5. (12 marks) Suppose a developer owns a parcel of land worth V(t)=V0K2t (measured in dollars) when developed at its highest and best use at time t0 (measured in years from today), where V0>0 is the value of the parcel today and K>1 is a parameter. Assume the only cost to the developer of owning the parcel is foregone interest, at an annual rate of r> 0 , on the capital tied up in the parcel. Letting A(t) be the present value of the parcel, the developer seeks to maximize A(t) by choosing the time at which the parcel is developed at its highest and best use. a. Derive the optimal time t at which to develop the parcel at its highest and best use, and then check the second-order condition to confirm that t indeed provides for a relative maximum. b. Use the result of Part (a) to evaluate t for the case of K=5e and r=5%, where e is Euler's number. 5. (12 marks) Suppose a developer owns a parcel of land worth V(t)=V0K2t (measured in dollars) when developed at its highest and best use at time t0 (measured in years from today), where V0>0 is the value of the parcel today and K>1 is a parameter. Assume the only cost to the developer of owning the parcel is foregone interest, at an annual rate of r> 0 , on the capital tied up in the parcel. Letting A(t) be the present value of the parcel, the developer seeks to maximize A(t) by choosing the time at which the parcel is developed at its highest and best use. a. Derive the optimal time t at which to develop the parcel at its highest and best use, and then check the second-order condition to confirm that t indeed provides for a relative maximum. b. Use the result of Part (a) to evaluate t for the case of K=5e and r=5%, where e is Euler's number