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

Delia	0	1	2	3	4
MACRS		33.33%	44.45%	14.81%	7.41%
Investment	-173,000
NWC	-2,900				2,900
Salvage					17,300
Sales		110,000	110,000	110,000	110,000
VC		-27,700	-27,700	-27,700	-27,700
FC		-12,300	-12,300	-12,300	-12,300
Depreciation		-57,661	-76,899	-25,621	-12,819
EBT		12,339	-6,899	44,379	57,181
Tax (40%)		-4,936	2,759	-17,751	-22,872
Net Income		7,403	-4,139	26,627	34,308
Cash Flows	-175,900	65,064	72,759	52,249	60,408
NPV	$15,776.19
IRR	16.32%

Depreciation = Investment x MACRS %

Cash Flows = Investment + NWC + Salvage x (1 - tax) + Net Income + Depreciation

NPV and IRR can be calculated using the same function in excel or calculator with 12% discount rate.

2) Best case scenario will be when sales are +5% and FC are - 5% => NPV = $26,920.22

Delia	0	1	2	3	4
MACRS		33.33%	44.45%	14.81%	7.41%
Investment	-173,000
NWC	-2,900				2,900
Salvage					17,300
Sales		115,500	115,500	115,500	115,500
VC		-27,700	-27,700	-27,700	-27,700
FC		-11,685	-11,685	-11,685	-11,685
Depreciation		-57,661	-76,899	-25,621	-12,819
EBT		18,454	-784	50,494	63,296
Tax (40%)		-7,382	313	-20,197	-25,318
Net Income		11,072	-470	30,296	37,977
Cash Flows	-175,900	68,733	76,428	55,918	64,077
NPV	$26,920.22

Worst case scenario will be when sales are - 5% and FC are + 5% => NPV = $4,632.15

Delia	0	1	2	3	4
MACRS		33.33%	44.45%	14.81%	7.41%
Investment	-173,000
NWC	-2,900				2,900
Salvage					17,300
Sales		104,500	104,500	104,500	104,500
VC		-27,700	-27,700	-27,700	-27,700
FC		-12,915	-12,915	-12,915	-12,915
Depreciation		-57,661	-76,899	-25,621	-12,819
EBT		6,224	-13,014	38,264	51,066
Tax (40%)		-2,490	5,205	-15,305	-20,426
Net Income		3,734	-7,808	22,958	30,639
Cash Flows	-175,900	61,395	69,090	48,580	56,739
NPV	$4,632.15

3) Sensitivity = Change in NPV / Change in input

For Sales, 1% increase in sales increases NPV by $2,004.65 which is its sensitivity.

For FC, 1% increase in FC, decreases NPV by $224.16, which is its sensitivity.