Question

The initial investment for this project will be $2.4 million. This amount is for depreciable equipment, which will be depreciated over 4 years using the straight-line method to zero book value. A working capital investment of $300,000 will also be made at the beginning of the project (Time T=0). The entire working capital investment will be recovered at the end of the project.

Initial marketing studies suggest that Earnings before Depreciation and Taxes for 6 years will be as shown in the table. At the end of the sixth year the equipment will be scrapped for $250,000. The company’s tax rate is 30% and the appropriate discount rate for this project is 10%.

Year	1	2	3	4	5	6
EbDT	800,000	1,000,000	1,200,000	1,400,000	1,200,000	800,000

1. List all 7 after-tax cash flows for this project (0 is the initial investment).
2. Compute the NPV.
3. Compute the IRR and payback.

Year	After-tax Cash Flow
0
1
2
3
4
5
6

NPV= __________________________

IRR = __________________________

Payback = ______________________

Answer 1

30% 800000 Tax Rate Wear Earning before depreciation and tax (EBDT) Depreciation Earnings before tax (EBT) = EBDT-depreciation Tax Component Cash Flow from operations Working Capital Initial Investment Scrap Value After tax cash flow Discount Rate 10% 11 3 800000 1000000 1200000 1400000 1200000 600000 600000 600000 600000 200000 400000 500000 800000 1200000 60000 120000 180000 240000 360000 740000 880000 1020000 1160000 840000 800000 240000 560000 300000 -300000 -2400000 250000 840000 1110000 -2700000 740000 880000 1020000 1160000 NPV IRR Payback period 1278887.89 25.28% - 60000 Formulas for the above calculations are as follows Depreciation = Initial investment/No. of years for depreciation in straight line method = 2400000/4=600000 each year Earnings Before Tax (EBT) = Earnings before depreciation and tax (EBDT) - Depreciation Applicable Tax every year = Tax %* EBT. Here, in the question, the given tax rate is 30% Cash Flow from operations = EBDT-Tax. It must be noted that depreciation is not deducted while calculating cash flow as depreciation is an non cash item but has tax benefit. Cash Flow After Tax (CFAT) = -Initial investment-Working Capital+ Scrap Value+ Cash Flow from operations NPV = Sum of all (CFAT/(1+Discounting Rate)"). Where n is the number of years post initial investment. Effectively NPV is the summation of the discounted cash flows every year. Here, the given discounting rate is 10% IRR = IRR is effectively the rate at which the NPV of all cash flows is 0. Hence, in the above equation, when you enter all CFATs and put NPV value as 0, the resultant calculated discounting rate is the IRR Effectively, Sum of all (CFAT/(1+IRR)")=0 Payback period is the period in which the initial investment has been returned in the form of cash flows Here, initial investment is 2700000 The total amount returned in first 3 years in the form of CFAT is 2640000. The fraction of year taken to return the balance 60000 of the initial investment in the fourth year is (60000/1160000) = 0.051 years. Hence, total payback period is 3.051 years