BIZOMAT MAKEOS · Money
After-Tax Net Present Value of Two Alternatives with Depreciation Recovery
For two mutually exclusive investments with the same life, what is the after-tax net present value of each, including the tax saved by straight-line depreciation and any gradient in the yearly expense, and which should I choose?
Net present value of two alternatives by the handbook’s present worth formulas: NPV = −P + (AR − AE − (A/G, i, n) G)(1 − TR)(P/A, i, n) + L ÷ (1 + i)ⁿ, plus the after-tax depreciation recovery ATDR = TR (P − L) ÷ n × (P/A, i, n) for straight-line depreciation, with (P/A) = ((1 + i)ⁿ − 1) ÷ (i (1 + i)ⁿ) and (A/G) = 1 ÷ i − n ÷ ((1 + i)ⁿ − 1), and the alternative with the larger NPV chosen.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| After-tax minimum attractive rate of return i | % | Rate of return after tax that an investment must earn. |
| Life of both alternatives n | years | Life in years, the same for both alternatives. |
| Income tax rate TR | % | Rate of income tax on the net income. |
| A: initial cost P | $ | Purchase and installation cost of alternative A. |
| A: salvage value L | $ | Value of alternative A at the end of its life. |
| A: annual revenue AR | $ | Yearly revenue or saving from alternative A. |
| A: annual expense AE | $ | Yearly operating and maintenance expense of alternative A in the first year. |
| A: yearly rise in expense G | $ | Amount by which the expense of A rises each year. |
| B: initial cost P | $ | Purchase and installation cost of alternative B. |
| B: salvage value L | $ | Value of alternative B at the end of its life. |
| B: annual revenue AR | $ | Yearly revenue or saving from alternative B. |
| B: annual expense AE | $ | Yearly operating and maintenance expense of alternative B in the first year. |
| B: yearly rise in expense G | $ | Amount by which the expense of B rises each year. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: After-tax minimum attractive rate of return i
- What it is
- Lowest rate of return after tax that the business accepts on an investment.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0.000001% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher rate lowers both present values.
- Get it right
- Use your company hurdle rate after tax.
What this means: Life of both alternatives n
- What it is
- Number of years both alternatives are kept and depreciated.
- Units and format
- Enter a number in years: years. The form accepts 1 years to 100 years. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 years as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the present worth factors and the yearly depreciation.
- Get it right
- Both must have the same life for this comparison.
What this means: Income tax rate TR
- What it is
- Share of the net income paid as income tax.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Reduces the cash flow and sets the depreciation tax saving.
- Get it right
- Use your marginal company tax rate, e.g. 25 or 30 per cent.
What this means: A: initial cost P
- What it is
- Purchase and installation cost of alternative A.
- Units and format
- Enter a number in $: an amount of money; use one currency for every money input. The form accepts $0 or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with $75000 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Lowers the NPV of A and raises its depreciation recovery.
- Get it right
- Include delivery, installation and commissioning.
What this means: A: salvage value L
- What it is
- Value alternative A can be sold for at the end of its life.
- Units and format
- Enter a number in $: an amount of money; use one currency for every money input. The form accepts $0 or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with $0 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Adds its present value and lowers the depreciation.
- Get it right
- Enter 0 if it will have no resale or scrap value.
What this means: A: annual revenue AR
- What it is
- Yearly revenue or saving that alternative A brings.
- Units and format
- Enter a number in $: an amount of money; use one currency for every money input. The form accepts $0 or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with $25000 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the NPV of A after tax.
- Get it right
- Multiply the yearly output by the selling price, or enter the saving.
What this means: A: annual expense AE
- What it is
- Yearly operating and maintenance cost of alternative A in the first year.
- Units and format
- Enter a number in $: an amount of money; use one currency for every money input. The form accepts $0 or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with $5000 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Lowers the NPV of A after tax.
- Get it right
- Include labour, power, maintenance and consumables.
What this means: A: yearly rise in expense G
- What it is
- Amount the yearly expense of alternative A rises each year.
- Units and format
- Enter a number in $: an amount of money; use one currency for every money input. The form accepts $0 or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with $0 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Adds a growing cost through the gradient factor.
- Get it right
- Enter 0 if the expense stays level.
What this means: B: initial cost P
- What it is
- Purchase and installation cost of alternative B.
- Units and format
- Enter a number in $: an amount of money; use one currency for every money input. The form accepts $0 or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with $35000 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Lowers the NPV of B and raises its depreciation recovery.
- Get it right
- Include delivery, installation and commissioning.
What this means: B: salvage value L
- What it is
- Value alternative B can be sold for at the end of its life.
- Units and format
- Enter a number in $: an amount of money; use one currency for every money input. The form accepts $0 or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with $0 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Adds its present value and lowers the depreciation.
- Get it right
- Enter 0 if it will have no resale or scrap value.
What this means: B: annual revenue AR
- What it is
- Yearly revenue or saving that alternative B brings.
- Units and format
- Enter a number in $: an amount of money; use one currency for every money input. The form accepts $0 or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with $20000 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the NPV of B after tax.
- Get it right
- Multiply the yearly output by the selling price, or enter the saving.
What this means: B: annual expense AE
- What it is
- Yearly operating and maintenance cost of alternative B in the first year.
- Units and format
- Enter a number in $: an amount of money; use one currency for every money input. The form accepts $0 or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with $8000 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Lowers the NPV of B after tax.
- Get it right
- Include labour, power, maintenance and consumables.
What this means: B: yearly rise in expense G
- What it is
- Amount the yearly expense of alternative B rises each year.
- Units and format
- Enter a number in $: an amount of money; use one currency for every money input. The form accepts $0 or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with $0 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Adds a growing cost through the gradient factor.
- Get it right
- Enter 0 if the expense stays level.
Method and formulas
- (P/A, i, n) = ((1 + i)ⁿ − 1) ÷ (i (1 + i)ⁿ); (A/G, i, n) = 1 ÷ i − n ÷ ((1 + i)ⁿ − 1).
- NPV before depreciation = −P + (AR − AE − (A/G) G)(1 − TR)(P/A) + L ÷ (1 + i)ⁿ.
- ATDR = TR × (P − L) ÷ n × (P/A) for straight-line depreciation.
- NPV = NPV before depreciation + ATDR; choose the larger NPV, and neither if both are negative.
- Example: NPV of A is 281.53 and of B 8,161.4.
Limitations
- Both alternatives must have the same life; for unequal lives compare equivalent uniform annual costs.
- Straight-line depreciation over the life is assumed for the tax saving; other schedules change ATDR.
- Tax is taken on the net income each year at a flat rate.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Compare two machines or processes on an after-tax basis
- Include the tax saved by straight-line depreciation
- Allow for a yearly rise in operating expense
Who it is for
- Business owners
- Engineering managers
- Accountants
What you get
- Present worth factor and gradient factor
- Before-depreciation NPV and depreciation recovery of each
- After-tax NPV of each
- The alternative to choose
Interpreting the result
- A positive NPV means the alternative earns more than the minimum rate of return after tax.
- Depreciation recovery favours the alternative with the larger depreciable cost.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 136–141. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Useful alongside · Library collection
NPV, IRR and payback answer different questions: reading investment measures when they disagree
In Investment Appraisal and Business Cases
What it covers: One option has the higher return percentage and faster payback; another creates more value. How to read NPV, IRR and payback together, spot when IRR misleads and make the trade-off visible.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
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