Question

You are contemplating the purchase of a new $1,840,000 computer-based dairy cow feeding system. The system will be depreciated straight-line over its ten-year life and have no value at the end of its life. You will earn $250,000 before taxes in the first year from additional milk production and expect an annual growth rate of 4%. Your tax rate is 25%, equity cost 10%, and debt cost 7%. Currently, your farm’s debt to asset ratio is 0.25 and you would like to keep the same financial ratio.

a. Compute the following for this project using after-tax cash flows: (1) payback period, (2) NPV, and (3) internal rate of return. Please also list cash flows for each year.

Answer 1

We compute the cash flows of each year. Following components needs to be considered Initial Capital Outlay, Tax Savings on Depreciation, Increase in Revenue.

Particulars	0	1	2	3	4	5
Capital Outlay (a)	-18,40,000
Tax Savings on Depreciation
Depreciation		1,84,000	1,84,000	1,84,000	1,84,000	1,84,000
Tax Savings (b)		46,000	46,000	46,000	46,000	46,000
Increase in Revenue/ Savings in Cost
Savings		2,50,000	2,60,000	2,70,400	2,81,216	2,92,465
Less Tax		50,000	52,000	54,080	56,243	58,493
Net Savings ©		2,00,000	2,08,000	2,16,320	2,24,973	2,33,972
Operating Cash Flow (b+c)	-	2,46,000	2,54,000	2,62,320	2,70,973	2,79,972
Net Cash Flow (a+b+c)	-18,40,000	2,46,000	2,54,000	2,62,320	2,70,973	2,79,972

6	7	8	9	10
1,84,000	1,84,000	1,84,000	1,84,000	1,84,000
46,000	46,000	46,000	46,000	46,000
3,04,163	3,16,330	3,28,983	3,42,142	3,55,828
60,833	63,266	65,797	68,428	71,166
2,43,331	2,53,064	2,63,186	2,73,714	2,84,662
2,89,331	2,99,064	3,09,186	3,19,714	3,30,662
2,89,331	2,99,064	3,09,186	3,19,714	3,30,662

a) Payback period is the period in which original investment shall come back as cash flows. We observe that cumulative cashflows upto 6th Year is 16,02,595 and upto 7th year it is 19,01,659. Hence Payback period is between 6th and 7th year.  Cash flow after 6th year required to cross original investment is Rs. 237,405 (1840,000 - 1602595) .

Hence, Final Payback period = 6years + 237405/ 299064 = 6.79 years

B) Now, we find the cost of capital.

Cost of debt = Int (1- Tax ) = 7 (1-0.25) = 5.25%

Cost of Equity = 10%

Weight of Debt = 0.25 AND of equity = 0.75

WACC

	Cost	Weight	WACC
Debt	5.25	0.25	1.31
Equity	10.00	0.75	7.50
	Total		8.81

Now we discount the cash flows calculated above @ WACC of 8.81% to find the present value.

Discount Factor for each year = 1/ (1+R)^N i.e for year 1 = 1/ ((1+8.81%)^1) = 0.9190

Particulars	0	1	2	3	4	5
Net Cash Flow (a+b+c)	-18,40,000	2,46,000	2,54,000	2,62,320	2,70,973	2,79,972
Discount Factor @10%	1.0000	0.9190	0.8446	0.7762	0.7134	0.6556
Present Value	-18,40,000	2,26,082	2,14,534	2,03,622	1,93,308	1,83,557

6	7	8	9	10
2,89,331	2,99,064	3,09,186	3,19,714	3,30,662
0.6025	0.5538	0.5089	0.4677	0.4298
1,74,334	1,65,608	1,57,351	1,49,535	1,42,134

Sum of Present Value is -29,935.

c) As we observe, NPV is negative. Hence Discount rate should be reduced such that NPV is zero which will be the IRR.

By various permutation of discount rate we find that @ 8.45987, NPV is nil and that rate is the IRR.

Particulars	0	1	2	3	4
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