Question

A firm believes it can generate an additional $4,000,000 per year in revenues for 5 years and then $4,500,000 per year in revenues for another 5 years (a total of 10 years) if it replaces existing equipment that is no longer usable with new equipment that costs $6,000,000. The existing equipment has a book value of $50,000 and a market value of $8,000. The firm expects to be able to sell the new equipment when it is finished using it (after 10 years) for $100,000. Variable costs are expected to be 55% of revenue annually. The additional sales will require an initial investment in net working capital of $400,000, which is expected to be recovered at the end of the project (after 10 years). Assume the firm uses straight line depreciation, its marginal tax rate is 20%, and the discount rate for the project is 12%. a) How much value will this new equipment create for the firm? b) At what discount rate will this project break even? c) Should the firm purchase the new equipment? Be sure to justify your recommendation. d) How would your analysis change if the firm believes the project is more risky than initially expected? Be specific.

Answer 1

a) Value new equipment will generate will be the NPV of the cash flows generated by Equipment
NPV = PV of Cash flows - Initial outlay
Initial Outlay = Price of new equipment + Net working capital inv - Market Value of old equipment + Tax rate(Market Value - Book Value of old equipment)
= 6000000 + 400000 - 8000 + 0.2(8000-50000) = 6392000 - 8400 = $6383600
Cash Flow = (Additional Sales-Additional cost)(1-tax rate) + tax rate(Depreciation)
Depreciation = (60000000-100000)/10 = 590000

So, Cash Flow from Year 1 to Year 5 i.e CF₁ to CF₅ = [4000000-0.55(4000000)](1-0.2) + 0.2(590000) =
1440000 + 118000 = 1558000
  Cash Flow from Year 6 to Year 10 i.e CF₆to CF₁₀ = [4500000 - 0.55(4500000)](1-0.2) + 0.2(590000) =
1620000 + 118000 = 1738000
Terminal Cash flow at the end of year 10 = Selling Price of new equipment (1-tax rate) + Net working Capital Inv recovered
= 100000(1-0.2) + 400000 = 480000

Calculating NPV using Texas BAII Plus Professional calculator

Insert CF₀ = -6383600 press Enter
Insert C01 = 1558000 press Enter Insert F01 = 5 ( Since CF₁ to CF₅ are same)
Insert C02 = 1738000 press Enter Insert F02 = 4
Insert C03 = 1738000 + 480000 = 2218000 press Enter Insert F03 = 1

Press NPV , Insert I = 12 ( Since discount rate is 12%) Press Insert NPV press CPT

NPV = $2,942,175.06

b) Discount rate at which Project break evens is IRR i.e Internal rate of return
In calculator Press IRR then CPT
IRR = 21.93%

c) Yes Firm should definitely purchase the new equipment since both NPV and IRR criterias are met as NPV is positive and IRR is much higher than given discount rate.

d) If the project is more risky than initially expected, we will repeat the analysis by taking the impact of risk change into consideration. Since IRR is much higher than discount rate and NPV is great , project can be accepted unless NPV becomes negative and IRR becomes less than discount rate.