Question

1. A 10-year steel pipe-producing project requires $66 million in upfront investment (all in depreciable assets), $20.40 million of which is borrowed capital at an interest rate of 6.28% per year. The expected pipe sales are 1,800,000 pipes per year. The expected price per pipe is $64 and the variable cost is $24 per widget. The fixed costs excluding depreciation are expected to be $14 million per year for ten years. The upfront investment will be depreciated on a straight line basis for the 10-year useful life of the project to $6 million book value. The expected salvage value of the assets is $14 million. The tax rate is 25% and the WACC applicable to the project is 14%.
   1. Calculate the accounting Break-even point.
   2. Calculate the DOL, DFL, and DCL (Do your own change in sales).
   3. Calculate the NPV breakeven annual cash flow for the project.
   4. Calculate the NPV break-even point

Answer 1

Answer-A:

Accounting Brak-even point is the point at which business generates zero profit or suffer no loss. It can be calculated as under:

BEP = Fixed Cost /Contribution Per Unit

Step-1: Calculation of Fixed Cost of Project

Fixed Cost= $14 Million + Depreciation

Deprecition (using SLM) = Cost of Project - Residual Value / Economic Life of Project

= (66 - 6)/ 10 = 6 Million

Fixed Cost = 14 + 6 = $20 Million

Step 2: Calculation of Contribution Per Unit:

Contribution per Unit = Sale Price per Unit - Variable Cost per Unit

= 64 - 24 = $ 40 per unit

Step: 3 Calculation of Accounting BEP:

= 20,000,000 / 40 = 500,000 units

Answer-b:

DOL, DFL, DCL are the concepts based on the marginal costing system, so first calculate the profit using marginal costing as follow:

Sales (1800000 * 64)	115200000
Less: Variable Cost (1800000 * 24)	43200000
Contribution	72000000
Less: Fixed Cost	20000000
EBIT	52000000
Less: Interest Payment (20.40 million * 6.28%)	1281120
EBT	50718880
Less: Tax (50718880 * 25%)	12679720
EAT	38039160

Degree of Operating Leverage = Contribution / EBIT = 72000000/52000000 = 1.38

Degree of Financial Leverage = EBIT / EBT = 52000000/50718880 = 1.02

Degree of Combined Leverage = DOL * DFL = 1.38 * 1.02 = 1.41

Answer- C: NPV Break Even Point is the point at which NPV of the project will be zero, It can be calculated using following formula:

EAC + (Annual Fixed Cost * (1 – Tc) – (Annual Depreciation * Tc) / ( Sale Price – Variable Cost)

Step- 1: EAC is the annual equivalent cost of the intial investment in project. It is calculated by dividing the intial investment by the annuity factor equal to economic life of project discount at the rate of cost of project:

    Initial Investment= 66,000,000

    Annuity Factor (10 years, discounted @14%) = 5.2161

EAC = 66,000,000/5.2161 =12,653,131.65

Step-2: Calculate after tax annual fixed cost of the project:

Annual fixed cost excluding depreciation = 14,000,000

Corporate Tax = 25%

After tax Annual Fixed Cost = 14,000,000 (1 – 25%) = 10,500,000

Step 3: Calculate annual tax savings on depreciation of the project:

    Annual depreciation = 6,000,000

    Tax rate = 25%

    Annual Savings = 6,000,000 * 25% = 1,500,000

NPV BEP = (12,653,131.65 + 10,500,000 - 1,500,000) / (64 – 24)

                = 21,653,131.65 / 40 = 541,328 units