ATPW - AFTER TAX PRESENT WORTH ATIRR - AFTER TAX INTERNAL RATE OF RETURN ATERR-

Question

ATPW - AFTER TAX PRESENT WORTH

ATIRR - AFTER TAX INTERNAL RATE OF RETURN

ATERR- AFTER TAX EFFECTIVE RATE OF RETURN

3. A small business makes an investment of $1,000,000 in equipment that qualifies as 5-year equipment for MACRS-GDS depreciation. The firm takes the maximum Section 179 expense deduction, as well as 50% bonus depreciation. The $CBTCF profile for the investment is given below, including a $200,000 constant dollar salvage value at the end of the 5-year planning horizon. A 40% tax rate and 4% inflation rate apply. The ATMARR, is 8%. Determine a) ATPW, b) ATIRR, and c) ATERR, (5 pts each) EOY SCBTCF 0 -$1,000,000 300,000 400,000 500,00 600,000 900,00 4. In Problem 3, suppose 50% of the investment capital is obtained by borrowing money at an annual compound interest rate of 10%, and 4 payments are scheduled to occur at EOY = 2, 3, 4, and 5, with each payment being $25,000 greater than the previous year's payment. Determine the ATPW. (15 pts) EOY SCBTCF 0 $1,000,000 300,000 400,000 500,000 600,000 900,000

Explanation / Answer

Investmet 1000000 MACRS Depreciation 5 years Year 1 2 3 4 5 6 MACRS Depreciation Rate 20% 32% 19.20% 11.52% 11.52% 5.76% Section 179 deprection Max Max allowable 500000 Residual value after Section 179 (Investment value - Section 179 Depn) =1000000-500000 500000 Bonus Depreciation 50% =50% residual value of investment 250000 Balance amount depreciable (Invt value - Sec 179 - Bonus Depn) =1000000 - 500000 - 250000 250000 Salvage value 200000 constant dollars Inflation rate 4% Salvage value adjusted for inflation = Salvage value *(1+inflation rate)^5 =200000*(1+0.04)^5 243330.6 Tax Rate 40% After Tax MARR 8% Year 0 1 2 3 4 5 Initial Flow -1000000 Before Tax cash Flow 300000 400000 500000 600000 900000 Salvage value 243330.6 300000 400000 500000 600000 1143331 Tax (40%) 120000 160000 200000 240000 457332.2 After Tax cash flow 180000 240000 300000 360000 685998.3 Depreciation 750000 80000 48000 28800 28800 (First year depn will be Sec 179 depn + bonus depn) subsequent will be based on residual investment value) Net cash flows -1000000 930000 320000 348000 388800 714798.3 Discount rate 8% Discount factor (1/(1+discount rate)^year 0.925926 0.925926 0.925926 0.925926 0.925926 Discounted value of cash flows (cash flows * discount factor) 861111.1 296296.3 322222.2 360000 661850.3 After Tax Present value (sum of cash flows) 2501480 After Tax Net Present Worth (AFPresent value - initial investment) 1501480 After Tax Internal Rate of Return =IRR(cash flows) 53% After Tax Effective Rate of Return =(1+afirr)^(1/years) - 1 =(1+0.53)^(1/5) - 1 0.088775 or 8.88% The effective rate is calculated using the following formula Let e be effective rate and n be nominal rate e = (1+n)^years - 1 e+1 = (1+n)^years (e+1)^(1/years) = 1+n n = (e+1)^(1/years) - 1 Borrowed amount 50% of investment =1000000*50% 500000 Rate of interest on loan 10% Repayment period 4 years starting from end of year 2 Instalment end of year with each subsequent payment 25000 higher than previous one Let x be the annual instalment at the end of year 2, then    500000 = x +(x+25000)+(x+25000+25000)+(x+25000+25000+25000) or 500000 = 4x + 150000 or 500000- 150000 = 4 x or 350000 = 4 x or X = 350000/4 = 87500 Hence the annual instalments are as follows Year 1 2 3 4 5 Instalment 0 87500 112500 137500 162500 Calculation of interest on loan 0 1 2 3 4 5 Loan amount 500000 repayment 0 87500 112500 137500 162500 Balance amount 500000 500000 412500 300000 162500 0 Interst at 10% 50000 50000 41250 30000 16250 Before Tax cash Flow -1000000 300000 400000 500000 600000 900000 Interest amount 50000 50000 41250 30000 16250 Cash flows net of interest 250000 350000 458750 570000 883750 Salvage value 243330.6 250000 350000 458750 570000 1127081 Tax at 40% 100000 140000 183500 228000 353500 After tax cash flow 150000 210000 275250 342000 530250 Add Depreciation 750000 80000 48000 28800 28800 Less Loan Instalment 0 87500 112500 137500 162500 Net Cash flows 900000 202500 210750 233300 396550 Discount rate 8% Discount factor 0.925926 0.925926 0.925926 0.925926 0.925926 Present value of cash flows (Net cash flow * discount rate) 833333.3 187500 195138.9 216018.5 367175.9 After Tax Net Present Worth (After tax present value - Initial invt) 799166.7

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