5. An investment of $1,250,000 is made in equipment that qualifies as 7-year equ

Question

5. An investment of $1,250,000 is made in equipment that qualifies as 7-year equipment for MACRS- GDS depreciation. Measured in constant dollars, the investment yields annual returns of $130,000, plus a salvage value of $500,000 at the end of the 10-year planning horizon, 80% of the investment capital is obtained by borrowing money at an annual compound interest rate of 12% and the loan is repaid with 5 annual payments. Each payment is 10% greater than the previous payment. The first payment is made 4 years after receipt of the borrowed capital. The maximum Section 179 deduction and 50% bonus depreciation are taken. A 40% tax rate and 3% inflation rate apply. The ATMARR, is 7%. Determine the after-tax present worth. (15 pts)

Explanation / Answer

Year 0 1 2 3 4 5 6 7 8 9 10 Initial Investment -1250000 Section 179 Deduction (Max 500000) 500000 Bonus Depreciation (invt value - Section 179 Depreciation) * 50% 375000 Balance to be depreciated 375000 Depreciation Rate 14.29% 24.49% 17.49% 12.49% 8.93% 8.92% 8.93% 4.46% Depreciation amount 875000 53588 91838 65588 46838 33488 33450 33488 16725 Loan amount (80% of investment) 1000000 Rate of interest (annual compounding 12% Principal at the beginning 1000000 1000000 1120000 1254400 1404928 1573519 1353225 1065583 698421 237697 Interest amount 120000 134400 150528 168591 144988 114170 74831 25468 0 Repayment amount 0 0 0 0 365283 401811 441992 486192 237697 Principal at the end 1120000 1254400 1404928 1573519 1353225 1065583 698421 237697 0 Associated cash Flows 0 1 2 3 4 5 6 7 8 9 10 Initial Investiment -1250000 Annual Return 130000 130000 130000 130000 130000 130000 130000 130000 130000 130000 Salvage Value 500000 Total Earnings (ann return+salvage value) 130000 130000 130000 130000 130000 130000 130000 130000 130000 630000 Tax Rate 40% After Tax cash flow (Earnings * (1-Tax rate) 78000 78000 78000 78000 78000 78000 78000 78000 78000 378000 Depreciation 875000 53587.5 91837.5 65587.5 46837.5 33487.5 33450 33487.5 16725 0 Interest -120000 -134400 -150528 -168591 -144988 -114170 -74831 -25468 0 0 Loan Repayment 0 0 0 0 -365283 -401811 -441992 -486192 -237697 0 Net Cash Flow 833000 -2812.5 19309.5 -25003.9 -385434 -404493 -405373 -400172 -142972 378000 ATMARR 7% Inflation rate 3% 3% 3% 3% 3% 3% 3% 3% 3% 3% Inflation adjusted discount rate 7.21 7.4263 7.649089 7.878562 8.114919 8.358366 8.609117 8.867391 9.133412 9.407415 discount factor (1/(1+discount rate)^year 0.932749 0.86652 0.801621 0.738345 0.676974 0.617768 0.560965 0.506778 0.455387 0.406942 Present value of discounted flow (net flow * discount factor) 776979.8 -2437.09 15478.89 -18461.5 -260929 -249883 -227400 -202798 -65107.6 153824.1 After Tax present worth (total of cash flows) -80733.6 Formula For calcuation of principal repayment Future Value of Investment at end of 4 years = Annual Instalment / (interest rate - growth in repayment){1-[(1+growth rate)/(1+interest rate)]^repayment period Future value of Loan amount at the end of 4 years is taken as there is no repayment in the first four years. growth rate of repayment 10% Annual Compounding rate 12% No of years for repayment 5

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