Question

The Webber Company is an international conglomerate with a real estate division that own the right to erect an office building on a parcel of land in downtown Sacramento over the next year. This building would cost $25M to construct. Due to low demand for office space in the downtown area, such a building is worth only $23.5M today. Therefore, the company will wait to see if demand increases next year before it makes the investment decision. If demand increases, the building would be worth $26.8M a year from today. If demand decreases, the same office building would be worth $22M in a year. The two states are equally likely. The cost of capital is 5%.

a) What is the NPV of the right to build an office building on the land?

b) A local competitor in the real estate business has recently offered $750,000 for the right to build an office building on the land. Should the company accept this offer?

Answer 1

Case A:

The construction cost of the building = $25 million

Current worth of such building = $23.5 million

If the demand increases the worth of the building = $26.8 million

If the demand decreases the worth of the building = $22.0 million

cost of capital = 5% = 0.05

present value factor (PVF) for 1 year @ 5% = 1/ (1+r)¹ = 1/ (1+0.05)¹ = 1/ 1.05 = 0.952

If the demand increases:

Net present value (NPV) = present value of cash inflows - present value of cash outflows

Present value of cash inflows = future value of cash inflows * PVF for 1 year @ 5%

= ($26.8 million * 0.952) - $25 million

= $25,513,600 - $25,000,000

NPV = $513,600

If the demand decreases:

Net present value (NPV) = present value of cash inflows - present value of cash outflows

= ($22.0 million * 0.952) - $25 million

= $20,944,000 - $25,000,000

NPV = - $4,056,000

There is a 50-50 chance to increase or decrease the demand in 1 year. So the company' positive NPV would be $513,600 if the demand increases and the negative NPV would be $4,056,000 if the demand decreases.

Case B:

If another competitor in the business offers $750,000 for the right to build an office building on the land then it is better to accept the proposal. Because If the company builds the office building it would get only a profit of $513,600 if the demand increases. But now, if the company accepts the proposal, it would get $750,000, which is more profitable than constructing the building by the company itself.