L9 Valuation of Land and Redevelopment

Condition when land is developed immediately question

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Unformatted text preview: y when the developer will wait until the last possible moment within the time constraint when the developer will develop some time between now and the time constraint 1. Condition When Land is Developed Immediately Question: Under what circumstances should the land be developed immediately at time t = 0. Value (V) At poin t A, A ∂V = − NOI 1 − e −( k − g ) N + [R (k − r ) − C ] < 0 ∂T ∂V <0 ∂T at T = 0 NOI 1 − e − ( k − g ) N > R (k − r ) − C NOI C 1 − e −( k − g ) N + >R k −r k −r ( ( ) ) ( ) 0 τ T im e Implication: Develop immediately if the value of future net operating income throughout the life of the building is greater than the construction cost net of the saved maintenance cost. 2. Condition When Land is Developed at the End of the Time Constraint τ Value (V) At poin t B, B ∂V >0 ∂T at T = τ 0 τ Τ∗ T im e ∂V = − NOI 1 − e− ( k − g ) N * e−( k − g )τ − [R(k − r ) − C ]* e− ( k − r )τ > 0 ∂T ( ) NOI 1 − e − ( k − g ) N * e gτ < [ R(k − r ) − C ] * e rτ ( ) What does this condition mean?? 2. Condition When Land is Developed at the End of the Time Constraint τ Recall from last slide NOI 1 − e − ( k − g ) N * e gτ < [ R (k − r ) − C ] * e rτ R(k − r ) − C ( g − r )τ e < NOI 1 − e −( k − g ) N ( ) ( ) RHS = Cost to Benefit ratio Implication: Develop as late as possible if the ratio of the construction cost net of the saved maintenance cost to value of future net operating income throughout the life of the building is greater than the threshold value exp(g-r)τ. 3. Optimal Development Between Time 0 and Time τ Question: Under what circumstances should the land be developed before time τ ? ∂V =0 ∂T Value (V) At poin t C, C at T = T* ∂V = − NOI 1 − e−( k −g ) N * e−( k −g )T − [R(k − r ) − C ]* e−( k −r )T = 0 ∂T ( ) 0 Τ∗ τ T im e The optimal time of development ⎛ R(k − r ) − C ...
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