Question

Question 4 (15 pts): Your firm is considering a new project to improve its sales channels. Buying a new truck for $100,000 to deliver more goods to customers will increase sales $35,000 and costs of goods sold $12,000 per year. The cost of the truck will be paid in 2 installments. The first installment will take place at the time of the purchase at year 0, at $60.000. The second installment will be paid at the end of year 1, $40,000. The truck will be depreciated straight-line to $10,000 at the end of year 5. Your company will be able to sell the truck for $8,000 when the project is completed. Your company will be able to reduce working capital by $70,000 at the beginning of the project. The tax rate is 30% and discount rate is 10%. a) (8 pts) Please find IRR and NPV of the project. (If you use excel to solve this question, please copy your solution and answers to this page).

b) is there a conflict or agreement with the NPV and IRR rules? How do you explain the situation?

c) would you do the project? why?

Answer 1

a). NPV = 16,560.91

IRR = 17.35%

Calculations are as shown below:

Formula	Year (n)	0	1	2	3	4	5
	Investment	-60,000.00	-40,000.00
	Sales		35,000.00	35,000.00	35,000.00	35,000.00	35,000.00
	Less: COGS		12,000.00	12,000.00	12,000.00	12,000.00	12,000.00
	Less: Depreciation		10,000.00	20,000.00	20,000.00	20,000.00	20,000.00
	EBIT		13,000.00	3,000.00	3,000.00	3,000.00	3,000.00
30% of EBIT	Less: Tax @30%		3,900.00	900.00	900.00	900.00	900.00
	Net income		9,100.00	2,100.00	2,100.00	2,100.00	2,100.00
	Add: Depreciation		10,000.00	20,000.00	20,000.00	20,000.00	20,000.00
Net income+Dep.	Operating cash flow		19,100.00	22,100.00	22,100.00	22,100.00	22,100.00

Depreciation calculation:

Straight-line depreciation for first payment = 60,000/5 = 12,000

Straight-line depreciation for second payment = 40,000/4 = 10,000

Since Book Value at the end of Year 5 is 10,000

So, depreciation expense for Year 1 = 12,000-2,000 = 10,000

Depreciation expense for Years 2 to 5 = (12,000+10,000)-2,000 = 20,000

Formula	Year (n)	0	1	2	3	4	5
	Investment	-60,000.00	-40,000.00
	Operating cash flow		19,100.00	22,100.00	22,100.00	22,100.00	22,100.00
	Change in net working capital	70,000.00					-70,000.00
Salvage value - tax-rate*(Salvage value-Book value)	After-tax salvage value						8,600.00
	Add: Total cash flow	10,000.00	-20,900.00	22,100.00	22,100.00	22,100.00	-39,300.00
	Discount factor @10%	1.00	0.91	0.83	0.75	0.68	0.62
	Present value of cash flow	10,000.00	-19,000.00	18,264.46	16,604.06	15,094.60	-24,402.21
	NPV	16,560.91
	IRR	17.35%

Note:

1. In after-tax salvage value calculation, since book value is greater than the salvage value, the tax amount is being saved and thus, added to the salvage value.

2. Since Net Working Capital is being reduced at the beginning of the project, it is will increased by the same amount, at the end of the project i.e. end of Year 5.

b). There is no conflict between the NPV and IRR rules since NPV is positive and IRR is greater than the cost of capital.

c). Since, NPV is positive and IRR is greater than the given cost of capital (10%), the project can be undertaken.