Inflation_Replacement_Analysis and taxes

inflation taxes and its details

1. TAXES compulsory contribution to state revenue, levied by the government on workers' income and business profits, or added to the cost of some goods, services, and transactions. Other words used in place of tax are; levy, tariff, duty, toll, excise, impost, contribution, assessment, tribute, tithe, charge, fee

2. INFLATION a general increase in prices and fall in the purchasing value of money.

3. INFLATION RATE the rate at which prices increase over time, resulting in a fall in the purchasing value of money. "the average inflation rate over the decade was 5 per cent"

4. Purchasing Power and Inflation Rates Suppose Ahmad wants to buy golf balls. Each ball costs $5. If he has $1000, how many balls can be purchased now? If he decides to invest $1000 in the bank at compound interest rate of 5.5%, how many ball he can purchase after one year if inflation rate is zero

5. Suppose Ahmad wants to buy golf balls. Each ball costs $5. If he has $1000, how many balls can be purchased now? If he decides to invest $1000 in the bank at compound interest rate of 5.5%, how many ball he can purchase after one year with inflation rate equal to zero Numner of Balls purchased after one year = 1055 / 5 = 211

6. Purchasing Power and Inflation Rates But inflation rate is not zero, it is 2%. How many balls can he purchase after one year?

7. Purchasing Power and Inflation Rates Suppose inflation rate is to be included in the problem, find the number of golf balls purchased after one year for following inflation rates: f = 2, 5, 10, 15

8. Purchasing Power with Increasing Inflation Rate Suppose inflation rate is to be included in the problem, find the number of golf balls purchased after one year for following inflation rates: f = 2, 5, 10, 15 Price after one year is Price * ( 1 + f % )

9. Inflation Free Interest Rate ( i‘)

10. CALCULATIONS WITH REAL INTEREST RATE You receive $ 1.2 million from your father in year 2017. You decide to deposit this gift in bank for a period of 55 years. Bank interest rate is 8% per year . How much you will receive after 55 years in terms of 2017_base year.

11. Suppose Inflation rate is 6%. What is real value of 82.7 Millions based on claculations in year 2017. Since, i = 8% and f = 6%, real ineterst rate i‘ will be

12. CALCULATION OF AFTER-TAX Internal Rate of Return (IRR) Including INFLATION RATE

13. When inflation factor is included in Cash Flow, Zero_Year based Cash Flow is converted to Actual Dollars ($) Cash flow. Example: Suppose a machine‘s initial price is $16000 and salvage value is $1000. It has a life of five years. It will generate cash flow as under: Year Cah Flow -16000 1 4000 2 4000 3 4000 4 4000 5 4000 5 (salvage value) 1000

14. (a) Now convert the Zero_Year based Cash Flow to Actual Dollars using inflation rate of 10% as under

15. Use straight line depreciation method (SLM) and generate After-Tax Cash flow , if Tax Rate is 40%. Solution: Since, B = $ 16000, S = $ 1000, N = 5 Years, d t = ( B – S) / N = ( 16000 – 1000 ) / 5 = $ 3000 Calculation of Taxable Income, Taxes and After-Tax Cash Flow is shown as under:

16. (c) What is ZERO-Year based After-Tax Cash Flow of the Actual Dollars cash flow as found in step (b) Solution: The Actual Dollars Cash Flow as found from part (b) is:

17. To convert the Actual Dollars cash flow to ZERO-Year based After-Tax Cash Flow, multiply it with corresponding (P/F, f, n) factor. ( where f = inflation factor) F ollowing Table shows the conversion of Cash Flow to Zero_Year based

18. Present Worth equation of zero_year based cash flow PW ( i) = -16000 + 3491 ( P / F , i ,1 ) + 3392 ( P / F , i ,2 ) + 3302 ( P / F , i ,3 ) + 3220 (( P / F , i ,4 ) + 3145 ( P / F , i ,5 ) + 1000 ( P / F , i ,5 ) When i = 3%, PW (3%) = 44.85 i = 4%, PW (4%) = -412.35 Interpolation gives us i* = 3.1 % So, After-Tax Internal Rate of Return ( IRR) = 3.1% when inflation factor is 10%

19. Solved Example

20. Before-Tax IRR

21. After-Tax IRR

22. Convert Zero_Year based cash flow to Actual_Dollars Cash flow if Inflation factor is 5%

23. Convert Zero_Year based cash flow to Actual_Dollars Cash flow for Inflation factor of 5%

24. Convert Actual_Dollars Cash flow to Zero_Year based cash flow using conversion factor ( P/F, inflation rate, year). Inflation rate is 5%

25. Find present worth of Zero_Year based cash flow using interest rate of 4 percent

26. Find present worth of Zero_Year based cash flow using interest rate of 5 percent

27. Find Internal Ra te of Return ( IRR )

28. CHOICE OF TECHNOLOGY (REPLACEMENT ANALYSIS)

29. OLD TECHNOLOGY PLANT Initial Price of Old Plant (P o ) Service Life of old Technology Plant (n o ) Operation & Maintenance Costs per year ( OM o ) Annual Equivalent Cost of old Plant ( A o ) Variable Cost per unit ( v o ) Total Fixed Cost of Old Plant ( FC o ) NEW (MODERN) TECHNOLOGY PLANT Initial Price of New Plant ( P n ) Service Life of new Technology Plant ( n n ) Operation & Maintenance Costs per year ( OM n ) Annual Equivalent Cost of new Plant (A n ) Variable Cost per unit ( v n ) Total Fixed Cost of New Plant ( FC n )

30. P o A o A o A o A o 0 1 2 3 n If Old Plant has initial cost P o and service life of n o years, then Annual Equivalent cost of plant A o is found using following formula Total Cost per year for Old Technology , TC o Since Operation & Maintenance cost per year of old Technology is OM o , total fixed cost will be; FC o = A o + OM o Therefore, Total cost of producing Q units per year will be;

31. P n A n A n A n A n 0 1 2 3 n If new Plant has initial cost P n and service life of n n years, then Annual cost of plant A n is found using following formula Total Cost per year for New Technology , TC n Since Operation & Maintenance cost per year of new Technology is OM n , total fixed cost will be; FC n = A n + OM n Therefore, Total cost of producing Q units per year will be;

32. BREAKEVEN QUANTITY Q* At Breakeven point Therefore

33. Quantity to be produced(Q) Costs Old Technology is better in this region New Technology is better in this region BREAKEVEN QUANTITY FOR TWO TECHNOLOGIES If Q < Q*, choose old Technology; if Q>= Q*, choose new Technology

34. Example: Two technologies are under consideration for a manufacturing plant. Company uses 8% as interest rate.   Technology 1 is old styled and has the following attributes: Purchase price = Rs 400,000, Service Life = 10 years, Annual Operation and Maintenance costs are Rs 7800. Variable cost of one unit is Rs 8.9.   Technology 2 is new (modern) and uses automated technology. It has the following attributes: Purchase price = Rs 8,600,000, Service Life = 13 years, Annual Operation and Maintenance costs are Rs 15,800. Variable cost of one unit is Rs 2.7.   Find break-even Quantity (Q*).

35. Solution: i = 8% For OLD Technology,   P o = Rs 400,000, n o = 1 0 years, OM o = Rs 7800. v o = Rs 8.9 per unit.   Find A o from the formula; A o = P o ( A o / P o , i %, n ) = P o ( A o / P o , 8%, 10) = 400,000 ( 0.14903 ) = 59,612 TC o = A o + OM o + v o Q = 59,612 + 7800 + 8.9 Q = 67,412 + 8.9 Q  

36. i = 8%   For NEW Technology P n = Rs 8,600,000, n n = 13 years, OM n = Rs 15800. v n = Rs 2.7 per unit.   Find A n from the formula; A n = P n ( A n / P n , i %, n ) = P n ( A n / P n , 8 %, 13) = 8,600,000 ( 0.12652 ) = 1,088,072 TC n = A n + OM n + v n Q = 1,088,072 + 15800 + 2.7 Q = 1,103,872 + 2.7 Q  

37. Quantity to be produced(Q) Costs Old Technology is better in this region New Technology is better in this region BREAKEVEN QUANTITY FOR TWO TECHNOLOGIES If Q < 167171, choose old Technology; if Q>= 167171, choose new Technology

38. How is unit cost v derived? If Plant/machine capacity is P ( number of units produced per hour) and Labor rate is L ( Rs per hour), then unit cost is Example Suppose Machine produces 3 units per hour ( P = 3) Labor rate is Rs 15 per hour ( L = 15 ) So, unit cost v = L / P = 15 / 3 = Rs 5 per unit

39. Example Suppose the two technologies have following Labor costs and Production rates; Old Technology Plant Labor cost ( L ) = Rs 16 per hour Production Rate ( P ) = 4 units per Hour New Technology Plant Labor cost ( L ) = Rs 8 per hour Production Rate ( P ) = 16 units per Hour Find unit costs v o and v n Note, unit variable cost of old technology is 8 times more than new technology