Rainbow Products is considering the purchase of a paint-making machine to reduce labor costs. The savings are expected to result in additional cash flows to Rainbow of $5000 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%

• Compute the payback, NPV, and IRR for this machine. Should Rainbow purchase it? Assume all cash flows (except initial purchase) occur at the end of the year and disregard taxes
• For $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 service contract, the machine would then produce cash flows of $4,500 per year in perpetuity. Should Rainbow purchase the machine with the service contract?
• 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 investing 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 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% investment. As long as the 20% reinvestment continues, the cash flows continue to grow at 4% in perpetuity. What should Rainbow do?

Rainbow Products is considering the purchase of a paint-making machine to reduce labor costs. The savings are expected to result in additional cash flows to Rainbow of $5000 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% Please Show the work and explanation a) Compute the payback, NPV, and IRR for this machine. Should Rainbow purchase it? Assume all cash flows (except initial purchase) occur at the end of the year and disregard taxes b) For $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 service contract, the machine would then produce cash flows of $4,500 per year in perpetuity. Should Rainbow purchase the machine with the service contract? c) 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 investing 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 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% investment. As long as the 20% reinvestment continues, the cash flows continue to grow at 4% in perpetuity. What should Rainbow do? Rainbow Products is considering the purchase of a paint-making machine to reduce labor costs. The savings are expected to result in additional cash flows to Rainbow of $5000 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% Please Show the work and explanation a) Compute the payback, NPV, and IRR for this machine. Should Rainbow purchase it? Assume all cash flows (except initial purchase) occur at the end of the year and disregard taxes Pay back = initial investment / annual cash flow = 35000/ 5000 = 7 years NPV = -35000 + 5000/(1+12%) + + 5000/(1+12%) 2.................. + 5000/(1+12%) 15 = NPV = -35000 + 34054 = -945.67 IRR by excel calculator = -35000 + 5000/(1+r) + + 5000/(1+r) 2.................. + 5000/(1+r) 15 = 0 IRR = 11.49% Since NPV is negative we should not accept the project b) For $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 service contract, the machine would then produce cash flows of $4,500 per year in perpetuity. Should Rainbow purchase the machine with the service contract? CF= 5000 - 500 = 4500 per year in perpetuity Cost of capital=12% Present value of perpetuity = CF / interest rate = 4500/12% = $ 37500 NPV=initial investment cash flow + Present value of perpetuity =35,000+(4500/.12)=2500 Since NPV is positive we should accept the project 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 investing 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 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% investment. As long as the 20% reinvestment continues, the cash flows continue to grow at 4% in perpetuity. What should Rainbow do? Formula for Value of growing perpetuity =c/ (rg) G= growth rate = 4%, r is cost of capital =12% C = cash flow after investment next year = $ 4000*(1+g) = $ 4000*(1+4%) = $ 4160 Value=4160/(12%4%)=52000 NPV=initial investment cash flow + Present value of growing perpetuity NPV=35,000+52000=$17,000 Since NPV is positive we should accept the project