An investor has projected three possible scenarios for a project as follows:

Pessimistic$$NOI will be $$200,000$ the first year, and then decrease $2$ percent per year over a five$-$year holding period. The property will sell for $$1\mathrm{.}8$ million after five years.

Most likely$$NOI will be level at $$200,000$ per year for the next five years $($level NOI$)$ and the property will sell for $$2$ million.

Optimistic$$NOI will be $$200,000$ the first year and increase $3$ percent per year over a five$-$year holding period. The property will then sell for $$2\mathrm{.}2$ million.

The asking price for the property is $$2$ million. The investor thinks there is about a $30$ percent probability for the pessimistic scenario, a $40$ percent probability for the most likely scenario, and a $30$ percent probability for the optimistic scenario.

a$.$ Compute the IRR for each scenario.

b$.$ Compute the expected IRR.

c$.$ Compute the variance and standard deviation of the IRRs.

d$.$ Would this project be better than one with a $12$ percent expected return and a standard deviation of $4$ percent?