Chapter 12, Problem 56P

1.

To determine

Calculate the maximum amount of annual variable operating expenses (pre-tax) that would make the attractive investment from a present-value standpoint.

Explanation of Solution

Calculate the maximum amount of annual variable operating expenses (pre-tax) that would make the attractive investment from a present-value standpoint as follows:

$\begin{array}{c}\begin{array}{l}\text{Maximum annual variable }\\ \text{operating expense (pre-tax)}\end{array}\}=\left(\begin{array}{l}\text{Annual operating expense }-\\ \text{Annuity amount (3)}\end{array}\right)\\ =\$200,000-\$93,970\\ =\$106,030\end{array}$

Working note (1):

Calculate the present value of salvage value.

$\begin{array}{c}\begin{array}{l}\text{Present value }\\ \text{of salvage value}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Salvage value}\times \\ \text{PV factor @12\% for 6th year}\end{array}\right)\\ =\$90,000\times 0.564\\ =\$50,760\end{array}$

Working note (2):

Calculate the net investment outlay.

$\begin{array}{c}\text{Net investment outlay = }\left(\begin{array}{l}\text{Investment outlay}-\\ \text{PV of salvage value (1)}\end{array}\right)\\ =\$460,000-\$50,760\\ =\$409,240\end{array}$

Working note (3):

Calculate the annuity amount.

$\begin{array}{c}\text{Annuity amount =}\frac{\text{ Net investment outlay (2)}}{\left(\begin{array}{l}\text{Present value of annuity }\\ \text{for 6 years @12\%}\end{array}\right)}\\ =\frac{\$409,240}{4.355}\\ =\$93,970\end{array}$

2.

To determine

Calculate the maximum amount of annual variable operating expenses (both pre-tax and after tax).

Explanation of Solution

Calculate the maximum amount of annual variable operating expenses (both pre-tax and after tax) as follows:

$\begin{array}{c}\begin{array}{l}\text{Maximum annual }\\ \text{after-tax variable }\\ \text{expense}\end{array}\}\text{ = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual post-tax operating}\\ \text{expense for exiting asset (9)}\end{array}\right)-\\ \text{Present value of annuity (11)}\end{array}\right]\\ =\$130,000-\$64,350\\ =\$65,650\end{array}$

$\begin{array}{c}\begin{array}{l}\text{Maximum pre-tax }\\ \text{variable operating}\\ \text{expenses}\end{array}\}\text{ =}\left[\frac{\left(\begin{array}{l}\text{Maximum annual after tax}\\ \text{variable operating expense}\end{array}\right)}{1-35\%}\right]\\ =\frac{\$65,650}{\left(1-35\%\right)}\\ =\$101,001\end{array}$

Working note (4):

Calculate the gain or loss on sales.

$\begin{array}{c}\text{Gain or (loss) on sales = }\left(\begin{array}{l}\text{Sellig price }-\\ \text{Net book value}\end{array}\right)\\ =\$40,000-\$60,00\\ =\$(20,000)\end{array}$

Working note (5):

Calculate the tax saving due to deductibility of loss.

$\begin{array}{c}\begin{array}{l}\text{Tax saving due }\\ \text{to deductibility}\\ \text{ of loss }\end{array}\}\text{=}\left(\begin{array}{l}\text{Loss on sales (4)}\times \\ \text{Tax rate}\end{array}\right)\\ =\$20,000\times 35\%\\ =\$7,000\end{array}$

Working note (6):

Calculate the net-of-tax initial investment outlay.

$\begin{array}{c}\begin{array}{l}\text{Net-of-tax initial }\\ \text{investment outlay}\end{array}\}=\left(\begin{array}{l}\text{Initial investment}-\\ \text{Tax saving due to deductibility of loss (5)}\end{array}\right)\\ =\$460,000-\$7,000\\ =\$453,000\end{array}$

Working note (7):

Calculate the net –of tax difference salvage value at the end of year 6.

$\begin{array}{c}\begin{array}{l}\text{Net –of tax difference }\\ \text{salvage value at the }\\ \text{end of year 6}\end{array}\}=\left(\begin{array}{l}\text{Different in salvage value at the end of 6 year}-\\ \left(\begin{array}{l}\text{Different in salvage value at the end of 6 year}\times \\ 35\%\end{array}\right)\end{array}\right)\\ =\$90,000-\left(\$90,000\times 35\%\right)\\ =\$90,000-31,500\\ =\$58,500\end{array}$

Working note (8):

Calculate the present value of differential depreciation tax shield at 8%.

$\begin{array}{c}\begin{array}{l}\text{Present value }\\ \text{of differential }\\ \text{depreciation }\\ \text{tax shield at 8\%}\end{array}\}=\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual tax shield for replacement asset}-\\ \text{Annual tax shield existing asset}\end{array}\right)\times \\ \text{Present value annuity @8\% for 6 years}\end{array}\right]\\ =\left(\$29,167-\$3,500\right)\times 4.623\\ =\$118,657\end{array}$

Working note (9):

Calculate the annual post-tax operating expense for exiting asset.

$\begin{array}{c}\begin{array}{l}\text{Annual post-tax }\\ \text{operating expense for }\\ \text{exiting asset}\end{array}\}=\left(\begin{array}{l}\text{Annual pre-tax operating expense}\times \\ \left(1-35\%\right)\end{array}\right)\\ =\$200,000-\left(1-35\%\right)\\ =\$130,000\end{array}$

Working note (10):

Calculate the present value of after-tax variable operating costs for replacement assets.

$\begin{array}{c}\begin{array}{l}\text{Present value of }\\ \text{after-tax variable }\\ \text{operating costs for }\\ \text{replacement assets}\end{array}\}=\left(\begin{array}{l}\text{After tax net investment outlay}-\\ \text{PV of after tax additional salvage value}-\\ \text{PV of differential tax savngs due to depreciation (8)}\end{array}\right)\\ =\$453,000-\$36,855-\$118,657\\ =\$297,488\end{array}$

Working note (11):

Calculate the present value of annuity.

$\begin{array}{c}\begin{array}{l}\text{Present value }\\ \text{of annuity }\end{array}\}\text{= }\frac{\left(\begin{array}{l}\text{Present value of after-tax }\\ \text{variable operating costs }\\ \text{for replacement assets (10)}\end{array}\right)}{\text{Annuity factor for 6 years @8\%}}\\ =\frac{\$297,488}{4.623}\\ =\$64,350\end{array}$

3.

To determine

State the strategic considerations that might affect the decision.

Explanation of Solution

State the strategic considerations that might affect the decision as follows:

• Competitors of the company,
• Environmental-management benefits with the new equipment and,
• Delivery time, response time and process efficiency.