Question

5 Years ago, Abel Corp spent $75,000 to explore the construction of a new plant, but decided not to. Now, a New plant is again under consideration. It would cost $1,000,000,000, and require an initial investment in working capital of $1,000,000. The plant would have a 25 year useful life, and be depreciated on a straight line basis. The initial level of working capital would increase by $500,000 every year for 25 years. In year 26, all pant activity would stop, so that the plant could be deconstructed (worthless) and the working capital could be reduced to 0. The plant would provide annual revenues of $60,000,000, and annual direct expenses of $15,000,000. Assume a corporate tax rate of 40%.

What is the NPV of the project at a discount tate of 4%?

What is the IRR, and can the simplified IRR rule be used for this project?

Answer 1

We are given an initial investment outlay of $1,000,000,000 (1 billion) + 1,000,000 in working capital. The amount spent on exploring the site is the sunk cost and will not be considered for calculating the NPV of the project.

Total life is 25 years and depreciation is charged on a straight-line basis so annual depreciation equals 1,000,000,000/25 = 40,000,000.

Annual revenue = $60,000,000

Annual expenses = $15,000,000

NPV = -Initial cash outflow + present value of cash flow from year1 + present value of cash flow from year2......... present value of cash flow from year25

We can calculate the cash flows by a formula  

Cash flow = (Sales - operating cost - annual depreciation)(1-Tax rate) + Annual Depreciation.

Depreciation is a non-cash operating expense and it reduces the amount of tax paid by the firm, so we add it back to the net income.

Initial Cash outlflow		1001000000
Total Life		25 yrs
Annual Depreciation		40000000
Revenue		60000000
Tax rate		40
Annual Expense		15000000
Increase in Working capital		500000	1000000	1500000	2000000	2500000	3000000	3500000	4000000	4500000	5000000	5500000	6000000	6500000	7000000	7500000	8000000	8500000	9000000	9500000	10000000	10500000	11000000	11500000	12000000	12500000
Year		1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25
Cash Flow	-1001000000	42700000	42400000	42100000	41800000	41500000	41200000	40900000	40600000	40300000	40000000	39700000	39400000	39100000	38800000	38500000	38200000	37900000	37600000	37300000	37000000	36700000	36400000	36100000	35800000	35500000
Present value of cash flows		41057692.31	39201183	37426747	35730815	34109975	32560958	31080639	29666022	28314245	27022567	25788363	24609124	23482447	22406033	21377683	20395292	19456846	18560417	17704162	16886317	16105193	15359176	14646721	13966349	13316646
		42700000/(1.04)^1	42400000/(1.04)^2
Sum of Cash flows		620231614.4
NPV		-380768386
IRR		-0.19%

We get a negative NPV and IRR less than the required rate of return(4%) so this investment is not suitable.