$2.)$ For #$2,$ assume NO leverage, i$.$e$.,$ that the investor uses $100\%$ equity to finance the project. $($Note: This material is covered in chapter $12$ and in class.$).$

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?

$3.)$ Use the same information as in problem $2.$ Now assume a loan for $$1\mathrm{.}5$ million is obtained at a $10$ percent interest rate and a $15-$year term.

a$.)$ Calculate the expected IRR on equity and the standard deviation of the return on equity.

b$.)$ Contrast the results from $($a$)$ with those from problem $3.$ Has the loan increased the risk? Explain.