Question

A project requires an initial investment of $1,000,000 and is depreciated straight-line to zero salvage over its 10-year life. The project produces items that sell for $1,000 each, with variable costs of $700 per unit. Fixed costs are $350,000 per year.

1) What is the accounting break-even quantity? What is theoperating cash flow at accounting break-even? What is degree of operating leverage (DOL) at that output level?And what does the DOL indicate?

2) What is the cash flow break-even quantity? What is the operating cash flow at this level of quantity?

3) What is the financial break-even quantity assuming the required rate of return is 10%? What is the DOL at that output level?

Answer 1

Given information:

Initial investment = $1,000,000

Salvage value = $0

Number of life = 10 years

Selling price (p) = $1,000

Variable cost (v) = $700

Fixed cost (FC) = $350,000

Calculations are:

(1)

Depreciation (D) = initial investment/no of life

= $1,000,000 / 10

= $100,000

Accounting breakeven = (FC + D) / (p - v)

= ($350,000+$1,000,000) /($1,000-$700)

= $450,000 / $300

= 1,500 points

Operating cash flow (OCF) = ( S - v - FC - D) + D

= (1500*$1,000 - 1500*$700 - $350,000 - $100,000) + $100,000

= ($1,500,000 - $1,050,000 - $350,000 - $100,000) + $100,000

= $100,000

Degree of operating level (DOL) = 1+(FC/OCF)

= 1 + ($350,000/$100,000)

= 1 + 3.5

= 4.5

(2)

Cash flow break even = (FC + OCF) / (p-v) where OCF = 0

= ($350,000+0)/($1,000-$700)

=1,166.667 points

(3)

N = 10; PV = $1,000,000; I = 10%;

OCF = PMT = $162, 745.39

By using excel formula: =PMT(rate,nper,pv,fv, type)

=PMT(10%,10,1000000,0,0)

$162,745.39

Financial break even = (FC+OCF) /(p-v)

= ($350,000+$162,745.39) / ($1,000-$300)

= $512, 745.39/$300

= 1,709.1513 points

DOL = 1+(FC/OCF)

= 1+($350,000/$162,745.39)

= 1+2.15

= 3.15