Marker’s Tattoo Studio wants to buy new laser therapy equipment

• Income Tax Expense = EBIT * Tax Rate
• Income Tax Expense = $28,000 * 0.25 = $7,000
• Annual Net Income = EBIT - Income Tax Expense
• Annual Net Income = $28,000 - $7,000 = $21,000

The expected increase in annual net income from investing in the new equipment is $21,000.

2. Accrual Accounting Rate of Return (AARR)

The accrual accounting rate of return is calculated as:

• AARR = (Average Annual Net Income) / (Average Investment)

We've already calculated the average annual net income as $21,000 (assuming it's consistent over the 5 years).

Now, let's calculate the average investment:

• Initial Investment = Purchase Cost + Installation Cost = $300,000 + $20,000 = $320,000
• Terminal Value (at the end of the life) = $20,000
• Average Investment = (Initial Investment + Terminal Value) / 2
• Average Investment = ($320,000 + $20,000) / 2 = $340,000 / 2 = $170,000

Now, we can calculate the AARR:

• AARR = $21,000 / $170,000 = 0.1235 or 12.35%

The accrual accounting rate of return based on average investment is 12.35%.

3. Net Present Value (NPV) Analysis

To determine if the investment is worthwhile from an NPV standpoint, we need to calculate the present value of all future cash flows and compare it to the initial investment.

Annual After-Tax Cash Flow:

• After-Tax Profit (excluding depreciation) = EBIT + Depreciation - Taxes
• After-Tax Profit (excluding depreciation) = $28,000 + $60,000 - $7,000 = $81,000
• Annual After-Tax Cash Flow = After-Tax Profit (excluding depreciation) + Depreciation
• Annual After-Tax Cash Flow = $81,000 + $60,000 - $60,000 (depreciation is a non-cash expense but provided a tax shield)
• Alternatively: Annual After-Tax Cash Flow = Incremental Margin - Incremental Cash Maintenance Costs - Taxes
• Annual After-Tax Cash Flow = $98,000 - $10,000 - $7,000 = $81,000

Terminal Year Cash Flow:

In the final year (year 5), Marker's will receive the terminal disposal value, which is an after-tax cash inflow since it's assumed to be the book value at that point due to depreciation to terminal value.

• Terminal Disposal Value (After-Tax) = $20,000

Calculate the Present Value of Each Cash Flow:

Using a discount rate of 10%:

• Year 1 PV = $81,000 / (1 + 0.10)^1 = $73,636.36
• Year 2 PV = $81,000 / (1 + 0.10)^2 = $66,942.15
• Year 3 PV = $81,000 / (1 + 0.10)^3 = $60,856.50
• Year 4 PV = $81,000 / (1 + 0.10)^4 = $55,324.09
• Year 5 PV (Operating Cash Flow) = $81,000 / (1 + 0.10)^5 = $50,294.63
• Year 5 PV (Terminal Value) = $20,000 / (1 + 0.10)^5 = $12,418.43

Calculate the Net Present Value (NPV):

• NPV = -Initial Investment + PV of Year 1 + PV of Year 2 + PV of Year 3 + PV of Year 4 + PV of Year 5 (Operating) + PV of Year 5 (Terminal Value)
• NPV = -$320,000 + $73,636.36 + $66,942.15 + $60,856.50 + $55,324.09 + $50,294.63 + $12,418.43
• NPV = $3,472.16

Summary: Since the NPV is positive ($3,472.16), the new equipment is worth investing in from a net present value standpoint at a required rate of return of 10%.

4. Impact of Depreciating to Zero

If the tax authorities allow depreciation down to zero over the 5-year useful life:

• Depreciable Basis = $300,000 + $20,000 - $0 = $320,000
• Annual Depreciation Expense (new) = $320,000 / 5 years = $64,000

Now, let's recalculate the annual net income and after-tax cash flow with this new depreciation schedule:

• EBIT (new) = $98,000 - $10,000 - $64,000 = $24,000

• Income Tax Expense (new) = $24,000 * 0.25 = $6,000

• Annual Net Income (new) = $24,000 - $6,000 = $18,000

• Annual After-Tax Cash Flow (new) = Incremental Margin - Incremental Cash Maintenance Costs - Taxes (new)

• Annual After-Tax Cash Flow (new) = $98,000 - $10,000 - $6,000 = $82,000

In the terminal year, the book value of the asset will be $0. When Marker's liquidates the equipment for $20,000, this will result in a taxable gain:

• Taxable Gain on Disposal = Selling Price - Book Value = $20,000 - $0 = $20,000
• Tax on Disposal = $20,000 * 0.25 = $5,000
• After-Tax Cash Flow from Disposal = $20,000 - $5,000 = $15,000

Recalculate the NPV with the new depreciation schedule:

• Year 1 PV = $82,000 / (1.10)^1 = $74,545.45

• Year 2 PV = $82,000 / (1.10)^2 = $67,768.59

• Year 3 PV = $82,000 / (1.10)^3 = $61,607.81

• Year 4 PV = $82,000 / (1.10)^4 = $56,007.10

• Year 5 PV (Operating Cash Flow) = $82,000 / (1.10)^5 = $50,915.55

• Year 5 PV (Terminal Value) = $15,000 / (1.10)^5 = $9,313.82

• NPV (new depreciation) = -$320,000 + $74,545.45 + $67,768.59 + $61,607.81 + $56,007.10 + $50,915.55 + $9,313.82

• NPV (new depreciation) = $30,158.32

Quantify the Impact:

The NPV with depreciation down to zero is $30,158.32, while the NPV with depreciation to the terminal value is $3,472.16.

• Impact on NPV = $30,158.32 - $3,472.16 = $26,686.16

Yes, if Marker's plans to liquidate the equipment in 5 years, it should take the option to depreciate the new equipment down to zero over its useful life. This choice increases the NPV of the investment by $26,686.16. The reason for this increase is the larger tax shield provided by the higher depreciation expense in the early years, which has a higher present value than the tax paid on the disposal gain in the final year.

Let's analyze Marker's Tattoo Studio's potential investment in the new laser therapy equipment.

1. Expected Increase in Annual Net Income

First, we need to calculate the annual depreciation expense for tax purposes:

• Depreciable Basis = Purchase Cost + Installation Cost - Terminal Value
• Depreciable Basis = $300,000 + $20,000 - $20,000 = $300,000
• Annual Depreciation Expense = Depreciable Basis / Useful Life
• Annual Depreciation Expense = $300,000 / 5 years = $60,000

Now, we can calculate the annual net income:

• Incremental Margin = $98,000
• Incremental Cash Maintenance Costs = $10,000
• Earnings Before Interest and Taxes (EBIT) = Incremental Margin - Incremental Cash Maintenance Costs - Depreciation Expense
• EBIT = $98,000 - $10,000 - $60,000 = $28,000