Chapter 5, Problem 3QP

Summary Introduction

To calculate: The future value of cash flow at 8%, 11%, and 24% of Company H.

Introduction:

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

Answer to Problem 3QP

The future value of cash flow of Company H at 8%, 11%, and 24% is $6,390.49, $6,632.94, and $7,785.55 respectively.

Explanation of Solution

Given information:

Company H has found a project of investment with cash flows which has a rate of discount of 8%, 11%, and 24%. The cash flow for year 1 is $1,075, for year 2 is $1,235, for year 3 is $1,510, and for year 4 is $1,965.

Formula to calculate the future value:

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

Note: PV denotes the present value, r denotes the rate of discount and t denotes the number of years.

Compute the future value for 8%, 11%, and 24%:

$\begin{array}{c}\text{Future cash flow for 8\%}=\text{PV}{\left(1+r\right)}^t\\ =\left(\begin{array}{l}\$1,075{\left(1+0.08\right)}^3+\$1,235{\left(1+0.08\right)}^2+\\ \$1,510\left(1+0.08\right)+\$1,965\end{array}\right)\\ =\left(\begin{array}{l}\$1,075{\left(1.08\right)}^3+\$1,235{\left(1.08\right)}^2+\\ \$1,510\left(1.08\right)+\$1,965\end{array}\right)\end{array}$

$\begin{array}{c}=\$1,075\left(1.259712\right)+\$1,235\left(1.1664\right)+\$1,510\left(1.08\right)+\$1,965\\ =\$1,354.19+\$1,440.504+\$1,630.80+\$1,965\\ =\$6,390.49\end{array}$

Note:

• The future cash flow of each year is calculated and then it is added.
• $1,075 receives 3 years interest, $1,235 receives 2 years interest, and $1,510 receives 1-year interest and $1,965 receives no interest as it is the final year and r is 0.08 or 8%.

Hence, the future value at 8% is $6,390.49.

Compute the future value for 11%:

$\begin{array}{c}\text{Future cash flow for 11\%}=\text{PV}{\left(1+r\right)}^t\\ =\left(\begin{array}{l}\$1,075{\left(1+0.11\right)}^3+\$1,235{\left(1+0.11\right)}^2+\\ \$1,510\left(1+0.11\right)+\$1,965\end{array}\right)\\ =\left(\begin{array}{l}\$1,075{\left(1.11\right)}^3+\$1,235{\left(1.11\right)}^2+\\ \$1,510\left(1.11\right)+\$1,965\end{array}\right)\end{array}$

$\begin{array}{c}=\$1,075\left(1.367631\right)+\$1,235\left(1.2321\right)+\$1,510\left(1.11\right)+\$1,965\\ =\$1,470.20+\$1,521.64+\$1,676.10+\$1,965\\ =\$6,632.94\end{array}$

Note:

• The future cash flow of each year is calculated and then it is added.
• $1,075 receives 3 years interest, $1,235 receives 2 years interest, and $1,510 receives 1-year interest and $1,965 receives no interest as it is the final year and r is 0.11 or 11%.

Hence, the future value at 11% is $6,632.94.

$\begin{array}{c}\text{Future cash flow for 24\%}=\text{PV}{\left(1+r\right)}^t\\ =\left(\begin{array}{l}\$1,075{\left(1+0.24\right)}^3+\$1,235{\left(1+0.24\right)}^2+\\ \$1,510\left(1+0.24\right)+\$1,965\end{array}\right)\\ =\left(\begin{array}{l}\$1,075{\left(1.24\right)}^3+\$1,235{\left(1.24\right)}^2+\\ \$1,510\left(1.24\right)+\$1,965\end{array}\right)\end{array}$

$\begin{array}{c}=\$1,075\left(1.906624\right)+\$1,235\left(1.5376\right)+\$1,510\left(1.24\right)+\$1,965\\ =\$2,049.21+\$1,898.94+\$1,872.40+\$1,965\\ =\$7,785.55\end{array}$

Note:

• The future cash flow of each year is calculated and then it is added.
• $1,075 receives 3 years interest, $1,235 receives 2 years interest, and $1,510 receives 1-year interest and $1,965 receives no interest as it is the final year and r is 0.24 or 24%.

Hence, the future value at 24% is $7,785.55.