Question

Mr. Agirich of Aggie Farms is thinking about investing in a center pivot irrigation system to irrigate 100 acres of land. The irrigation system costs $70,000. Mr. Agirich expects that the irrigation system will increase yield and thus operating receipts by $15,000 per year but it will cost $4,000 a year to pay for electricity, maintenance, and additional labor. Mr. Agirich plans on keeping the irrigation system for 4 years before replacing it with a new one and he thinks he can sell it for $50,000 at the end of 4 years. Assume that the Mr. Agirich expects that the inflation rate will be 4% and that operating receipts, operating expenses, and terminal value will increase at the rate of inflation (i.e., operating receipts, operating expenses and terminal value are stated as real dollars, thus, you must convert them to nominal dollars). The bank has offered to lend Mr. Agirich $60,000. The loan will be fully amortized at a 10% interest rate over six years (annual payments). Mr. Agirich anticipates that his marginal tax rate over the next four years will be 20%. The IRS will allow Aggie Farms to depreciate the investment using straight-line over 10 years. Mr. Agirich requires at least a 13% pre-tax, risk-free return on capital and a 2% risk premium on projects of comparable risk to the irrigation system.

THIS QUESTION HAS MULTIPLE PARTS

What is the accumulated depreciation over the four years?

What is the after-tax risk adjusted discount rate?

What is the present value of the after-tax net returns?

What is the present value of tax savings from depreciation?

What is the annual loan payment?

What is the loan balance at the end of the third year?

What is the tax savings from interest payments in the fourth year?

What is the Net Cash Flow after debt flows at the end of the second year?

Financial feasibility is not a problem. True or False?

Answer 1

Accumulated depreciation over 4 years:

Accumulated Depreciation = cost - salvage vale

Cost = $70,000

Salvage value in nominal terms

= $50,000×(1.04)^4 = $58,493

Accumulated Depreciation

= 70,000 - 58,493

= $11,507

After tax risk adjusted discount rate:

Tax rate = 20%

Risk free rate = 13%

After tax Risk free rate = 13×(1-0.20) = 10.4%

Inflation rate = 4%

Risk premium = 2%

After-tax risk adjusted Nominal Rate:

=[ (Post tax Risk free rate) × (Inflation rate) × (Risk premium)] - 1

=[( 1.104)(1.04)(1.02)] - 1

= 17.11%

Therefore After tax risk adjusted discount rate = 17.11%

Present value of after tax net returns:

Calculation of present value of operating cash inflows:

Particulars	year 1	2	3	4
Operating Receipts	11,000×(1.04) = 11,440	11,440×(1.04) = 11,897.6	11,897.6×(1.04) = 12,373.50	12,373.50×(1.04) = 12,868.44
Less: Operating costs	4,000×(1.04) = 4,160	4,160×(1.04) = 4,326.4	4,326.4×(1.04) = 4,499.46	4,499.46×(1.04) = 4,679.44
Net Operating income	7,280	7,571.2	7,874.1	8,189.04
Less: Depreciation [11,507]÷4	2,876.75	2,876.75	2,876.75	2,876.75
EBIT	4,403.25	4,694.45	4,997.35	5,312.29
Less: Interest[ Refer WN 1]	6,000	5,222	4,367	3,426
EBT	(1,596.75)	(527.55)	630.35	1,886.29
Less: Tax@20%	(319.35)	(105.51)	126.07	377.258
EAT	1,916.1	(633.06)	504.28	1,509.032
Add: Depreciation	2,876.75	2,876.75	2,876.75	2,876.75
CFAT	960.65	2,243.69	3,381.03	4,385.78
[email protected]%	0.854	0.729	0.623	0.532
Present value of operating cash inflows	820.395	1,635.65	2,106.38	2,333.23

Present value of operating cash inflows = $6,895.65

Calculation of present value of Terminal cash inflows:

=[ 50,000×(1.04)^4]× PVF(17.11%,4)

= 58,493×0.5316 = $31,095

Present value of Net Returns

= 6,895.65+31,095-70,000

= -32,009.34

WN -1: Amortization of loan:

Year	Opening Balance of principal	Interest@10%	Installment	Principal	Closing Balance of principal
1	60,000	6,000	13,777	7,777	52,223
2	52,223	5,222	13,777	8,555	43,668
3	43,668	4,367	13,777	9,410	34,258
4	34,258	3,426	13,777	10,351	23,907
5	23,907	2,391	13,777	11,386	12,521
6	12,521	1,256	13,777	12,521	-

Present value of tax savings from Depreciation:

= 2,876.75×20% = 575.35

Present value = 575.35×PVAF(17.11%,4)

= 575.35×2.7373

= $1,574.90

Annual Loan Payment:

= 60,000÷PVAF(10%,6)

= 60,000÷4.355

= $13,777

Loan Balance at the end of 3rd year:[ Refer WN 1]

= $34,258

Tax savings on interest on loan for 4th year: [Refer WN 1]

= 3,426×20% = $685.2

Net cash flows after debt at the end of 2nd year:

Operating income for year 2 = 7,571.2

Less: Annual repayment of debt = 13,777

Net cash flows = (6,205.8)

Financial Feasibility:

Financial Feasibility is not a problem - False

As Net Returns from this project is negative, It is not Financially Feasible. Hence Financial Feasibility is a problem