The Dallas Development Corporation is considering the purchase of an apartment project for $100,000. They estimate that they will receive $15,000 at the end of each year for the next 10 years. At the end of the 10th year, the apartment project will be worth nothing. If Dallas purchases the project, what will be its internal rate of return, compounded annually? If the company insists on an 8 percent return compounded annually on its investment, is this a good investment?

For the first question, you need to find the rate that makes the present value of a stream of ten constant annual payments of $15,000 equal to the $100,000 investment.

The formula that returns the present value of a constant payment is called the annuity formula and is:

[tex]Present\text{ }value=payment\times \bigg[\dfrac{1}{r}-\dfrac{1}{r(1+r)^t}\bigg][/tex]

In your problem you know:

Present value: $100,000
payment: $15,000
r: ?
t: 10

You cannot solve for r directly. You must guess a value and calculate the right side of the equation until to you find the rate that makes it equal to 100,000.

Try 5%:

[tex]\$15,000\times \bigg[\dfrac{1}{0.05}-\dfrac{1}{0.05(1+0.05)^{10}}\bigg]=\$115,826[/tex]

Then, the rate of return is greater than 5%. After several trials you will find that the rate of return is 8.15%.

Since this rate is higher than 8%, which is what the company requires, this is a good investment.