Question

1. Athens Book Nook is experiencing flat sales growth and seeks to grow the business. A proposed project will add a coffee shop to the store. The goal is to create extra book sales by bringing more customers into the store.

The cost of the coffee shop investment will be $250,000 today. The store estimates that the cash flows from ONLY the coffee shop will be $30,000 per year (after-tax cash flows) over a 11-year project period.

The owners of the store estimate that the new coffee area will bring in an additional 200 customers per week. (52 weeks per year) For these new customers, 40% will purchase books and magazines. The average purchase by a customer is $25.00 for books and magazines. The after-tax operating margin for the store is 15%. These cash flows are valued on an annual basis.

The cost of capital for the store is 12% APR, while the marginal tax rate is 34%.  

What is the NPV of the coffee shop project?

2. A company just purchased a new manufacturing machine at a cost of $280,000 today. The machine will require an immediate expense of $20,000 for installation and delivery. The company will depreciate the machine using a 5-year MACRS schedule. What will the depreciation be for this machine in the first year?

Answer 1

1. NPV of the coffee shop project

Step 1:

Calculation of revenue from customers purchasing books and magazines

Number of customers per week = 200

Number of weeks per year = 52

Thus, number of customer per year = 200 * 52 = 10,400 customer

40% will purchase books and magazines, thus 40% of 10,400 customers will purchase = 10,400*40% = 4,160 customers

Average purchase price by customers = $25 per book, thus total purchase = 4,160 customers * $25 = $104,000

After tax operating margin = 15%,

Thus, after tax operating margin = $104,000*15% = $15,600

Step 2:

Discount factor at 12%

Year 1 = 1/(100%+12%)^1 = 0.893

Year 2 = 1/(100%+12%)^2 = 0.797

Year 3 = 1/(100%+12%)^3 = 0.712

Year 4 = 1/(100%+12%)^4 = 0.636

Year 5 = 1/(100%+12%)^5 = 0.567

Year 6 = 1/(100%+12%)^6 = 0.507

Year 7 = 1/(100%+12%)^7 = 0.452

Year 8 = 1/(100%+12%)^8 = 0.404

Year 9 = 1/(100%+12%)^9 = 0.361

Year 10 = 1/(100%+12%)^10 = 0.322

Year 11 = 1/(100%+12%)^11 = 0.287

Calculation of Net Present Value:

Years	Investment in coffee shop	Cash-flows (after tax) from coffee shop	After tax operating margin purchasing books	Cash-flows	Discount factor at 12%	Present value of cash-flows
	(A)	(B)	(C)	(D) = (A)=(B)+(C)	(E)	(D) * (E)
0	(250,000)			(250,000)	1.000	(250,000)
1		30,000	15,600	45,600	0.893	40,714
2		30,000	15,600	45,600	0.797	36,352
3		30,000	15,600	45,600	0.712	32,457
4		30,000	15,600	45,600	0.636	28,980
5		30,000	15,600	45,600	0.567	25,875
6		30,000	15,600	45,600	0.507	23,102
7		30,000	15,600	45,600	0.452	20,627
8		30,000	15,600	45,600	0.404	18,417
9		30,000	15,600	45,600	0.361	16,444
10		30,000	15,600	45,600	0.322	14,682
11		30,000	15,600	45,600	0.287	13,109
Total						20,759

NPV of the coffee shop project = $20,759 (total of all present value of cash flows)

Note:

1. All the cash-flows given in the question are after tax cash-flows. Hence tax rate of 34% is not relevant here.

2. No information is given on depreciation and hence no impact considered on account of depreciation.

2. Depreciation as per MACRS schedule

Cost of equipment = $280,000

Installation and delivery = $20,000

Total Cost of equipment on which depreciation can be claimed = $300,000 ($280,000+$20,000)

Depreciaton schedule for a 5 year class =

Year 1 = 20%

Year 2 = 32%

Year 3 =19.20%

Year 4 = 11.52%

Year 5 = 11.52%

Year 6 = 5.76%

Thus, depreciation per annum =

Year 1 = $300,000* 20% = $60,000

Year 2 = $300,000* 32% = $96,000

Year 3 = $300,000* 19.2% = $57,600

Year 4 = $300,000* 11.52% = $34,560

Year 5 = $300,000* 11.52% = $34,560

Year 6 = $300,000* 5.76% = $17,280

Thus, depreciation for this machine at first year = $60,000