Chapter 5, Problem 5.1ACQ

Summary Introduction

To discuss: The method for calculating the future value for a cash flow series

Introduction:

The future value of cash flow is the accumulated value including interest after a specified period. It is utilized to take effective decision at present or to assess the investment potentiality.

Explanation of Solution

The future cash flow value can be obtained using a formula, which is as follows:

$\text{Future cash flow}=\text{PV}{\left(1+\text{r}\right)}^{\text{t}}$

PV is the present value, r is the rate of interest, and t is the number of years. The computation of series of cash flow in the future is shown in an example.

Example, if a person deposits $100 in a year, and $200 in two years, and $300 in three years with an interest rate of 7%, then calculate the future amount after three years. Note that $100 receives 2 years interest, $200 receives 1-year interest, and $300 receives no interest as it is the final year

Calculate the future cash flow for each amount:

$\begin{array}{c}\text{Future cash flow for \$100}=\text{PV}{\left(1+\text{r}\right)}^{\text{t}}\\ =\$100{\left(1+0.07\right)}^2\\ =\$100{\left(1.07\right)}^2\end{array}$

$\begin{array}{c}=\$100\left(1.1449\right)\\ =\$114.49\end{array}$

$\begin{array}{c}\text{Future cash flow for \$200}=\text{PV}{\left(1+\text{r}\right)}^{\text{t}}\\ =\$200{\left(1+0.07\right)}^1\\ =\$200{\left(1.07\right)}^1\end{array}$

$\begin{array}{c}=\$200\left(1.07\right)\\ =\$214.00\end{array}$

$\begin{array}{c}\text{Future cash flow for \$300}=\text{PV}{\left(1+\text{r}\right)}^{\text{t}}\\ =\$300{\left(1+0.07\right)}^0\\ =\$300{\left(1.07\right)}^0\end{array}$

$\begin{array}{c}=\$300\left(1\right)\\ =\$300\end{array}$

Calculate the total future cash flow for three years:

$\begin{array}{c}\text{Total future cash flow for three years}=\$114.49+\$214+\$300\\ =\$628.49\end{array}$

Hence, the total future cash flow for three years is $628.49.