Section _4--Breakeven

# Section _4--Breakeven - Section#4 Solutions Breakeven...

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Section #4 Solutions Breakeven Analysis and Operating Leverage September 22nd, 2010

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1. Net Income and Operating Cash Flow With Taxes NI = [ (P v)Q FC D ][ 1 t c ] a. Write an expression for net income in terms of quantity sold, price, variable cost, fixed cost, depreciation, and the corporate tax rate.
b. Write an expression for operating cash flow. OCF = (P v)Q FC Tax Taxable Income = [ (P v)Q FC ][ 1 t c ] + t c D = (P v)Q FC t c [(P v)Q FC D] = [ (P v)Q FC ][ 1 t c ] + t c D D + D = [ (P v)Q FC ][ 1 t c ] D[1 t c ] + D = [ (P v)Q FC D ][ 1 t c ] + D = NI + D

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What does operating cash flow equal when net income is zero? When NI=0, OCF=D … in words, when net income equals 0 the operating cash flow equals the depreciation expense for that period. (This was stated on page 350, line 1, of your text (RWJ, 2010) in the first sentence of the "Payback and Break-Even" subsection.)
c. Solve for Q from the expression in (b) in terms of OCF and the other variables: OCF = [ (P v)Q FC ][ 1 t c ] + t c D OCF t c D = [ (P v)Q FC ][ 1 t c ] OCF t c D 1 t c = (P v)Q FC OCF t c D 1 t c + FC = (P v)Q Q = OCF t c D 1 t c + FC P v

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If t c =0, the previous result is the same as Equation (11.3) on page 350 of Ross, Westerfield, and Jordan (2010): Q = OCF + FC P v Contribution Margin
2. Breakeven Analysis and Operating Leverage a. What is the project’s annual operating cash flow? From the solution to question #1(b), OCF = [ (P v)Q FC D ][ 1 t c ] + D OCF Q=35,000 tons = [ (\$230/ton \$185/ton)(35,000 tons) \$450,000 \$640,000 ][ 1 .38 ] + \$640,000 So, = [ \$1,575,000 \$450,000 \$640,000 ][.62] + \$640,000 = [\$485,000][.62] + \$640,000 = \$300,700 + \$640,000 = \$940,700

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b. What is the project’s accounting breakeven? The accounting break-even is defined as the
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Section _4--Breakeven - Section#4 Solutions Breakeven...

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