Verdsettelse, Gjeldsgrad og Finansiering

1
Verdsettelse, Gjeldsgrad og Finansiering

• Forelesningsplan Lørdag 8. mars 2003

• Verdifastsettelse ved hjelp av opsjoner
  (repetisjon verdisetting av tomt)
• Verdiforhandlinger
• Børsintroduksjoner (Intitial Public Offerings)
• Markedet for selskapskontroll (Beta, 1992)
  (fusjoner og oppkjøp)
• Gjeldsgrad og Egenkapital-/Gjeldshaver konflikter
• Forskningsarbeider 1. Kapitalmarkedet i Norge,
  USA, UK og Japan
• 2. Volatilitetsklynger for prisserier i Norge
• 3. Stokastisk Volatilitet i Norge?

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Valuing a Mine with No Strategic Options
Since F1 and F2 represent current forward prices,
the forward contracts under 1) costs nothing. The
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?
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Cash Flows of Forward Contracts to Exchange Qt
Units of Copper for Cash at Future Date t
4
Cash Flows of Copper Mine versus Portfolio of
Forward Contracts and Zero-Coupon Bonds
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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.
• The future value of the copper mine (the
  derivative asset) can be tracked by a portfolio
  of two traded investments which, according to the
  no-arbitrage assumption, implies that the value
  of the mine is simply the cost of the tracking
  portfolio.

Example Company A will produce 75000 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. What is the present value of the mine?
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Payoffs of a Copper Mine with a Shutdown Option
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Valuing a Mine with an Abandonment Option
Scenario 1 Copper mine closed down value zero
Scenario 2 Copper mine profitable CF is
7500750000(0.90-0.80)

• Simultaneous solving the equations gives the
  tracking portfolio
• x18750 pounds received from a one-year forward
  contract and y1785.714 invested in zero-coupon
  bonds.
• Value 1786
• Some practical considerations (1) simplification
  (no extraction in the future)
• (2) analogous to an exchange option

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Valuing a Mine with an Abandonment Option
Result 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.
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Valuing Vacant Land
An option to turn vacant land into developed land.
The derivatives valuation approach can be used to
determine the worth of an option to construct one
of a number of possible buildings with strike
prices equal to the buildings construction
costs. One can value this option, and thus the
land, by first computing the risk-neutral
probabilities associated with various
outcomes. Example.
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Valuing Vacant Land
Six Condominium units Construction costs are
80000 per unit Nine Condominium 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
Present time Building nine Condominium
units Building six Condominium units Building
now The decision is to build six units giving
120000 profit.
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Binomial Trees for Land Valuation
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Valuing Vacant Land
Risk Neutral probabilities
Current value of the land under the assumption
that it will remain vacant until next year
Since 141071 is greater than 120000 profit that
would be realized by building a six-unit
condominium immediately, it is better to keep the
land vacant.
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Valuing Vacant Land
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.
Titman (1985) shows that development
restrictions, such as ceilings on building height
or density, may reduce uncertainty, leading to
both a lower value for vacant land and a greater
desire to exercise the option- that is, to
develop the land. Hence, the benefit of waiting
is larger when the degree of uncertainty about
the options terminal value is greater.