Question

I UILJ.IILI TUN CITUT y JIJ 15: You own a fast food restaurant. It costs you $35,000/yr (before taxes) to employ a cashier. At a tax rate of 35%, you are considering installing an automated kiosk. This would effectively increase your after-tax cash flow by (1-35%)x the $35k the cashier costs you. The machine can be depreciated over 3 years, straight-line, and costs $120,000. It will last 5 years. Should you buy it? (Use a 10% nominal annual discount rate.) The below table may help you; I filled some of it in already. 1 2 3 4 $22,750 $22,750 $22,750 $22,750 $22,750 N/A N/A Year: Increase to CF from lowering labor cost Depreciation tax break Total CF: Advantage to buying machine:

Answer 1

Solution

(Say) You are earning a Gross Profit (Total Revenue - Cost of Goods Sold) is $ 100,000 and it remains stable over the 5 years.

Year	1	2	3	4	5
Tax - Without Cashier (@35%)	$ 35,000	$ 35,000	$ 35,000	$ 35,000	$ 35,000
Tax - With Cashier (@35%)	$ 22,750	$ 22,750	$ 22,750	$ 22,750	$ 22,750
Tax - With Machine (@35%)	$ 21,000	$ 21,000	$ 21,000	$35,000	$35,000
Benefit in terms of Tax	$ 1,750	$ 1,750	$ 1,750	- $12,250	-$12,250

As we can see,by using the automated kiosk,the benefit in the form of taxes @ $1750 is reaped by the business in the initial 3 years when the depreciation is @ 40,000 per year ($120,000 / 3 years) since it can be depreciated only over the 3 years.But since it can be used over a total of 5 years,eventhough the tax paid in this option is additonal $ 12,250 per year but the benefit of not employing the cahier is evident.

In the year 4 and Year 5 , the company (need not make any investment but can reap the benefit equivalent to that of having the cashier.

Gross profit = $ 100,000

Tax = $35,000

After Tax CF = $(100,000 - 35,000) i.e., $65,000

In case they are opted for the 1 st option of using a cashier,in the year 4 and year 5 they would have have:

After Tax CF = $ ( 100,000 - 35,000) * (1-0.35) i.e., $42,250

So now calculating the after tax CF benfits in the year 1 to 3 (when company opted for automated kiosk)

is [ ((100,000 - 35,000) * (1-0.35)) - ((100,000 - 40,000) * (1 - 0.35))]

$3250 per year

Calculating the after tax CF benfits in the year 4 and 5 (when company opted for automated kiosk)

[ (100,000 * (1-0.35)) - ((100,000 - 35,000) * (1 - 0.35))]

i.e., $ 22,750 per year

So,now calcualting the present value of the benefits over the 5 years :

= (3,250 / 1.10) + (3,250 / (1.10 ^ 2)) + (3,250 / (1.10 ^ 3)) + (22,750 / (1.10 ^ 2)) + (22,750 / (1.10 ^ 2))

= 2954.54 + 2685.95 + 2441.77 + 15,538.55 + 14,125.96

= $37,746.77

In terms of percentage 37.74% in savings.

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