Sink and Tap Inc. is looking at a 4-year project for making taps. Initial investment in equipment will be $754,000. Each unit will be sold for $230. Annual fixed costs, not including depreciation, will be $333,000. Variable costs per unit will be $102.40. The applicable discount rate is 12 percent, and the tax rate is 21 percent. Assume straight- line depreciation to zero and no market salvage value. Use goal seek (or any other method) to find the present value break-even point in units per year. Select one:
a. 5340
b. 5930
c. 4848
d. 4680
e. 5200

the present value break-even point in units per yea is 4680 units. the option (d) is correct

Explanation:

Solution

Given that:

The initial cash flow = $754,000

The project life is  = four years

Thus,

Contribution = sales - variable costs

So,

Sales = quantity * the price

Let the Quantity be Y

$230 Y - $102.40 Y

=127.60 Y

Now,

The operating income = Contribution -fixed costs

which is,

127. 60 Y- (Other depreciation or decrease + decrease)

127. 60 Y- ( $333,000 + ($754,000/4))

= 127. 60 Y- ( $333,000 + $188,500)

Thus,

127. 60 Y - $521, 500

Now,

Tax rate at 21% on operating income is =26.796 Y - 109. 515

The profit after tax = operating income - tax

(127. 60 Y - $521, 500) -(26.796 Y - 109. 515)

= 100.804 Y - 411, 985

Additional depreciation = $188, 500

The operating cash inflow per year = 100.804 Y - 411, 985 +  $188, 500

Thus,

The PVAF for 12 years , 4% = 3.037349

PV of operational cash inflow = 306.18 Y - 678, 802.02

However,

For the break even point: the initaila cash flow = The PV of functioning or operational cash inflow

So,

306.18 Y  - 678, 802.02 =$ 754,400

306.18 Y = 1, 432, 802.02

Y = 4680 Units

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