Question

Q3. (25 marks) A project requires an initial fixed asset investment of $600,000, which will be depreciated straight line to zero over the six-year life of the project. The pre-tax salvage value of the fixed assets at the end of the project is estimated to be $50,001. Projected sales volume for each year of the project is shown below. The sale price is $50 per unit for the first three years, and $45 per unit for years 4 through 1. A $30,000 initial investment in net working capital is required, with additional investments equal to 75% of annual sales for each year of the project. Variable costs are $35 per unit, and fixed costs are $50,000 per year. The firm has a tax rate of 34% and a required retum on investment of 12% Year Sales 3 15,625 10,000 12,500 19531 24.414 30.518 Calculate NPV by showing detailed calculations O 17 hp ID & A¢ % 5 0) 8 O a 2 3 VA

Answer 1

Requirement:- Calculate NPV by showing detailed calculation.

Solution:- Net present value = Net present value of cash flow - Initial cash outflow

Discounted at required rate of return i.e. 12%

Net present value = [ $100,000 / (1.12)¹ + $124,750 / (1.12)² + $155,688 / (1.12)³ + $194,357 / (1.12)⁴ + $162,132 / (1.12)⁵ + $265,419 / (1.12)⁶] - $630,000

Net Present Value = [ $89,285.71 + $99,450 + $110,810 + $98,912 + $92,015.90 + $134,457.45 ] - $630,000

Net Present Value = $624,931.06 - $630,000

Net Present Value = (5,068.94)

Calculation of Cash flow

Cash flow for year = {[(Revenue - Cost)] * (1 - Tax rate)} + Tax shield due to depreciation

Cash flow for year 1 ={[10,000 * (50 - 35) - $50,000] * (1 - 0.34)} + (600,000 * 0.34) / 6

Cash flow for year 1 = $66,000 + $34,000

Cash flow for year 1 = $100,000

Cash flow for year 2 = {[12,500 * (50 - 35) - $50,000] * (1 - 0.34)} + (600,000 * 0.34) / 6

Cash flow for year 2 = $90,750 + $34,000

Cash flow for year 2 = $124,750

Cash flow for year 3 = {[15,625 * (50 - 35) - $50,000] * (1 - 0.34)} + (600,000 * 0.34) / 6

Cash flow for year 3 = $121,687.5 + $34,000

Cash flow for year 3 = $155,688

Cash flow for year 4 = {[19,531 * (50 - 35) - $50,000] * (1 - 0.34)} + (600,000 * 0.34) / 6

Cash flow for year 4 = $160,357 + $34,000

Cash flow for year 4 = $194,357

Cash flow for year 5 = {[24,414 * (45 - 35) - $50,000] * (1 - 0.34)} + (600,000 * 0.34) / 6

Cash flow for year 5 = $128,132 + $34,000

Cash flow for year 5 = $162,132

Cash flow for year 6 = {[30,518 * (45 - 35) - $50,000] * (1 - 0.34)} + (600,000 * 0.34) / 6

Cash flow for year 6 = $168,419 + $34,000

Cash flow for year 6 = $202,419

Flow for year 6 = Previous amount + Release of Inventory + After tax salvage value

Flow for year 6 = $202,419 + $30,000 + $50,000 (1-0.34)

Flow for year 6 = $265,419

Initial cash outlay = Purchase cost + Increase in Capital

Initial cash outlay = $600,000 + $30,000

Initial cash outlay = $630,000