L9 Valuation of Land and Redevelopment

Dcf contd t n recall v pv of all future noi after

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Unformatted text preview: ance Cost Until Development – PV of Construction Cost. DCF Contd T +N Recall V = PV of all future NOI after construction – PV of all Maintenance Cost Until Development – PV of Construction Cost. If the land site is to be developed at time T, then the value of the land site is V= T ∫ ( NOIe gt )e −kt dt − ∫ (Ce ct )e −kt dt − (Re rT )e −kT 0 T After integration, the value of land becomes C NOI −( k − g ) N − ( k − g )T V= 1− e ×e − 1 - e -(k -c)T − (Re rT )e − kT k−g k −c Question: When it is optimal to develop the land so that the value of the land is maximized? ( ) ( ) DCF Contd The objective of the developer is to choose the optimal time T * to develop so that V is maximized. First-order derivative of V with respect to T: ∂V = − NOI 1 − e −( k − g ) N e −( k − g )T − Ce −( k −c )T + (k − r )(Re rT )e −kT = 0 ∂T ( ) Solving for T* gives the general solution for the optimal time to develop. To simplify our analysis further, we assume that c = r. ∂V = − NOI 1 − e −( k − g ) N e −( k − g )T − [R (k − r ) − C ]e −( k − r )T = 0 ∂T ( ) DCF Analysis For land sites inside an urban area, the land owner usually is required to develop the land site within a certain number of years (usu. 3 years in Hong Kong). If the developer fails to develop the land site within the time constraint, the government may re-enter the land and re-auction it to another developer. Our next discussion will focus on the conditions underlying the timing of development of the land site. We want to understand when the developer will develop immediatel...
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