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Unformatted text preview: R(k − r ) − C 1 ln⎜ g − r ⎜ NOI (1 − e −( k − g ) N ⎝ ⎞ ⎟ ⎟ ⎠ V [T = 0] = NOI 1 − e −( k − g ) N − R k−g ( ) V= NOI C 1 − e − ( k − g ) N e − ( k − g )T * − 1 - e -(k -c)T* − (Re rT * )e −kT * k−g k −c ( ) ( ) Case Analysis Contd
How does the result compare with the auction outcome?? What are the implications?? II. Option Pricing Approach
Derivative—cannot exist on its own Land is derived asset and land value does not exist unless the land can be developed into BEST & HIGHEST use !! Important concept:
Land = Call Option
Call option : The right to buy an asset at a predetermined price at the end of (or within) a period. Exercise Price = Construction/Development Cost Price of the Underlying Asset = Price of the property to be developed on the land site OPM: With Time Constraint (τ) to Develop:
P ayoff to Land Owner Payoff at time τ +ve The following diagram describes the value of land at the end of the time to develop (τ ) 0 R Land Price -ve Property Value Analysis with Time Constraint:
R = Construction Cost (Constant between time 0 and time t) There exists a riskless interest rate r. Land users are price takers. Completed buildings are sold immediately. Property price (S) follows the Wiener process OPM Approach Contd
L an d Valu e V = V(S, σ, R, r, τ)
P a yoff a t t im e τ: The Value of Land before time
τ and at time τ L a n d Va lu e Befor e τ 0 R P roperty Valu e The land value is given by the Black-Scholes Option Pricing Model V = SN (d1 ) − Re − rτ N (d 2 )
d1 = ln(S / R) + (r + σ 2 / 2)τ στ d 2 = d1 − σ τ OPM Approach Contd
Recall Land Value as given by BS-OPM V = SN (d1 ) − Re − rτ N (d 2 )
S = Value of Underlying Property R*exp(-rτ) = Present value of construction/development cost N(.) = Normal Distribution Function N(d1) = Sensitivity of land value to the change in value of the underlying property N(d2) = Probability that the...
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This note was uploaded on 09/06/2010 for the course FINA FINA0805 taught by Professor Tse during the Spring '09 term at HKU.
- Spring '09