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In: Finance

Break-even calculations are most often concerned with the effect of a shortfall in sales, but they...

Break-even calculations are most often concerned with the effect of a shortfall in sales, but they could equally well focus on any other component of cash flow. Dog Days is considering a proposal to produce and market a caviar-flavored dog food. It will involve an initial investment of $90,000 that can be depreciated for tax straight- line over 10 years. In each of years 1 to 10, the project is forecast to produce sales of $100,000 and to incur variable costs of 50% of sales and fixed costs of $30,000. The corporate tax rate is 30%, and the cost of capital is 10%.

  1. a) Calculate the NPV and accounting break-even levels of fixed costs.

  2. b) Suppose that you are worried that the corporate tax rate will be increased immediately after you commit

    to the project. Calculate the break-even rate of taxes.

  3. c) How would a rise in the tax rate affect the accounting break-even point?

Solutions

Expert Solution

CALCULATION OF NPV
I Initial Cash Flow ($90,000)
a Annual Sales $100,000
b=a*50% Annual Variable costs $50,000
c=a-b Annual contribution margin $50,000
d Annual Fixed Cost (excluding depreciation) ($30,000)
e Annual depreciation =90000/10 -$9,000
f=c+d+e Annual Operating Profit (Before Tax) $11,000
g=f*(1-0.3) Annual Operating Profit after tax $7,700
h Add: Annual Depreciation (Non Cash expense) $9,000
i=g+h Annual Operating Cash Flow $16,700
Rate Discount Rate =Cost of Captal 10%
Nper Number of years of cash inflow 10
Pmt Annual Operating cash flow $16,700
PV Present Value of annual operating cash inflow $102,614.27 (Using PV function of excel with Rate=10%, Nper=10, Pmt=-16700)
NPV=PV+I Net Present Value (NPV) $12,614.27
ACCOUNTING BREAKEVEN OF FIXED COST
a Annual contribution margin $50,000
b Annual Depreciation -$9,000
c=a+b Accounting Breakeven Fixed Cost $41,000
(b) BREAKEVEN RATE OF TAXES
a Initial Investment $90,000
b Required Present Value of Cash inflows $90,000
PMT Annual after tax cash inflow required for breakeven $14,647 (Using PMT function of excel with Rate=10%, Nper=10, Pv=-90000)
c Annual Depreciation $9,000
d=PMT-c Annual after tax Operating Profit Required $5,647
e Annual Before tax Operating Profit $11,000
11000*(1-Tax Rate)=5647
BREAKEVEN RATE OF TAXES=1- (5647/11000) 0.486628587
BREAKEVEN RATE OF TAXES=1- (5647/11000) 48.66%
.(c) A Rise in taxes will reduce the after tax accounting profit
This will NOT affect the Break Even sales
Break Even Sales =Fixed Cost/(Contribution Margin Ratio)
These figures are not affected by tax rate

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