Time Value of Money: Uneven Cash Flows

Many financial decisions require the analysis of uneven, or nonconstant, cash flows. stock dividends typically increase over time and investments in capital equipment almost always generate uneven cash flows. The term cash flow $($CFt$)$ denotes cash flows, while payment $($PMT$)$ designates cash flows coming at regular intervals.

The present value of an uneven cash flow stream is the sum of the PVs of the individual cash flows. The equation is:

Similarly, the future value of an uneven cash flow stream is found by compounding each payment to the end of the stream and then summing the future values. Many calculators have an NFV key that lets you obtain the FV$.$ However, if your calculator doesn't have a net future value $($NFV$)$ key, you can calculate the NFV as follows:

NFV $=$ NPV$(1+$ I$)$N

One can also find the interest rate of the uneven cash flow stream with a financial calculator and solving for the using the key.

Quantitative Problem: You own a security with the cash flows shown below.

Periods $01234$

Cash flows $0670365260330$

If you require an annual return of $12\%,$ what is the present value of this cash flow stream? Do not round intermediate calculations. Round your answer to the nearest cent.