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Suppose a homeowner has an existing mortgage loan with these terms: Remaining balance of $150,000, interest rate of 8 percent, and remaining term of 10 years (monthly payments). This loan can be replaced by a loan at an interest rate of 6 percent, at a cost of 8 percent of the outstanding loan amount. Should the homeowner refinance? What difference would it make if the homeowner expects to be in the home for only five more years rather than ten?

You have just signed a contract to purchase your dream house. The price is $120,000 and you have applied for a $100,000, 30-year, 5.5 percent loan. Annual property taxes are expected to be $2,000. Hazard insurance will cost $400 per year. Your car payment is $400, with 36 months left. Your monthly gross income is $5,000. Calculate:

**a.** The monthly payment of principal and interest (PI).

**b.** One-twelfth of annual property tax payments and hazard insurance payments.

**c.** Monthly PITI (principal, interest, taxes, and insurance).

**d.** The housing expense (front-end) ratio.

**e.** The total obligations (back-end) ratio.

If you purchase a parcel of land today for $25,000, and you expect it to appreciate 10 percent per year in value, how much will your land be worth 10 years from now assuming annual compounding?

You are considering the purchase of a small income-producing property for $150,000 that is expected to produce the following net cash flows.

Assume your required internal rate of return on similar investments is 11 percent. What is the net present value of this investment opportunity? What is the going-in internal rate of return on this investment? Should you make the investment?

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 $1.8 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 $2.2 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.*

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