1. Rainbow Products is considering the purchase of a paint-mixing machine in order to reduce labor costs. The savings are expected to provide the additional cash flows of $5,000 per year.

The machine costs $35,000 and will last for 15 years. The cost of capital for this investment is 12% a) The payback period of this project is 7 years. The sum of cash flows during the first seven years equal the initial investment. The net present value (NPV) and IRR of this project is -$945. 8, and 11. 49% respectively.

As the project has negative NPV and the IRR is lower than the cost of capital, Rainbow should not purchase the machine. b) If Rainbow pays additional $500 per year, Rainbow can get a service contract that keeps the machine in new condition forever. As a result, the net cash flows per year would be $4,500. The NPV of this project can be calculated as follows.

NPV = Initial cost + Present Value of All Cash Flows = -$35,000 + (4,500/0. 12) = $2,500In this case, Rainbow should purchase the machine with this service contract as the NPV of this investment is positive. c) Instead of the service contract mentioned in b), Rainbow can reinvest 20% of the annual cost savings in new machine parts, resulting in the increase in cost saving at 4% annual rate.

Additionally, as long as Rainbow reinvest at 20%, the cash flows will continue to grow at 4% in perpetuity. Table 1 Net annual cost savings calculations DescriptionYear 0Year 1Year 2Year 3Year 4….. Annual Cost Savings-35,000 5,000. 0 5,200. 00 5,408.

00 5,624. 32 ….. Reinvest 1,000. 00 1,040.

00 1,081. 60 1,124. 86 ….. Net Annual Cost Savings 4,000. 00 4,160. 00 4,326. 40 4,499.

46 ….. The calculations of the net cost savings in each year are shown in Table 1. NPV of this option can be calculated as follows. NPV = Initial cost + Present Value of All Cash Flows = -$35,000 + [4,000/(0.

12-0. 04)] = $15,000 Hence, Rainbow should reinvest 20% of the annual cost savings into the machine parts as it results in the NPV of $15,000.