Question

PC Shopping Network may upgrade its modem pool. It last upgraded 2 years ago, when it spent $85 million on equipment with an assumed life of 5 years and an assumed salvage value of $25 million for tax purposes. The firm uses straight-line depreciation. The old equipment can be sold today for $70 million. A new modem pool can be installed today for $150 million. This will have a 3-year life and will be depreciated to zero using straight-line depreciation. The new equipment will enable the firm to increase sales by $23 million per year and decrease operating costs by $11 million per year. At the end of 3 years, the new equipment will be worthless. Assume the firm’s tax rate is 30% and the discount rate for projects of this sort is 10%. Required: a. What is the net cash flow at time 0 if the old equipment is replaced? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.) b. What are the incremental cash flows in years (i) 1; (ii) 2; (iii) 3? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.) c. What is the NPV of the replacement project? (Do not round intermediate calculations. Enter the NPV in millions rounded to 2 decimal places.) d. What is the IRR of the replacement project? (Do not round intermediate calculations. Enter the IRR as a percent rounded to 2 decimal places.)

Answer 1

Depreciation on Old Machinery for 2 Years : ($ 85 Million - $ 25 Million) x 2 Years / 5 Years

= $ 24 Million

Book Value of the Asset for tax purpose = 85 - 24 = $ 61 Million

Profit on Sale of Old Machinery= 70 - 61 = $ 9 Million

Increase in Income after New Machine = Increase in Sales + Saving in Cost = 23 + 11 = $ 44 Million per year

Discounting Factors are calulated as under :

End of Year 0 = 1

End of Year 1 = 1/ (1+0.1) = 0.9091

End of Year 2 = 1/(1+0.1)^2 = 0.8264

End of Year 3 = 1/(1+0.1)^3 = 0.7513

Calculation of Net Income after Tax as under :

(In Millions)
Year	Particulars	Income	Depreciation	Net Income before tax	Taxes	Net Income after Tax
1	Selliing of Old Machinery	53	-50	3	-0.9	2.1
		(9+44)
2		44	-50	-6	1.8	-4.2
3		44	-50	-6	1.8	-4.2

Calculation of Cash Inflows and Net Present Value :

Year	Particulars	Cash Inflow	Cash Outflow	Net Income After Tax	Depreciation	Net Cash Inflow	Discount Factor	Discounted Cash Flows
0	Sale of Old Machinery	70
	Purchase of New Machinery		-150		0	-80	1	-80.00
1				2.1	50	52.1	0.9091	47.36
2				-4.2	50	45.8	0.8264	37.85
3				-4.2	50	45.8	0.7513	34.41
							Net Present Value	39.63

a. Net Cash Outflow at Year 0 will be $ 80 Million ( 150 -70)

b. Incremental Cash Flows in Year 1 , 2 and 3 are as under :

Year	Net Cash Inflow
1	52.1
2	45.8
3	45.8

c. NPV of the replacement project is $ 39.63 Million.

d. IRR of the replacement project :

For this we need to calculate NPV at a rate at which NPV will be negative. For Discounting Rate of 40% NPV is negative which is shown as under :

Year	Net Cash Inflow	Discount Factor	Discounted Cash Flows
0	-80	1.0000	-80.00
1	52.1	0.7143	37.21
2	45.8	0.5102	23.37
3	45.8	0.3644	16.69
		Net Present Value	-2.73

Now, lets calculate IRR = Lower Rate + NPV at lower rate X (Differece in Dis. Rates)

(NPV at lower rate - NPV at higher Rate)

= 10% + {39.63 X (40-10) / [39.63 - (-2.73)]}

= 10 % + 28.07 % = 38.07 %

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