Question

b) (3+1+3) You are considering a new investment project, which lasts for three years. The project requires a purchase of a new machine, which costs $300,000. This initial investment can be depreciated to zero over the next three years according to a straight line depreciation rule. The machine has no salvage value at the end. Operating revenue is projected to be $200,000 per year. Operating costs for raw materials are $50,000 The corporate tax rate is 30% and the risk-adjusted discount rate is 10%. (i) Compute after-tax cash flows every year. (ii) Should we take the project and why? (iii) Suppose that you need to purchase an inventory of raw materials now (year 0) instead of year by year in the next three years. This will require an initial expense of $150,000 in inventory, which will then be depleted, by equal amount every year in the next three years. How would your answers to the above questions change?

Answer 1

Dear Student

Please note the solution

(i) After tax cash inflows

Particulars	Calculation	Amount
Operating Revenue		200,000
Less: Operating Cost		(50,000)
Less: Depreciation	300000/3	(100,000)
Profit Before tax		50,000
Less: Tax	50000*30%	(15,000)
Profit After Tax		35,000
Add: Depreciation		100,000
After Tax cash flows		135,000

(ii) Decision

If the NPV is positve then project should be taken otherwise not be taken.

NPV = Present Value of Cash inflow - Present Value of Cash Outflow

• Present Value of Cash inflow = After Tax Cashinflows * Present value annuity factor ( rate, years )

= 135,000 * [ 1/1.10 + 1/1.10² +1/1.10³ ]

= 135,000 * 2.4869

= 335,725.02

• Present Value of Cash Outflow = 300,000

• NPV = 335,725.02 - 300,000

= 35,725.02 Answer

Since NPV is positive hence project should be undertaken.

(iii)  

After tax cash inflow

Particulars	Calculation	Amount
Operating Revenue		200,000
Less: Operating Cost		(50,000)
Less: Depreciation	300000/3	(100,000)
Profit Before tax		50,000
Less: Tax	50000*30%	(15,000)
Profit After Tax		35,000
Add: Depreciation		100,000
Add: Cost of Raw Material		50,000
After Tax cash flows		185,000

NPV = Present Value of Cash inflow - Present Value of Cash Outflow

• Present Value of Cash inflow = After Tax Cashinflows * Present value annuity factor ( rate, years )

= 185,000 * [ 1/1.10 + 1/1.10² +1/1.10³ ]

= 185,000 * 2.4869

= 460,067.62

• Present Value of Cash Outflow = 300,000 + 150,000

= 450,000

• NPV = 460,067.62 - 450,000

= 10,067.62 Answer

Since NPV is positive hence project should be undertaken.

Stay Safe!!