A project has the following estimated data: price = $79 per unit; variable costs = $41.87...

A project has the following estimated data: price = $79 per unit; variable costs = $41.87 per unit; fixed costs = $6,900; required return = 9 percent; initial investment = $10,000; life = six years. Ignore the effect of taxes.

a. What is the accounting break-even quantity?

b. What is the cash break-even quantity?

c. What is the financial break-even quantity?

d. What is the degree of operating leverage at the financial break-even level of output?

Solutions

Expert Solution

Accounting BEP:
- (SP-VC) x BEP units = Fixed Cost
- (79-41.87) x BEP units = 6900
- BEP Units = 185.8335578
- As there cant be partial units, we should assume it to be 186 units, the next highest integer
Cash BEP:
- We reduce the Fixed cost by depreciation as it is a non cash expense
- (SP-VC) x BEP units = Fixed Cost - Depreciation
- Depreciation = initial investment/life
- Depreciation = 10000/6 = 1666.666667
- (79-41.87) x BEP units = 6900 - 1666.666667
- BEP Units = 140.946225
- As there cant be partial units, we should assume it to be 141 units, the next highest integer

FInancial BEP is when the NPV = 0

$NPV = CF_{0}+\frac{CF_{1}}{(1+r)^1}+\frac{CF_{2}}{(1+r)^2}+...+\frac{CF_{6}}{(1+r)^6}$
$0 = -10000 +\frac{(SP-VC) \times BEP_{units}-FC+Dereciation}{(1.09)^1}+\frac{(SP-VC) \times BEP_{units}-FC+Dereciation}{(1.09)^2}+...+\frac{(SP-VC) \times BEP_{units}-FC+Dereciation}{(1.09)^6}$
Depreciation is added back as it is a non cash expense

$10000 = +\frac{(79-41.87) \times BEP_{units} -6900 +1666.666667}{(1.09)^1}+\frac{(79-41.87) \times BEP_{units} -6900 +1666.666667} {(1.09)^2}+... +\frac{(79-41.87) \times BEP_{units} -6900 +1666.666667}{(1.09)^6}$

Year		0	1	2	3	4	5	6
Units	Calculated		200.983872	200.983872	200.983872	200.983872	200.983872	200.983872
SP	Given		79	79	79	79	79	79
Sale	SP x BEP units		15877.72589	15877.72589	15877.72589	15877.72589	15877.72589	15877.72589
VC per unit	Given		41.87	41.87	41.87	41.87	41.87	41.87
Total VC	VC per unit x BEP units		8415.194719	8415.194719	8415.194719	8415.194719	8415.194719	8415.194719
Fixed cost	Given		6900	6900	6900	6900	6900	6900
Depreciation	Calculated above		1666.666667	1666.666667	1666.666667	1666.666667	1666.666667	1666.666667
EAT	Sale-VC-FC+Depreciation		2229.197833	2229.197833	2229.197833	2229.197833	2229.197833	2229.197833
FCINV	Given	-10000
FCF		-10000	2229.197833	2229.197833	2229.197833	2229.197833	2229.197833	2229.197833
Discount rate factor		1/1.09^0	1/1.09^1	1/1.09^2	1/1.09^3	1/1.09^4	1/1.09^5	1/1.09^6
Discount factor		1	0.917431193	0.841679993	0.77218348	0.708425211	0.649931386	0.596267327
DCF	FCF x Discount factor	-10000	2045.135627	1876.271217	1721.34974	1579.219945	1448.825638	1329.197833
NPV	Sum of all DCF	0

BEP Units = 200.983872
As there cant be partial units, we should assume it to be 201 units, the next highest integer

- $DOL = \frac{(79-41.87) \times 200.983872}{(79-41.87) \times 200.983872 -6900}$
- $DOL = 33494.52$

jeff jeffy answered 2 months ago

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