Present Value of Annuities and Perpetuities

A company is evaluating a project that will generate cash flows of $5,000 at the end of each year for 10 years. If the company's required rate of return is 6%, what is the present value of these cash flows? Additionally, if the company plans to invest in this project for perpetuity after the 10th year at the same cash flow, what would be the present value of the perpetuity?

To find the present value of the annuity, use the formula:

$$ PV_{ ext{annuity}} = C imes\frac{1 - (1 + r)^{-n}}{r} $$

where:

• $PV_{ ext{annuity}}$ = present value of the annuity
• $C$ = annual cash flow
• $r$ = interest rate (as a decimal)
• $n$ = number of periods

Then, for the perpetuity, use the formula:

$$ PV_{ ext{perpetuity}} =\frac{C}{r} $$

Note that since the project cash flows will last forever, the perpetuity starts after year 10.