Chapter 11, Problem 10P

a)

Summary Introduction

To determine: Net present value of the project.

Explanation of Solution

Given information:

Initial investment cost is $200,000

Increase in working capital is $40,000

Tax rate is 40%,

Project’s required rate of return is 15%

Calculation of net investment:

$\begin{array}{c}\text{Net investment}=\text{Initial investment}+\text{net increase in WC}\\ =\$200,000+\$40,000\\ =\$240,000\end{array}$

Calculation of depreciation:

$\begin{array}{c}\text{Depreciation}=\frac{\text{Initial investment}}{\text{Life}}\\ =\frac{\$200,000}{10}\\ =\$20,000\end{array}$

Formula for calculating net cash flows:

$\begin{array}{c}\text{Net cash flow}=\Delta \text{operating earnings after taxes}+\Delta \text{depreciation}\\ -\Delta \text{net working capital }\end{array}$

Calculation of net cash flows from year 1 to 5:

$\begin{array}{c}\text{Net cash flow}=\left[\left(\begin{array}{l}\Delta \text{Revenues}-\Delta \text{operating costs}\\ -\Delta \text{depreciation}\end{array}\right)\times \left(1-\text{t}\right)\right]+\Delta \text{depreciation}\\ =\left[\left(\$200,000-\$90,000-\$20,000\right)\times \left(1-0.4\right)\right]+\$20,000\\ =\text{\$74,000}\end{array}$

Calculation of net cash flows from year 6 to 9:

$\begin{array}{c}\text{Net cash flow}=\left[\left(\begin{array}{l}\Delta \text{Revenues}-\Delta \text{operating costs}\\ -\Delta \text{depreciation}\end{array}\right)\times \left(1-\text{t}\right)\right]+\Delta \text{depreciation}\\ =\left[\left(\$210,000-\$105,000-\$20,000\right)\times \left(1-0.4\right)\right]+\$20,000\\ =\text{\$71,000}\end{array}$

Calculation of net cash flows from year 10:

$\begin{array}{c}\text{Net cash flow}=\left[\left(\begin{array}{l}\Delta \text{operating earnings after taxes}+\Delta \text{depreciation}\\ -\Delta \text{NWC}+\text{salvage value}-\text{Tax on sale of assets}\end{array}\right)\times \left(1-\text{t}\right)\right]\\ =\left[\left(\$71,000+\$50,000\right)\times \left(1-0.4\right)+\$40,000\right]\\ =\text{\$141,000}\end{array}$

Calculation of net cash present value at 15%:

$\begin{array}{c}\text{NPV}=-C_0+\frac{C_{1-5}}{{\left(1+15\%\right)}^{1-5}}+\frac{C_{6-9}}{{\left(1+15\%\right)}^{6-9}}+\mathrm{.....}+\frac{C_{10}}{{\left(1+15\%\right)}^{10}}\\ =-\$240,000+\$74,000\left(3.352\right)+\text{\$71,000}\left(2.855\right)\left(0.497\right)\\ +\text{\$141,000}\left(0.247\right)\\ =\text{\$143,619}\end{array}$

Therefore, net present value at 15% is $143,619

b)

Summary Introduction

To determine: Net present value when discount rate is 24%.

Explanation of Solution

Calculation of net cash present value at 15%:

$\begin{array}{c}\text{NPV}=-C_0+\frac{C_{1-5}}{{\left(1+24\%\right)}^{1-5}}+\frac{C_{6-9}}{{\left(1+24\%\right)}^{6-9}}+\mathrm{.....}+\frac{C_{10}}{{\left(1+24\%\right)}^{10}}\\ =-\$240,000+\$74,000\left(2.745\right)+\text{\$71,000}\left(2.404\right)\left(0.341\right)\\ +\text{\$141,000}\left(0.116\right)\\ =\text{\$37,689}\end{array}$

Therefore, net present value at 24% is $37,689