Question

PC Shopping Network may upgrade its modem pool. It last upgraded 2 years ago, when it spent $110 million on equipment with an assumed life of 5 years and an assumed salvage value of $20 million for tax purposes. The firm uses straight-line depreciation. The old equipment can be sold today for $80 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 $24 million per year and decrease operating costs by $12 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 8%.

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

a)Calculation of the Net cash flows in at time 0, if the old equipment is replaced:-

Depreciation on Old machine :-

Depreciation = (cost of machine - salvage value) / no . of years asset useful = ($ 110 million - $ 20 million) / 5 = $ 18 million

Book value of old machine at end of second year = $110 million - $18 million *2 years =  $ 74 million

Sale proceeds of old machine = $ 80 million

Book value of old machine at the time of sale = $ 74 million

Gain on sale of old machine = $ 6 million

Tax on gain on old machine ($ 6 million *30%) = $1.8 million

Net sale proceeds of old machine after tax = $80 million - $1.8 Million =$ 78.2 million

Net Cash flows:-

Particulars	amount
Cost of the new machine	(150 million)
Less- Net proceeds of old machine	78.2 million
Net Cash outflows at time 0 if the old equipment is replaced	($ 71.8 million)

2) the incremental cash flows in years 1, 2,3 :-

Incremental depreciation expense:-

Depreciation of New machine ( 150/3)	$ 50 million
Depreciation of old machine ( 150/3)	$ 18 million
Incremental in depreciation expense	$ 32million

incremental cash flows in years 1,2,3.

		In millions)
Years	1	2	3
Incremental Sales	24	24	24
Incremetnal Savings in operating cost	12	12	12
Incremetal in depreciation expense	(32)	(32)	(32)
Net incremental earnings before tax	4	4	4
Less- Tax @30%	(1.20)	(1.20)	(1.20)
Net incremental earnings after tax	2.80	2.80	2.80
Add- incremental depreciation	32	32	32
Incremental cash flow per year	34.80	34.80	34.80

Incremental cash flow in year 1 = $ 34.80 million

Incremental cash flow in year 2 = $ 34.80 million

Incremental cash flow in year 3 = $ 34.80 million

3) Calcualation of NPV of the replacement project :-

Calculation of the present value of cash inflows:-

Year	Cash inflows	PV F @8%	Present value
1	34.8	0.9259	32.22million
2	34.8	0.8573	29.83million
3	34.8	0.7938	27.62million
TOTAL	89.68 miilion

Initial investment = Net cash outflows at the start of the project = $ 71,8 million

NPV = present value of cash inflows -initial cash investmen

NPV = $ 89.68 million - $ 71.8 Million = $ 17.88 million

4) Calculation of the IRR of the replacement project :-

we would find the IRR, we taken 20% & 25% two discounts rate.

Year	Cash inflows	PV F @20%	Present value @20%	PV F @25%	Present value @25%
0	-71.8	1	-71.80	1	-71.80
1	34.8	0.8333	29.00	0.8000	27.84
2	34.8	0.6944	24.17	0.6400	22.27
3	34.8	0.5787	20.14	0.5120	17.82
		NPV@20%	1.50	NPV@25%	-3.87

IRR = lower rate + [ NPV at lower rate / ( NPV at lower rate - NPV at higher rate)] * ( Higher rate - lower rate )

IRR = 20% + [ 1.50 / ( 1.50 - (-3.87)] * ( 25% -20%) =21.40%

aehe