XYZ Steel Corporation is deciding whether to expand operations. The expansion would require purchasing a new...

XYZ Steel Corporation is deciding whether to expand operations. The expansion would require purchasing a new machine for $500,000, with additional $30,000 shipping and installation fees. The machine will be depreciated using a 7-year recovery period (use the percentages given in table 7-3 in the textbook). This project is expected to last 6 years, and the machine is expected to be sold for $200,000 at the end of year 6. In each of the six years of the project (years 1-6) there will be additional revenues of $125,000, and additional expenses of $45,000. Assume 35% tax rate, and 12% cost of capital.

a) Calculate after-tax annual cash flows from the project for years 0-6.

b) Calculate the NPV and the IRR of the project, determine whether it should be accepted, and explain why.

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Expert Solution

Answer :

Purchasing Cost of new Machine = $ 500000

Add: Shipping and Installation Cost = $ 30000

Initial Investment = $ 5,30,000

(a)

	Annual Revenues	125000
Less	Annual Expenses	45000
	Annual Profit	80000
Less	Annual Depreciation	50000
	Profit before tax	30000
Less	Tax	10500
	Profit after tax	19500
Add	Depreciation	50000
	Net Annual Profit After Tax	69500

(b) NPV = Aggregate of PV of cash inflow - Initial Investment

Aggregate of PV of cash inflow = PV of annual cash inflow from 1 to 6 year + PV of terminal cash inflow

= 69500*4.111 + 200000*0.507 = 387114.5

NPV = 387114.5 - 530000 = $ 142886

Calculation of IRR:

IRR is the rate where NPV becomes zero. When r is 3%, NPV is positive and when r is 4%, NPV is negative.

at r=3%, NPVa = 14081.5

at r = 4%, NPVb = -7681

Therefore, IRR lies in between 3 and 4%.

IRR = LDR + (NPVa)*(HDR-LDR)/(NPVa - NPVb)

Where LDR is lower discount rate i.e. 3%

HDR is higher discount rate i.e. 4%

NPVa = 14081.5 (NPV at 3%)

NPVb = -7681 (NPV at 4%)

IRR = 3 + (14081.5 ) * (4 - 3) / (14081.5 +7681) = 3.6471%

IRR of the project = 3.6471%

The project should not be accepted because its NPV is negative and its IRR is even lower than its cost of capital.

jeff jeffy answered 1 year ago

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