Is it worth buying land for a development project if the business plan shows a negative NPV?
The initial reaction is “no,” but the decision is not that simple. The point is that owning land comes with the option to delay the project in time—and that option has value. This component of land value is called the Option Premium.

I can buy the land and proceed with the project immediately, or I can wait and monitor developments, and then decide whether to proceed. This flexibility is valuable.

The table presents a simple example, ignoring the fact that construction takes time. The first column shows a version where the project is executed immediately. Since we know today’s prices, we also know that the value of the completed building will be 100 million, with a cost of 88.24 million, resulting in a net value of 11.76 million.

But if I use the option and delay the project by one year, the completed building might be worth more or less, while construction costs will increase with inflation. The example includes two scenarios: A (bad) and B (good).

In Scenario A, the building’s value is 78.62 million, and the cost is 90 million. This means I won’t proceed with the project in this case. In Scenario B, the result of the project is 23.21 million. The weighted average of these two scenarios is 16.25 million. Assuming a 20% required return for this level of risk and discounting the result by one year gives us 13.54 million, which is 1.78 million higher than the immediate execution case. This difference is the Option Premium.

Now, the question arises: why did we discount at 20%?

In reality, this 20% is an incorrect figure. To arrive at the correct rate, we can use the replicating portfolio method. Through a combination of debt and equity investment, we can build a portfolio that replicates the outcome of the option. In our case, for example, we can purchase 67% of the building’s apartments, partially financed with debt.

As shown in the table below, this type of purchase will result in the same outcomes in scenarios A and B as the option to delay.

What’s interesting here is that we know the value of this portfolio. The expected value of the building, weighted by scenario probabilities, is 94.34 million, and the debt is 51.22 million. The portfolio’s net value is:
94.34 × 67% − 51.22 = 12.09 million.
(The 67% and leverage level can be derived using formulas, arranged to match the option outcomes.)

Since we know this portfolio’s present value is 12.09 million, and the expected value after one year is 16.25 million, the implied discount rate is 34.43%.

Now, why does the option valuation model work?

In our example, we used 9% to discount the development project, assuming the risk premium without leverage is 6% (= 9% − 3%). But when leveraged, we ended up with 34.43%.

Note that:
34.43 / 6 = 5.24

Now let’s look at the range of uncertainty, or the spread.
For the development project:
(78.62 + 113.21) / 94.34 = 36.7%
(where 94.34 is the expected value, discounted at 6%).

For the option (or corresponding portfolio), the spread is:
(0 + 23.21) / 12.09 = 192%

192 / 36.7 = 5.24

So, the discount rates and uncertainty range are aligned under market forces:

See the chart below.

Excel Option Valuation Model for Land

Source:
Commercial Real Estate Analysis and Investments by D. M. Geltner, N. G. Miller, J. Clayton, P. Eichholtz