Question

Delia Landscaping is considering a new 4-year project. The equipment necessary would cost $173,000 and be depreciated on a 3-year MACRS to a book value of zero. The MACRS percentages each year are 33.33 percent, 44.45 percent, 14.81 percent, and 7.41 percent, respectively. At the end of the project, the equipment can be sold for 10 percent of its initial cost. The project will have annual sales of $110,000, variable costs of $27,700, and fixed costs of $12,300. The project will also require net working capital of $2,900 that will be returned at the end of the project. The company has a tax rate of 40 percent and the project's required return is 12 percent.                                                1. What is the NPV of this project? What is the project's IRR? (5 points/question)                                               2. You feel that both sales and fixed costs are accurate to +/-5 percent. What are the NPVs of this project for both the best and the worst-case scenarios? (15 Points)                                              

"3. How sensitive is the NPV to changes in the sales? How sensitive is the NPV to changes in the fixed cost? (15 points)
sold?"                                              

Answer 1

Step-1 : Depreciation calculation

Depreciation per year = Cost of equipment * MACRS percentage for the year

For Year-1, it shall be 173,000*33.33%. Similarly calculate for others

Cost of equipment (a)

Year	Precentage	Depreciation per year
1	33.33%	57,661
2	44.45%	76,899
3	14.81%	25,621
4	7.41%	12,819

Step-2 Cash outflow at the begining of the project = Cost of Equipment + Net Working Capital = 173000+2900 = 175900

Step-3 Calculation cash inflows &NPV

Particulars	Year-1	Year-2	Year-3	Year-4
Sales	1,10,000	1,10,000	1,10,000	1,10,000
Less Variable Costs	(27,700)	(27,700)	(27,700)	(27,700)
Less Fixed Costs	(12,300)	(12,300)	(12,300)	(12,300)
Less Depreciation	(57,661)	(76,899)	(25,621)	(12,819)
Profit before Tax (PBT)	12,339	(6,899)	44,379	57,181
Less: Tax @ 40% (PBT * 40%)	(4,936)	2,759	(17,751)	(22,872)
Profit after Tax	7,403	(4,139)	26,627	34,308
Add: Depreciation	57,661	76,899	25,621	12,819
Cash Flow before considering Working Capital	65,064	72,759	52,249	47,128
Add: Net Working Capital	-	-	-	2,900
Add: After tax value of equipment				10,380
Final Cash Flows (a)	65,064	72,759	52,249	60,408
Discount rate @ 12% (b)	0.893	0.797	0.712	0.636
Discounted Cash Flows (a/b)	72,872	91,269	73,405	95,053
Total DCF				3,32,600
Cash outflow				(1,75,900)
NPV				1,56,700

After tax value = (Sale value - Book Value)* (1-tax) = (17,300-0)*(1-0.40)

IRR is the rate at which NPV of the project equals to zero. For this we need to estimate a discount rate and calculation the discounted cashflows. There is no shortcut to identify the discount rate. By trail and error method, IRR should be close to 28%

2 Best case: When sales increases by 5% and Fixed costs decreases by 5%

Particulars	Year-1	Year-2	Year-3	Year-4
Sales	1,15,500	1,15,500	1,15,500	1,15,500
Less Variable Costs	(27,700)	(27,700)	(27,700)	(27,700)
Less Fixed Costs	(11,685)	(11,685)	(11,685)	(11,685)
Less Depreciation	(57,661)	(76,899)	(25,621)	(12,819)
Profit before Tax (PBT)	18,454	(784)	50,494	63,296
Less: Tax @ 40% (PBT * 40%)	(7,382)	313	(20,197)	(25,318)
Profit after Tax	11,072	(470)	30,296	37,977
Add: Depreciation	57,661	76,899	25,621	12,819
Cash Flow before considering Working Capital	68,733	76,428	55,918	50,797
Add: Net Working Capital	-	-	-	2,900
Add: After tax value of equipment				10,380
Final Cash Flows (a)	68,733	76,428	55,918	64,077
Discount rate @ 12% (b)	0.893	0.797	0.712	0.636
Discounted Cash Flows (a/b)	76,981	95,872	78,560	1,00,826
Total DCF				3,52,239
Cash outflow				(1,75,900)
NPV				1,76,339

Worst Case: Sales decreases by 5% and fixed costs increases by 5%

Particulars	Year-1	Year-2	Year-3	Year-4
Sales	1,04,500	1,04,500	1,04,500	1,04,500
Less Variable Costs	(27,700)	(27,700)	(27,700)	(27,700)
Less Fixed Costs	(12,915)	(12,915)	(12,915)	(12,915)
Less Depreciation	(57,661)	(76,899)	(25,621)	(12,819)
Profit before Tax (PBT)	6,224	(13,014)	38,264	51,066
Less: Tax @ 40% (PBT * 40%)	(2,490)	5,205	(15,305)	(20,426)
Profit after Tax	3,734	(7,808)	22,958	30,639
Add: Depreciation	57,661	76,899	25,621	12,819
Cash Flow before considering Working Capital	61,395	69,090	48,580	43,459
Add: Net Working Capital	-	-	-	2,900
Add: After tax value of equipment				10,380
Final Cash Flows (a)	61,395	69,090	48,580	56,739
Discount rate @ 12% (b)	0.893	0.797	0.712	0.636
Discounted Cash Flows (a/b)	68,763	86,667	68,251	89,279
Total DCF				3,12,960
Cash outflow				(1,75,900)
NPV				1,37,060

3 Since even in the worst case the company is earning positive NPV, the company is not sensitive to any of the factors