Question

You work in the Finance Division of a medium size company that is considering a project to supply a customer with 50,000 widgets annually. You will need an initial investment of $4,000,000 in new equipment to get the project started and you estimate that this project will remain active for five years.

The Accounting Department estimated $1,000,000 in annual fixed costs and a variable costs of $200 per unit. Additionally, they told you they will depreciate the initial fixed asset investment straight-line to zero over the five-year project life. Additionally, they are expecting a salvage value of $500,000 after dismantling costs.

The Marketing Department is confident that they will be able to negotiate a contract with the customer to pay $300 per unit. Finally, the Engineering Department informed that they will need an initial net working capital investment of $350,000.

You require a return of 15 percent and face a marginal tax rate of 40 percent on this project.

DOL = 1 + [FC × (1 − T) − T × D]/OCF

1) Suppose you’re confident about your own projections, but you’re not sure if your customer really needs the 50,000 widgets annually.

A) What is the sensitivity of the project OCF to changes in the quantity supplied?

B) What about the sensitivity of NPV to changes in quantity supplied?

C) Given the sensitivity number you calculated, is there some minimum level of output below which you wouldn’t want to operate? Why?

*Please No Handwritten explanations. Also, please provide explanation on how to asses and answer these types of questions.*

Answer 1

a) Calculation of Operating Profit and Operating Cash Flows:

Description	Quantity	Rate/Unit	Value
Sales	50,000 Widgets	$300	$15,000,000
Variable Cost	50,000 Widgets	$200	$10,000,000
Operating Margin	$5,000,000
Fixed Cost	$1,000,000
EBITDA	$4,000,000
Depreciation ($4,000,000-$500,000 (Salvage Value)/5)	$700,000
Earning before interest and Tax (EBIT)	$3,300,000
Tax @ 40%	$13,20,000
Net Profit	$19,80,000
Capital Employed (Initial Investment- $4,000,000 + Working Capital Investment $350,000= $4,350,000)	$4,350,000
Return on Investment (1,980,000/4,350,000)	45.55%

b) Degree of Operating Leverage

Sales-$15,000,000

Fixed Cost (Including Depreciation)-1,700,000

Variable Cost-10,000,000

Degree of Operating Leverage= (Sales-Variable Cost)/(Sales-Variable Cost-Fixed Cost)

=5,000,000/3,300,00

=1.515

c) Break Even Point=Fixed Cost/(Operating margin / unit)

=1,700,000/(5,000,000/50,000)

=17,000 Units

d) Units to be Sold to Earn ROI of 15%

Capital Employed: $4,350,000

After Tax Return ($4,350,000 * 15%) =$652,500

EBIT=$652,500 /(1-40% (tax rate)= 1,087,500

Add Fixed Cost = 1,087,500 + 1,700,000=27,87,500

No. of Units to be Sold= 2,787,500/100= 27875

1) The minimum no. of units required to be sold to achieve 15% ROI is 27875 based on the projections above.

2) Sensitivity of the Project OCF:

OCF=Net Profit + Depreciation

=19,80,000 + 700,000

= 26,80,000

Sensitivity of OCF to Change in Quantity Sold:

Let us consider the case of Units sold of 40,000

OCF= Operating Margin= $100 * 40,000= $ 4,000,000

Tax= (Operating Margin- Fixed Cost-Depreciation)*40%

=($4,000,000-1,000,000-7,00,000)*40%

=920,000

Net Profit=2,300,000-920,000=13,80,000

OCF=Net Profit + Depreciation=1,380,000+ 700,000=2,080,000

The sensitivity of Changes in quantity sold is

(26,80,000-20,80,000)/(50,000-40,000)

600,000/10,000=60

3) I would not want to operate sales below 27,875 units as the return below this level would be less than 15%