Chapter 6, Problem 10QP

Calculating EAC You are evaluating two different silicon wafer milling machines. The Techron I costs $245,000, has a three-year life, and has pretax operating costs of $39,000 per year. The Techron 11 costs $315,000, has a five-year life, and has pretax operating costs of $48,000 per year. For both milling machines, use straight-line depreciation to zero over the project’s life and assume a salvage value of $20,000. If your tax rate is 35 percent and your discount rate is 9 percent, compute the EAC for both machines. Which do you prefer? Why?

Summary Introduction

To identify: The EAC of both the machines and the machine to be preferred.

Equivalent Annual Cost (EAC):

Equivalent annual cost is the cost incurred to maintain and operate a machine during its life. It can be used in capital budgeting decision and helps in comparing various assets.

Explanation of Solution

Machine T I

Given,

Cost of machine is $245,000.

Operating costs is $39,000.

Estimated life of machine is 3 years.

Market price of machine after 3 years $20,000.

Tax rate is 35%.

Discount rate is 9%.

Calculated values,

Net present value is $-\$226,781$ (working note).

Present value interest factor (PVIFA) at 9% for 3 years is 2.531.

Formula to calculate equivalent annual cost,

$\text{Equivalent}\text{annual}\text{cost}=\frac{\text{Net}\text{present}\text{value}}{\text{PVIFA}}$

Substitute $-\$226,781$ for net present value and 2.531 for PVIFA.

$\begin{array}{c}\text{Equivalent}\text{annual}\text{cost}=\frac{-226,781}{2.531}\\ =-\$89,601.34\end{array}$

Machine T II

Given,

Cost of machine is $315,000.

Operating costs is $48,000.

Estimated life of machine is 5 years.

Market price of machine after 5 years $20,000.

Tax rate is 35%.

Discount rate is 9%.

Calculated values,

Net present value is $-\$342,144.8$ (working note).

Present value interest factor (PVIFA) at 9% for 5 years is 2.531.

Formula to calculate equivalent annual cost,

$\text{Equivalent}\text{annual}\text{cost}=\frac{\text{Net}\text{present}\text{value}}{\text{PVIFA}}$

Substitute $-\$342,144.8$ for net present value and 3.89 for PVIFA.

$\begin{array}{c}\text{Equivalent}\text{annual}\text{cost}=\frac{-342,144.8}{3.89}\\ =-\$87,954.96\end{array}$

Working notes:

Machine T I

Calculation of after tax salvage value of asset,

$\begin{array}{c}\text{After}\text{tax}\text{salvage}\text{value}\text{of}\text{asset}=\left(\begin{array}{l}\text{Salvage}\text{value}\times \left(1-\text{Tax}\text{rate}\right)\\ \times \frac{1}{{\left(1+\text{Annual}\text{interest}\text{rate}\right)}^{\text{years}}}\end{array}\right)\\ =\$20,000\times \left(1-0.35\right)\times \frac{1}{{\left(1+0.09\right)}^3}\\ =\$20,000\times 0.65\times 0.772\\ =\$10,036\end{array}$

Calculation of operating cash flows,

$\begin{array}{c}\text{Operating}\text{cash}\text{flow}=\left(-\text{Cost}\times \left(1-\text{Tax}\text{rate}\right)\right)+\left(\frac{\text{Cost}\text{of}\text{asset}}{\text{Life}\text{of}\text{asset}}\times \text{Tax}\text{rate}\right)\\ =-\$39,000\times \left(1-0.35\right)+\left(\frac{\$245,000}{3\text{years}}\times 0.35\right)\\ =-\$25,350+\$28,583.33\\ =\$3,233.33\end{array}$

Calculation of net present value,

$\begin{array}{c}\text{Net}\text{Present}\text{Value}=\left(\begin{array}{l}\left(\text{Operating}\text{cashflow}\times \text{PVIFA}\right)\\ -\text{Initial}\text{investment}+\text{Salvage}\text{value}\end{array}\right)\\ =\left(-\$3,233.33\times 2.531\right)-\$245,000+\$10,036\\ =-\$8,183-\$234,964\\ =-\$243,147\end{array}$

Machine T II

Calculation of after tax salvage value of asset,

$\begin{array}{c}\text{After}\text{tax}\text{salvage}\text{value}\text{of}\text{asset}=\left(\begin{array}{l}\text{Salvage}\text{value}\times \left(1-\text{Tax}\text{rate}\right)\\ \times \frac{1}{{\left(1+\text{Annual}\text{interest}\text{rate}\right)}^{\text{years}}}\end{array}\right)\\ =\$20,000\times \left(1-0.35\right)\times \frac{1}{{\left(1+0.09\right)}^5}\\ =\$20,000\times 0.65\times 0.6499\\ =\$8,448.7\end{array}$

Calculation of operating cash flows,

$\begin{array}{c}\text{Operating}\text{cash}\text{flow}=\left(-\text{Cost}\times \left(1-\text{Tax}\text{rate}\right)\right)+\left(\frac{\text{Cost}\text{of}\text{asset}}{\text{Life}\text{of}\text{asset}}\times \text{Tax}\text{rate}\right)\\ =-\$48,000\times \left(1-0.35\right)+\left(\frac{\$315,000}{5\text{years}}\times 0.35\right)\\ =-\$31,200+\$22,050\\ =-\$9,150\end{array}$

Calculation of net present value,

$\begin{array}{c}\text{Net}\text{Present}\text{Value}=\left(\begin{array}{l}\left(\text{Operating}\text{cashflow}\times \text{PVIFA}\right)\\ -\text{Initial}\text{investment}+\text{Salvage}\text{value}\end{array}\right)\\ =-\$9,150\times 3.89-\$315,000+\$8,448.7\\ =-\$35,593.5-\$306,551.3\\ =-\$342,144.8\end{array}$

Conclusion

Hence, EAC of machine T I and T II is $-\$89,601.34$ and $-\$87,954.96$ respectively, as machine T II has less negative EAC so it must be preferred.