For PART C, what\'s the IRR and the Payback period? I have already solved for pa

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For PART C, what's the IRR and the Payback period? I have already solved for parts A and B.

Investment Analysis and Lockheed Tri Star 1. Rainbow Products is considering the purchase of a paint-mixing machine to reduce labor costs. The savings are expected to result in additional cash flows to Rainbow of $5,000 per year. The machine costs $35,000 and is expected to last for 15 years. Rainbow has determined that the cost of capital for such an investment is 12%. A Compute the payback, net present alue (NPV), and internal rate of return (IRR) for this machine. Should Rainbow purchase it? Assume that all cash flows (except the initial purchase) occur at the end of the year, and do not consider taxes. B] For a $500 per year additional expenditure, Rainbow can get a "Good As New" service contract that essentially keeps the machine in new condition forever. Net of the cost of the servioe contract, the machine would then produce cash flows of $4,500 per year in perpetuity. Should Rainbow Products purchase the machine with the service contract? IC] Instead of the service contract, Rainbow engineers have devised a different option to preserve and actually enhance the capability of the machine over time. By reinvesting 20% of the annual cost savings back into new machine parts, the engineers can increase the cost savings at a 4% annual rate. For example, at the end of year one, 20% of the $5,000 cost savings ($1,000) is reinvested in the machine, the net cash flow is thus $4,000. Next year, the cash flow from cost savings grows by 4% to $5,200 gross, or $4,160 net, of the 20% reinvestment. As long as the 20% reinvestment continues, the cash flows continue to grow at 4% in perpetuity. What should Rainbow Products do? payout of SC HINT: The formula for the present value (Vof an initial end-of-year perpetuity (growing at g%) per period, with a discount rate of k%, is:

Explanation / Answer

(A) Additional Annual Cash Flows = $ 5000 per annum, Machine Cost = $ 35000, Tenure = 15 years and Cost of Capital= 12 %

PV of Additional Annual Cash Flow = 5000 x (1/0.12) x [1-{1/(1.12)^(15)}] = $ 34054.32

NPV = 34054.32 - 35000 = - $ 945.68

Payback Period = Machine Cost / Additional Annual Cash Flows = 35000 / 5000 = 7 years

IRR is the cost of capital which equates the PV of Additional Annual Cash Flows to the initial machine cost. Let the IRR be denoted by r.

Therefore, 35000 = 5000 x (1/r) x [1-{1/(1+r)^(15)}]

Using the EXCEL Goal Seek Function to solve the above equation, we get:

r = 0.1149 or 11.49 %

(B) Extra Annual Expenditure = $ 500, Additional Annual Cash Flows = $ 4500 perpetually, Cost of Capital = 12 %

PV of perpetual annual cash flows = 4500 / 0.12 = $ 37500

NPV of the Project = 37500 - 35000 = $ 2500

As the project's NPV is positive one must undertake this contract.

(C) Reinestment Proportion = 20 % of the annual cost, Growth Rate = 4 % to perpetuity, Cost of Capital = 12 %

Year 1 Cash Flow = $ 4000

PV of Perpetually Growing Cash Flows = 4000 / (0.12 - 0.04) = $ 50000

NPV = 50000 - 35000 = $ 15000

As this alternative generates NPV greate than that generated by a service contract, Rainbow Products should go ahead with this option.

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