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

Answer : (a.) Calculation of NPV breakeven annual cash flow for the project :

Net Present Value = Present Value of Cash Inflow - Present Value of Cash Outflow

0 = Present Value of Cash Inflow - Present Value of Cash Outflow

Present Value of Cash Outflow = Present Value of Cash Inflow

Let x be the number of units

66,000,000 = {[Number of Units * (Selling Price - Variable Cost)] - Fixed Cost } * (1 - Tax rate) * (PVAF @ 14% for 10 years)  + (Tax shield on Depreciation) * (PVAF @ 14% for 10 years) + (After Tax salvage Value) * (PVF @ 14% fo 10th year)

66,000,000 = {[x * (64 - 24) - 14,000,000} * (1 - 0.25) * (5.21611564608) + {[(66,000,000 - 6,000,000) / 10] * Tax rate * (PVAF @ 14% for 10 years) + (After Tax salvage Value) * (PVF @ 14% fo 10th year)

After tax salvage value is calculated in Working Note

66,000,000 = {40x - 14,000,000} * [(0.75) * (5.21611564608)] + {6,000,000 * 25% * 5.21611564608} + [12,000,000 * 0.26974380949]

66,000,000 = [{40x - 14,000,000} * 3.91208673456] + 7,824,173.46912 + 3,236,925.71388

66,000,000 - 7824173.46912 - 3236925.71388 = 156.483469382x - 54,769214.2837

54,938,900.8171 + 54769,214.2837 = 156.483469382 x

==>156.483469382x = 109,708,115.1

x = 701,084.373533 units

NPV break Even Cash Flows for 1 - 9 years = {[Number of Units * (Selling Price - Variable Cost)] - Fixed Cost } * (1 - Tax rate) * (PVAF @ 14% for 10 years)  + (Tax shield on Depreciation) * (PVAF @ 14% for 10 years)

   = {[(701,0.84.373533 * 40) - 14,000,000} * 0.75] + {[(66,000,000 - 6,000,000) / 10] * Tax rate

= {[28,043,374.9413 - 14,000,000] * 0.75} + {6,000,000 * 0.25}

= 10,532,531.2059 + 1,500,000

= 12,032,531.2059

Annual Cash Flows for 10th year = Annual Cash Flow + After tax salvage Value

= 12,032,531.2059 + 12,000,000

= 24,032,531.2059

(b.) NPV break-even point is the number of units i.e 701,084.373533 units   

Working Note :

After tax salvage Value = Salvage Value - Tax on Gain on Sale

= 14,000,000 - [(Salvage Value - Book Value) * Tax rate]

= 14,000,000 - [(14,000,000 - 6,000,000) * 25%]

= 14,000,000 - [8,000,000 * 25%]

= 14,000,000 - 2,000,000

= 12,000,000