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After-Tax Analysis

After-Tax Analysis. October 25, 2013. Summary of Last Lecture. Our business has to pay taxes. We can deal with this either by doing a pretax analysis and increasing our MARR to take account of the fact that some of our profits will go in tax

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After-Tax Analysis

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  1. After-Tax Analysis October 25, 2013

  2. Summary of Last Lecture Our business has to pay taxes. We can deal with this either by doing a pretax analysis and increasing our MARR to take account of the fact that some of our profits will go in tax Or by doing an after-tax analysis, which is more work but more realistic.

  3. Pre-Tax Analysis

  4. After-Tax Analysis

  5. Pre-Tax and After Tax MARR The company wants an after-tax profit that gives a 20% rate of return on investment. Some portion of the pre-tax profit will be taken away in taxes: Profitpre = Profitafter + taxes $pre = $pre(1-t) + $pret So, must the pre-tax rate of return on investment be greater or less than 20%?

  6. Pre-Tax and After Tax MARR Therefore, our pre-tax MARR should be greater than our after-tax MARR. A good estimate for the pre-tax MARR would be MARRpre = MARRafter/(1-t) where t is the tax rate.

  7. After-Tax Analysis Same as pre-tax analysis, except we use the after-tax MARR and adjust the cash flows to take account of the effects of taxation. Taxation has two main effects: Operating costs and incomes are affected by the tax rate (simple) Capital costs are affected by the tax rate and depreciation allowances (a bit complicated) Details depend on the country we’re in.

  8. Capital Cost Allowance When a company buys a capital asset, it can’t deduct the cost of the purchase from its income. But it can deduct the subsequent annual depreciation of the asset from its income. The rules for how and how fast things depreciate vary from one country to another.

  9. For an after-tax analysis, we reduce the initial cost of a capital acquisition by the present value of the taxes saved by depreciating it. The government groups all possible capital acquisitions into a small number of classes, and sets rules for how fast the assets in a given class can depreciate. You begin each year with a certain amount in each asset class – the `Undepreciated Capital Cost’, or `UCC’ – and depreciate it by the Capital Cost Allowance, or `CCA’.

  10. Algorithm for Calculating Deductions in a CCA Class Start with the undepreciated capital cost UCCn-1 Subtract proceeds from assets sold during the year Add 50% of the cost of asset additions 4. Carry forward the 50% balance from any assets added last year 5. Subtract government assistance payments or tax credits Calculate the CCA for this asset class from the total at step 5: CCA = UCCn-1 * d 7. UCCn = UCCn-1 - CCA

  11. CCA Recapture You buy an asset for $P. It is the only asset in its class, and it depreciates over n years. At the beginning of year n, its book value is UCC(n) If we now sell it for $S, then: 1. If S < UCC(n), no tax is owed. 2. If P > S > UCC(n), you owe tax on S-UCC(n) 3. If S > P, you owe tax on P – UCC(n), and S-P is a capital gain.

  12. Example A start-up company buys a truck for $20,000 After two years, it buys a second truck. The next year, it sells a truck for $16,000 If the company makes $100,000 a year, and the tax rate is 21%, how much tax does the company pay each year? (Trucks are in Asset Class 10, with a CCA rate of 30%)

  13. The CTF When we buy an asset for $P, we can depreciate it in future years at a rate d. Each year we subtract the depreciation amount, P(1-d)nd, from our pre-tax cash flow. So each year we save an amount of money P(1-d)ndt which we would otherwise have paid in taxes. This series of savings has a present worth PW that can be calculated from P,d, t, and our cost of capital, i. So the effective present cost, in an after-tax analysis, is P – PW, or P (1-W). The factor (1-W) is called the CTF

  14. Suppose you are an engineer trying to persuade • your boss to buy a spectrum analyser. • It will be easier to make the case for its purchase • if the CTF is • Higher (closer to 1) • Lower (closer to 0)

  15. CTF = 1 – td/(i+d) The CTF Including the first-year rule, the CTF is: If we ignore the first-year rule, the CCTF is: CTF = 1 - (On no account should you memorise these.)

  16. As the tax rate, t, increases, does the CTF get bigger or smaller? The CTF

  17. As the tax rate, t, increases, does the CTF get bigger or smaller? The CTF As depreciation, d, increases, does the CTF get bigger or smaller?

  18. As the tax rate, t, increases, does the CTF get bigger or smaller? The CTF As depreciation, d, increases, does the CTF get bigger or smaller? As the MARR, i, increases, does the CTF get bigger or smaller?

  19. The tax relief resulting from the depreciation of a capital asset reduces its effective purchase price by the amountP(1-CTF) Possible confusion The tax relief resulting from the depreciation of a capital asset reduces its effective purchase price by the factorCTF

  20. Example: The maintenance department requests $45,000 to buy a new machine. It has an expected life of five years and no salvage value. It will save $23,000 a year, but costs $7,300 a year to operate. It’s in Class 8 (20% CCA), and the company pays tax at 42%. If your after-tax MARR is 12%, should the machine be purchased?

  21. Do a quick pre-tax analysis: If the after-tax MARR is i%, and the company is taxed at t%, then the pre-tax MARR, j, is j = i/(1-t) So in this case the pre-tax MARR is 12/(1-0.42) = 22% So PWpre-tax = -45,000+(23,000-7,300)(P/A,22,5) = $61

  22. This is marginal, so we should do an after-tax analysis for greater certainty: PWafter-tax = -45,000×CTF+(23,000-7,300)(P/A,12,5)(1-t) CTF = 1 - = 1 - = 1 – 0.248 = 0.752

  23. PWafter-tax = -45,000×0.752+(23,000-7,300)(P/A,12,5)(1-0.42) = -33,841 + 15,700 ×3.605 × 0.58 = -$1,014 So in this case, the results of the after-tax analysis contradict those of the pre-tax analysis.

  24. The CTF and Salvage Costs Just as the after-tax first cost of an asset is reduced by the present value of the decreases in tax load resulting from its depreciation… …in the same way, the after-tax salvage value of an asset is reduced, since its depreciation can no longer be deducted from our pre-tax income… CSF = 1 – td/(i+d)

  25. Example: A machine has an undepreciated capital cost of $10,000, and has five years remaining in its physical life (which is also how long its function will be needed.) Its operating costs are $19,000 per year. After the five years are over, its salvage value will be $1,000. A new machine of advanced design can perform the same function with an annual operating cost of $12,000. This new machine costs $24,000, and will have a salvage value of $6,000 in five years. If we sell the old machine now, we’ll only get $8,000. The company pays taxes at 52% and requires an after-tax rate of return of 20%. Both machines are in Class 8 (declining balance at 20% depreciation per year.) Should the old machine be replaced?

  26. We calculate the after-tax present value of upgrading to the new machine: All values in thousands of dollars: Sell old machine: 8×CSF – 1×CSF×(P/F,i,5) Buy new machine: - 24 × CTF + 6×CSF×(P/F,i,5) Annual difference in costs = (19 – 12)(1 – t) PW(Annual difference in costs) = (19 – 12)(1 – t) (P/A,i,5) CSF =1 – td/(i+d) = 1 – 0.52 ×0.2 /(0.2 + 0.2) = 1-0.26 = 0.74 CTF = 1 – 0.26 (1+0.5i)/(1+i) = 1 – 0.26×1.1/1.2 = 0.76 So PW = 8×0.74 – 1×0.74×0.402 – 24×0.76+6×0.74×0.402+7×0.48×3.0 = - $761. (It’s not worth buying the new machine, but it’s close)

  27. So we decide not to buy the new machine. The very next day, two things happen: the old machine blows up, and a representative of Acme Leaseco calls, offering to lease us one of the new machines at $10,000 a year. Do we buy it, or do we lease it?

  28. So we decide not to buy the new machine. The very next day, two things happen: the old machine blows up, and a representative of Acme Leaseco calls, offering to lease us one of the new machines at $10,000 a year. Do we buy it, or do we lease it?

  29. Find the after-tax present worth of leasing rather than buying: Don’t buy new machine: PW =24 × CTF - 6×CSF×(P/F,i,5) = 24×0.76 – 6×0.74×0.402 = 16.44 Pay lease costs: PW = - 10(1-t)(P/A,i,5) = -10×0.48×3.0 = -14.4 (So we should lease)

  30. Depletion Allowance Natural resource companies can sometimes claim a depletion allowance, which is analogous to the depreciation allowance. (This ceased to apply in Canada in 1991, but still holds in the US forest industry, for example.)

  31. Depletion Allowance Example: a tract of timber is purchased for $500,000. There are estimated to be 4,718 cubic metres of timber on the tract, with a market value of $420,000. If 1,036 cubic metres are logged in one year, yielding a profit of $50,000, what depletion allowance should appear on the company books? Depletion allowance = Cost of unit × Units sold/Total Units = 420,000 × 1036 / 4718 = $92,226

  32. Carryback and Carryforward Corporate non-capital losses can be carried back to the previous three years, or forward to the following five years. Capital losses can be carried forward forever. As a result of these carryovers, only about half of Canadian corporations have any taxable income, even in good years.

  33. Carryback and Carryforward Example: a firm sustained a capital loss of $175,000 in 2008. In the preceding three years, it paid the following taxes: What tax refund can they get this year?

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