Pessimistic$-$NO$/$ 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 $$200,000$ per year for the next five years $($level NO$)$ and the property will sell for $$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.

Now assume that a loan for $$1\mathrm{.}5$ million is obtained at a $10$ percent interest rate and a $15-$year term.

Required:

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

b$.$ Without the loan, the project has an expected IRR of $10\mathrm{.}01\%$ and a standard deviation of $1\mathrm{.}62\%.$ Has the loan increased the risk?

Without the loan, the project has an expected IRR of $10\mathrm{.}01\%$ and a standard deviation of $1\mathrm{.}62\%.$ Has the loan increased the risk?