Chapter 17, Problem 56P

(a):

To determine

Calculate the cash flow after tax.

Explanation of Solution

The cash flow after tax (CFAT) for defender in year 0 is equal to its market value. Thus, the cash flow after tax for the defender is -$100,000.

The cash flow after tax (CFAT) for challenger can be calculated as follows:

$\begin{array}{c}{\text{CFAT}}_{\text{Challenger}}=-{\text{First cost}}_{\text{Challenger}}+\left({\text{First cost}}_{\text{Defender}}-2\left({\text{Depreciation}}_{\text{Defender}}\right)-{\text{Market value}}_{\text{Defender}}\right)\times {\text{T}}_{\text{e}}\\ =-420,000+\left(300,000-2\left(60,000\right)-100,000\right)\times 0.35\\ =-392,000\end{array}$

The cash flow after tax for the challenger is -$392,000.

Thus, select alternate B.

(b):

To determine

Calculate the cash flow after tax for three years.

Explanation of Solution

The cash flow after tax (CFAT) of defender for first three years can be calculated as follows:

$\begin{array}{c}{\text{CFAT}}_{\text{Defender}}=-{\text{Chargeable expense}}_{\text{Defender}}-\left(-{\text{Chargeable expense}}_{\text{Defender}}-{\text{Depreciation}}_{\text{Defender}}\right)\times {\text{T}}_{\text{e}}\\ =-120,000-\left(-120,000-\left(60,000\right)\right)\times 0.35\\ =-57,000\end{array}$

The cash flow after tax of the defender is -$57,000.

The cash flow after tax (CFAT) of challenger for first three years can be calculated as follows:

$\begin{array}{c}{\text{CFAT}}_{\text{Defender}}=-{\text{Chargeable expense}}_{\text{Challenger}}-\left(-{\text{Chargeable expense}}_{\text{Challenger}}-\left({\text{Depreciation}}_{\text{Challenger}}\right)\right)\times {\text{T}}_{\text{e}}\\ =-30,000-\left(-30,000-\left(140,000\right)\right)\times 0.35\\ =29,500\end{array}$

The cash flow after tax of the defender is -$57,000.

(c):

To determine

Calculate the annual worth.

Explanation of Solution

The time period is indicated by ‘n’. The MARR is indicated by ‘i’. The annual worth (AW) of defender can be calculated as follows:

$\begin{array}{c}{\text{AW}}_{\text{Defender}}=-{\text{CFAT}}_{\text{Defender in year 0}}\left(\frac{\text{i}{\left(1+\text{i}\right)}^{\text{n}}}{{\left(1+\text{i}\right)}^{\text{n}}-1}\right)-{\text{CFAT}}_{\text{Defender for three years}}\\ =-100,000\left(\frac{\text{0}\text{.15}{\left(1+\text{0}\text{.15}\right)}^{\text{3}}}{{\left(1+\text{0}\text{.15}\right)}^{\text{3}}-1}\right)-57,000\\ =-100,000\left(0.43798\right)-57,000\\ =-100,798\end{array}$

The annual worth of the defender is -$100,798.

The annual worth (AW) of challenger can be calculated as follows:

$\begin{array}{c}{\text{AW}}_{\text{Challenger}}=-{\text{CFAT}}_{\text{Challenger in year 0}}\left(\frac{\text{i}{\left(1+\text{i}\right)}^{\text{n}}}{{\left(1+\text{i}\right)}^{\text{n}}-1}\right)-{\text{CFAT}}_{\text{Challenger for three years}}\\ =-392,000\left(\frac{\text{0}\text{.15}{\left(1+\text{0}\text{.15}\right)}^{\text{3}}}{{\left(1+\text{0}\text{.15}\right)}^{\text{3}}-1}\right)-29,500\\ =-392,000\left(0.43798\right)-29,500\\ =-142,188\end{array}$

The annual worth of the defender is -$100,798. Since the annual worth of the defender is greater than the challenger, keep the defender.

(d):

To determine

Calculate the annual worth through spreadsheet.

Explanation of Solution

The annual worth of defender and challenger can be calculated using spreadsheet as follows: