Question

If we consider the effect of taxes, then the degree of operating leverage can be written as:

DOL = 1 + [FC × (1 – TC) – TC × D]/OCF

Consider a project to supply Detroit with 28,000 tons of machine screws annually for automobile production. You will need an initial $4,800,000 investment in threading equipment to get the project started; the project will last for 5 years. The accounting department estimates that annual fixed costs will be $1,150,000 and that variable costs should be $215 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the 5-year project life. It also estimates a salvage value of $525,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $320 per ton. The engineering department estimates you will need an initial net working capital investment of $460,000. You require a return of 14 percent and face a tax rate of 25.

Required:
a. What is the percentage change in OCF if the units sold changes to 28,000?
b. What is the DOL at the base-case level of output?

Answer 1

a) 0% change

b) 0.393

Step-by-step explanation:

Degree of operating leverage: DOL = 1 + [FC × (1 – TC) – TC × D]/OCF

Machine screws to be supplied = 28,000 tons

Initial investment in threading equipment = $4,800,000

project period = 5 years

annual fixed cost = $1,150,000

variable cost = $215 per ton = 215 * 28,000 = $6,020,000

salvage value of project after dismantling costs = $525,000

selling price of project = $320 per ton = $8,960,000

initial networking capital investment = $460,000

Return = 14%

tax rate = 25% = 0.25

a) Determine the percentage change in OCF if the units sold changes to 28,000

Given : DOL = 1 + [FC × (1 – TC) – TC × D]/OCF

OCF = [(contribution * number of units sold) - fixed costs] * ( 1-tax) + depreciation*tax ----------- ( 1 )

contribution = sales price - variable cost = 320 - 215 = $105

number of units sold = 28,000

depreciation = 4,800,000 / 5 = $960,000

back to equation 1

OCF = [[ ( 105 *28,000) - 1,150,000 ] * ( 1 - 0.25 ) + 960,000 * 0.25 ]

= $1,582,500

Hence the percentage change = 0% ( Initial units to be sold as given in the question = 28,000 as well )

b) Determine the DOL at the base-case level of output

DOL = 1 + [FC × (1 – TC) – TC × D] / OCF

= 1 + [ 1,150,000 * ( 1 - 0.25 ) - 0.25 * 960,000 ] / 1,582,500

= 622501 / 1,582,500 = 0.393