Question

cost cutting problem: a company is considering the purchase of a new machine. the machine has a cost of $1,500,000. the company believes that revenues will remain at their current levels, however operating costs will be reduced by $380,000 per year. the machine is expected to operate for 10 years. it will be sold for its salvage value of $80,000 at year 5. the company’s current investment in operating net working capital is $150,000. if the company purchases the new machine it can reduce its investment in operating net working capital (nwc) to $110,000. the cca rate is 30%, the tax rate is 40% and the cost of capital is 8%. questions:

1) what is the present value of the salvage value?

2) what is the initial investment in operating net working capital? (hint is there an investment or a reduction?)

3) what is the present value of the operating net working capital recovered at the end of the project? (hint with the new machine does the company recover a larger amount of operating net working capital at the end of the project or a smaller amount?)

4) what is the present value of the operating cash flow (list) approach or what is the present value of the unlevered net income?

5) what is the present value of the cca tax shield?

6) what is the npv?

7) should the firm acquire the new machine?

Answer 1

Ans 1)

First we calculate Depreciation as per CCA rate and Book Value of the Machine after 10 Years.

• Depreciation = CCA Rate * Previous Year Book Value of the Machine = 30% *Previous Year Book Value of the Machine [ For Year 01 Previous Year Book Value will be Purchase price of the M/C ]
• Book Value = Previous Year Book Value of the Machine - Current Year Depreciation

So from the Depreciation table calculate Below Year 10th Book Value = 42371.3

Salvage Value after Year 10 =  $80,000

Applicable Tax on Salvage = ( Salvage Value -  Book Value) * Tax Rate = ( 80,000 - 42371.3) * 40% = 15,051.5

So net cash Flow after 10 Year due to Salvage Value = s = Salvage Value - Applicable Tax = $80,000 - $15,051.5 = $ 64,948.5

pv of the Salvage Value = S / ( 1+r)^n

Here n = 10 Years

r = 8%.

pv of the Salvage Value = S / ( 1+r)^n =  $ 64,948.5 / ( 1+8%) ^ 10 = 30083.7

Ans : present value of the salvage value = $ 30,083.7 (Ans)

Ans 2)

Initial Investment in Net Working Capital =  current investment in operating net working capital - investment in operating net working capital after the Project =  $150,000. - $110,000. = $ 40,000 (Ans) [ + Ve Sign Represent Reduction]

Ans 3)

Investment in Working Capital will recovered after 10 Years of Project.

pv of Recovered Working Capital =  Working Capital /  ( 1+r)^n =  $110,000 / ( 1+8%) ^ 10 = 50,951.3

the present value of the operating net working capital recovered at the end of the project = 50,951.3

Ans :  the present value of the operating net working capital recovered at the end of the project = 50,951.3 (Ans)

4) what is the present value of the operating cash flow (list) approach or what is the present value of the unlevered net income :

Reduction in Cost =  $380,000 per year.

After Tax Reduction in Cost per year. R = $380,000 * ( 1- Tax Rate) = $380,000 * ( 1 - 40%) = 228,000

pv of After Tax Reduction in Cost  

= 228,000 * 6.71

= 1529,880

Ans :  present value of the operating cash flow 1529,880 (Ans)

5)

To calculate PV of CCA Tax shield used cca table :

• Depreciation Tax Shield eachYear = Depreciation * Tax Rate
• PV of Depreciation Tax Shield = Depreciation Tax Shield / ( 1 + r%) ^ Year
• PV of CCA Tax shield = SUM of  PV of Depreciation Tax Shield

Ans : PV of CCA Tax shield = 467,486.5

6)

npv = - ( Initial Investment) + Salvage Value of the N/C (PV) + Reduction in Working Capital + PV of pv of Recovered Working Capital + present value of the operating cash flow + PV of CCA Tax shield

= - 1,500,000 + $ 30,083.7 + $ 40,000 + $ 50,951.3 + $ 1529,880 + $ 467,486.5

= $ 588,503.5

Ans : npv =   $ 588,503.5 (Ans)

7)

should the firm acquire the new machine :

As NPV > 0

Firm Should acquire the machine. (Ans)

1-(1+r)" R* 7

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