 1



A risk-free zero-coupon bond paying F2Q 2  K 2  at date 2

Since F1 and F2 are current forward prices, contracts have zero value at t = 0 and cost nothing, we can use PV:

PV 

F1Q 1  K 1 F2Q 2  K 2
, where

2
1  r1
1 r2 

rt ,t  1, 2 - yield to maturity of ZCB maturing at date t. EXAMPLE: Lincoln Copper Company has a mine that will produce 25k pounds at the end of year 1, and 50k pounds at the end
of year 2. Extraction costs are constant at £0.10 per pound. Current

forward

prices

are

£0.65

per

pound

for

1-year

ECOM051 Business Finance, Lecture 4 (Dr Giles Spungin, G.Spungin@qmul.ac.uk, www.excalibur24.com, QMUL©2010-11)

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contract and £0.60 per pound for 2-year contract. Risk-free rates are 5% for 1-year ZCB and 6% for 2-year ZCB.
Q: What is the value of the copper mine?
A: Mine value



25k  £0.65  £0.10
50k  £0.60  £0.10

 £35, 345
2
1  0.05
1  0.06

See the table below for details. ■

ECOM051 Business Finance, Lecture 4 (Dr...
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