Question

PC Shopping Network may upgrade its modem pool. It last upgraded 2 years ago, when it spent $95 million on equipment with an assumed life of 5 years and an assumed salvage value of $18 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 $25 million per year and decrease operating costs by $10 million per year. At the end of 0 years, the new equipment will be worthless. Assume the firm’s tax rate is 35% and the discount rate for projects of this sort is 10%.

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.)

(95-18)/5=15.4 Annual depreciation

95-(2x15.4)=64.2 Book value at time of sale

b. What are the incremental cash flows in years 1, 2, and 3? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.)

Incremental cash flow = 34.86 million per year

  

c. What are the NPV and IRR of the replacement project? (Do not round intermediate calculations. Enter the NPV in millions rounded to 2 decimal places. Enter the IRR as a percent rounded to 2 decimal places.)

Answer 1

Answers:

a. The Net Cash Flow at the year 0 when the old equipment is replaced shall consist of Cash Inflow from sale of old equipment and Cash Outflow for purchase of new equipment; that is

$ 80 million cash inflow and $ 150 million cash outflow;

thus, net cash flow = $ 150 million - $ 80 million = $ 70 million net cash outflow at year 0

Note: here we have ignored taxation on gain on sale of old equipment; if we need to calculate 35% tax on gain on sale of old equipment than net cash outflow shall increase by 35% of (sale value - book value) = 35% of (80-64.20) = $ 5.53 million

Or we can say that the Net Cash outflow shall be $ 70 + 5.53 = $ 75.53 million

b. Incremental cash flows in year 1, 2 and 3 shall consist of increase in sales by $ 25 million annually + decrease in operating cost by $ 10 million annually + increased tax saving on incremental depreciation due to purchase of new equipment - after tax terminal value that is salvage value of old equipment

Note: Incremental depreciation = Annual Depreciation of new equipment - Annual Depreciation of old equipment = $ 50 million - $ 15.40 million = $ 34.60 million

Saving in tax due to increased depreciation = 35% of $ 34.60 = $ 12.11 million

After tax terminal value of old equipment = 18*(1-0.35) = $ 11.70 million

So,

Total Incremental Cash Inflow = 25 + 10 + 12.11 - 11.70 = $ 35.41 annually

c. NPV and IRR for replacement project:

NPV of replacement project = Present Value of Cash Inflow for years 1,2,3 - Present Value of Incremental cash outflow for year 0 when old equipment is sold

Present Value of Incremental Cash Outflow at year 0 = $ 70 million (if we ignore taxation on gain)

Present Value of Incremental Cash inflow for years 1,2,3 = Annual Incremental Cash Inflow * Present Value Annuity Factor at 6% for 3 years = $ 35.41 million * [(1/1.06)^1 + (1/1.06)^2 + (1/1.06)^3] = $ 35.41 million*2.6730119494616 = $ 94.651353 or $ 94.65 million

So, NPV = 94.65 million - $ 70 million = $ 24.65 million

or NPV = 94.65 - 75.53 = $ 19.12 million

IRR is the rate of return at which NPV is zero. That is at IRR, NPV = $70 million (if we ignore taxation on sale of equipment)

That means we need a Present Value Annuity Factor for 3 years that has a value of $ 70 million / $ 35.41 million = 1.9768

or 75.53/35.41 = 2.13301 if we consider tax on gain on sale of equipment

On seeing the Present Value Annuity Table for 3 years we find that 2.13301 comes for approx 19.20% and 1.9768 comes for approx 24.15%

So, IRR = 19.20% if we consider tax on gain on sale of equipment

and IRR = 24.15% if we ignore tax on gain on sale of old equipment