Question

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: PV = Similarly, the future value of an uneven cash flow stream is the sum of the FVs of the individual cash flows. 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+1) One can also find the interest rate of the uneven cash flow stream with a financial calculator and solving Quantitative Problem: You own a security with the cash flows shown below 700 355 240 320 If you equire an annual retum of 10%, what is the present value of this cash flow stream? Round your answer to the nearest cent. Do not round intermediate calculations.

Answer 1

Answer:

       

           $\large\boxed{\large\boxed{\ 1,328.63}}$

Explanation:

Since the four-cash-flow stream is uneven, the manual calculation involves the calculation of four separate present values which you have to add.

The cash flows are:

• Year 1: 700

• Year 2: 355

• Year 3: 240

• Year 4: 320

The required rate of return is r = 10% = 0.10

The formula that you must use is:

               $PV=\frac{CF_1}{(1+i)^1}+\frac{CF_2}{(1+i)^2}+\frac{CF_3}{(1+i)^3}+\frac{CF_4}{(1+i)^4}$

Where PV is the present value; CF₁, CF₂, CF₃, CF₄ are the cash flows of the years 1, 2, 3, and 4 respectively, and i is the annual return.

Substituting:

             $PV=\frac{700}{(1+0.10)^1} +\frac{355}{(1+0.10)^2} +\frac{240}{(1+0.10)^3} +\frac{320}{(1+0.10)^4}$

             $PV=\ 636.36+\ 293.39+\ 180.31+\ 218.56=\ 1,328.63$