Valuing a Texas Vineyard

$($Real Options$)$

You have been asked by an entrepreneur to value a potential vineyard in the Texas Hill Country,

an area west of Austin, Texas, USA. The cost of establishing a vineyard is reported in Table $1$

below. The cost of operating a vineyard is given in Table $2$ below. The current price of the

relevant grapes is $$1,\frac{500}{t}n.$ Historically, grape prices have grown on average by $3\mathrm{.}5\%$ per year

and the standard deviation of the log$-$returns on Texas grapes has, historically, been $10\%.$ Your

client uses a WACC of $12\%$ for similar projects but is unsure whether this would be an

appropriate RADR for this project. The land that your client is thinking of purchasing has a yield

of $4$ tons of grapes per acre. Yields are not expected until $3$ years after the land has started to be

cultivated. Capital expenditure is depreciated linearly over $10$ years, and the corporate tax rate

is $37\mathrm{.}5\%.$ You are asked to advise on the optimal time to invest in a winery.

Table $1$: Required investment to establish a vineyard $($$$/$acre$)$

Table $2$: Average Annual Operating Costs $($$$/$acre$)$