Question

PC Shopping Network may upgrade its modem pool. It last upgraded 2 years ago, when it spent $90 million on equipment with an assumed life of 5 years and an assumed salvage value of $17 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.)

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.)

  

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

Greetings,

a.) Net Cah flow at t = 0

Assuming that old equipment was depriciated excluding salvage value of 17m estimated at that time,

annual depriciation would be = (90-17)/5 = 14.60m.

So total depriciation over two year period will be 14.60*2= 29.20m

Remaining Value today = 90 - 29.20 = 60.80m Sale Price today = 80m

Therefore capital gain = 80 - 60.80 = 19.20 Tax on capital gain = 35% of 19.20m = 6.72m

Therefore proceeds net of taxes = 80 - 6.72 = 73.28m (Inflow today)

Outflow today = cost of new modem = 150m Therfore net outflow today = 150 - 73.28 = 76.72 m

b.) Incremetal Annual sales = 25m Annual Cost Saving = 10m Total Benefit = 35m

Post tax Benefit = 35m*0.65 = 22.75m

Depriciation on new equipment = 150/3 = 50m Depriciation on old equipment = 14.60m

Therfore Extra Depriciation = 50 -14.60 = 35.40m

Tax Benefit of the same = 35.40*0.35 = 12.39m

Therefore incremental cash flow in years 1/2 = 22.75 + 12.39 = 35.14m

In year 3, there will be sale of new equipment for NIL, but had we not replaced the old one then it would have fetched us salvage valu of 17m. There would be no capital gains tax on the same as sale price = book value. So due to replacement, there is a loss of 17m in year 3.

Hence year 3 cash flow would be = 35.14 - 17 = 18.14m

Note - Alternatively one may argue that 17m was only for Income tax purpose, hence sale price at year end 3 would have been NIL, so whole 17m would have been loss under tax laws. Therefore tax shield on the same has been lost due to relacement of old equipment as old modem is sold today only at t =0. So tax shield on capital loss would be 17m *0.35 = 5.95m

Hence year 3 cash flow would have been = 35.14 - 5.95 = 29.19m

c.) NPV can be easily calculated in excel as under -

= NPV(rate,value1,value2,......)

=NPV(0.10,35.14,35.14,18.14) = 74.62m minus initial cash flow = 76.72m = -2.10m

IRR can be calculated as under -

=IRR(Values,Guess)

Guess may or may not be entered in excel. But since there is a loss or negative NPV, so IRR got to be less than 10% say 9%.

=IRR(select the range of cells in excel containing Ist outflow and three inflows, guess = 9) = 8.27%