Chapter 13, Problem 7P

a)

Summary Introduction

To determine: Cash flows at year 0.

Explanation of Solution

Calculation of cash flows at year 0:

$\begin{array}{c}\text{Cash flows at year 0}=\text{Cost}+\text{Installation}\text{cost}+\text{Working}\text{capital}\\ =\left(-\$70,000\right)+\left(-\$15,000\right)+\left(-\$4,000\right)\\ =-\$89,000\end{array}$

Therefore, the year 0 cash flow is -$89,000

b)

Summary Introduction

To determine: Net operating cash flows for 3 years.

Explanation of Solution

Calculation of depreciation under MACRS:

Cost of the machine is $85,000 ($70,000+$15,000)

$\begin{array}{c}\text{Year 1 depreciation}=\$85,000\times 0.3333\\ =\$28,331\end{array}$

$\begin{array}{c}\text{Year 2 depreciation}=\$85,000\times 0.4445\\ =\$37,783\end{array}$

$\begin{array}{c}\text{Year 3 depreciation}=\$85,000\times 0.1481\\ =\$12,589\end{array}$

Calculation of operating cash flows:

$\begin{array}{c}\text{Operating cash flow at year 1}=\text{Annual}\text{after}\text{tax}\text{savings}+\left(\text{Depreciation}\times \text{Tax}\text{rate}\right)\\ =\$15,000+\left(\$28,331\times 40\%\right)\\ =\$26,332.4\end{array}$

Therefore, the net operating cash flow at year 1 is $26,332.4

$\begin{array}{c}\text{Operating cash flow at year 2}=\text{Annual}\text{after}\text{tax}\text{savings}+\left(\text{Depreciation}\times \text{Tax}\text{rate}\right)\\ =\$15,000+\left(\$37,783\times 40\%\right)\\ =\$30,113.2\end{array}$

Therefore, the net operating cash flow at year 2 is $30,113.2

$\begin{array}{c}\text{Operating cash flow at year 3}=\text{Annual}\text{after}\text{tax}\text{savings}+\left(\text{Depreciation}\times \text{Tax}\text{rate}\right)\\ =\$15,000+\left(\$12,589\times 40\%\right)\\ =\$20,035.6\end{array}$

Therefore, the net operating cash flow at year 2 is $20,035.6

c)

Summary Introduction

To determine: Additional year-3 cash flow required.

Explanation of Solution

$\begin{array}{c}\text{Book value}=\text{Total}\text{cost}-\text{total}\text{cost}\times \left(\text{sum}\text{of}\text{depreciation}\text{rates}\right)\\ =\$85,000-\$85,000\times \left(33.33\%+44.45\%+14.81\%\right)\\ =\$6,298.50\end{array}$

Book value is $6,298.50

Calculation of profit on sale:

$\begin{array}{c}\text{Profit on sale}=\text{Salvage}\text{value}-\text{Book value}\\ =\$30,000-\$6,298.50\\ =\$23,701.50\end{array}$

Therefore, profit on sale is $23,701.50

Calculation of taxes on salvage value:

$\begin{array}{c}\text{Taxes on salvage value}=\$30,000-\left(\$23,701.50\times 40\right)\\ =\$20,519.40\end{array}$

Therefore, taxes on salvage value is $20,519.40

Calculation of additional cash flow at year 3:

$\begin{array}{c}\text{Additional }\text{cash flow}=\text{After tax salvage value}+\text{Net}\text{working}\text{capital recovery}\\ =\$20,519.40+\$4,000\\ =\$24,519.40\end{array}$

Therefore, additional cash flow required is $24,519.40

d)

Summary Introduction

To determine: Whether the firm should accept the project or not.

Explanation of Solution

Calculation of NPV:

Excel workings:

Excel spread sheet:

Therefore, the net present value is negative (-$6,704.63). So, it is better to reject the project.