Question

This problem concerns the effect of taxes on the various break-even measures. Consider a project to supply Detroit with 30,000 tons of machine screws annually for automobile production. You will need an initial $4,400,000 investment in threading equipment to get the project started; the project will last for three years. The accounting department estimates that annual fixed costs will be $650,000 and that variable costs should be $250 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the three-year project life. It also estimates a salvage value of $260,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $390 per ton. The engineering department estimates you will need an initial net working capital investment of $440,000. You require a return of 18 percent and face a marginal tax rate of 30 percent on this project. Calculate the accounting, cash, and financial break-even quantities. (Do not round intermediate calculations and round your final answers to the nearest whole number, e.g., 32.) Cash break-even Accounting break- even Financial break- even

Answer 1

CASH BREAK EVEN QUANTITY
At the cash break-even, the OCF is zero. Setting the tax shield equation equal to zero and solving for the
quantity, we get:
OCF = [(selling price per unit– variable cost per unit)Quantity- Fixed cost](1- tax rate) + tax rate(initial investment/ number of years)

OCF = 0 = [($390 – $250)QC– $650,000](0.70) + 0.30($4,400,000/3)
0 = (140QC - 650,000)0.7 + 440,000
0 = 98QC-455000 + 440000
98QC= 15000
QC = 153.06
CASH BREAK EVEN QUANTITY = 153

ACCOUNTING BREAK EVEN QUANTITY
The accounting breakeven is calculated as:
QA =[fixed costs+ (initial investment/ number of years)]/(selling price per unit– variable cost per unit)
QA = [$650,000 + ($4,400,000/3)]/($390 – 250)
QA= 2116666.67/ 140
QA= 15,119.05
ACCOUNTING BREAK EVEN QUANTITY = 15,119

FINANCIAL BREAK EVEN QUANTITY
Using the tax shield approach, the OCF is:
OCF = [($390 – 250)(30,000) – $650,000](0.70) + 0.30($4,400,000/3)
OCF= (4200000- 650000)0.7 + 440,000
OCF= 2485000 + 440000
OCF = $2,925,000
And the NPV is:
NPV= - initial investment- net working capital + OCF (PVIFA)_{RATE OF RETURN, NO. OF YEARS}) + + [net working capital - salvage value (1 – tax rate)]/(1 + rate of return ^{no of years})
NPV = –$4,400,000 – 440,000 + $2,925,000(PVIFA_18%,3)
+ [$440,000 + $260,000(1 – .30)]/1.183
NPV= –$4,400,000 – 440,000 + $2,925,000( 2.1743)
+ [$440,000 + $260,000(1 – .30)]/1.643032
NOV = -4840000 + 6359827.5 + 258000/1.643032
NPV= -4840000 + 6359827.5 + 157026.765
NPV = $1,676,854.265‬
To calculate the sensitivity to changes in quantity sold, we will choose a quantity of 35,000. The OCF at
this level of sales is:
OCF = [($390 – 250)(35,000) – $650,000](0.70) + 0.30($4,400,000/3)
OCF= (4900000- 650000)0.7 + 440,000
OCF= 2975000 + 440000
OCF = $3,415,000
The sensitivity of changes in the OCF to quantity sold is:
ΔOCF/ΔQ = ($$2,925,000 – 3,415,000)/(30,000 – 35,000)
ΔOCF/ΔQ = - $490000/-5000
ΔOCF/ΔQ = +98
The NPV at this level of sales is:
NPV == –$4,400,000 – 440,000 + $3,415,000(PVIFA_18%,3)
+ [$440,000 + $260,000(1 – .30)]/1.183
NPV= –$4,400,000 – 440,000 + $3,415,000( 2.1743)
+ [$440,000 + $260,000(1 – .30)]/1.643032
NOV = -4840000 + 7425234.5 + 258000/1.643032
NPV= -4840000 + 7425234.5 + 157026.765
NPV = $2,742,261.265‬
And the sensitivity of NPV to changes in the quantity sold is:
ΔNPV/ΔQ =( $1,676,854.265‬- $2,742,261.265‬))/(30,000 – 35,000)
ΔNPV/ΔQ = -$1,065,407/ -5000‬
ΔNPV/ΔQ = +$213.08
You wouldn’t want the quantity to fall below the point where the NPV is zero. We know the NPV changes
$213.08 for every unit sold, so we can divide the NPV for 30,000 units by the sensitivity to get a change in
quantity. Doing so, we get:
$1,676,854.265‬= $213.08 (ΔQ)
ΔQ = 7869.59 = 7870
For a zero NPV, we need to decrease sales by 7870 units, so the minimum quantity is:
QF= 30,000 – 7870
FINANCIAL BREAK EVEN QUANTITY = 22,130‬
NOTE: As per given instructions intermediate calculations are not rounded off. End calculation are rounded off to nearest whole number