Question

1. A 10-year steel pipe-producing project requires $66 million in upfront investment (all in depreciable assets). 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 NPV breakeven annual cash flow for the project.
   2. Calculate the NPV break-even point

Answer 1

Initial investments = $66 millions

Useful life = 10 years

S.P. = $64 per pipe, Variable cost = $24 per widget

Fixed cost = $14 million per year

Depreciation = ($66-$6) million/10 years = $6 million

Salvage value = $14 million

Tax rate = 25%

WACC = 14%

Tax on Capital Gains = (Salvage value – Book value at the end of 10 years)*Tax rate

= ($14-$6) million*0.25

= $2 million

Recovery of Salvage Value after Tax = Salvage value before tax – Tax on capital gains

= $14 million - $2 million

= $12 million

(a)

NPV break even cash flow = Annual cash flow at which NPV is equal to Zero.

Therefore, $66 millions = Cumulative present value of Annual Cash flow for 10 years +Present value of Salvage value after tax

$66 millions = Annual Cash flow*(PVIFA_{14%,10 years})+$12 millions*(PVFA_{14%,10 years})

$66 millions = Annual Cash flow*5.2161+$12 millions*0.2697

$66 millions - $3.2369 million = Annual Cash flow*5.2161

Annual Cash flow = $62.7631 million/5.2161

Annual Cash flow = $12.0326 million

Therefore, Break even Annual cash flow = $12.0326 million

(b) Calculation of NVP Break-even Point:

Annual cash flow at Break even = $12.0326 million

Particulars	Amount ($)
Sales Per pipe	64
Less: Variable Cost per pipe	24
Contribution per pipe	40

Profit after tax = Cash flow - Depreciation

=$12032600-$6000000

= $6032600

Profit before tax = $6032600/0.75 = $8043467

Total Contribution = Profit before tax + Fixed Cost + Depreciation

= $8043467+$14000000+$6000000

= $28043467

Break-even units = Total contribution/Contribution per unit

= $28043467/$40

= 701086 Units