Answer:
Provided the developer offers you more than $321,599.84 in five years, the shorter contract is the better option.
Step-by-step explanation:
We have two options, a ten-year rental and sale or a five-year rental and sale. The problem wants us to figure out how much you need to sell the land for in the five-year case in order to prefer it to the ten-year case. In this setting, we can find the sale price that makes us indifferent, and any amount larger will be preferable.
Step 1: Solve for the PV in the 10-year case.
PV = PV (Rental Annuity) + PV (Sale)
PV = 20000 ×
PV = 20000 ×
PV = 20000 × [8.1109] + 168891.04
PV = 162217.92 + 168891.04
PV = $331, 108.96
Step 2: Solve for the five-year sale price that will match the 10-year case PV.
PV = PV (Rental Annuity) + PV (Sale)
331108.96 = 15000 ×
331108.96 = 15000 ×
331108.96 = 15000 × [4.4518] +
331108.96 = 66777.33 +
Sale Price = (331108.96 − 66777.33) ×
Sale Price = (264331.63) ×
Sale Price = $321, 599.84
Provided the developer offers you more than $321,599.84 in five years, the shorter contract is the better option.