Question

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%Rainbow

1. 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
2. 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?
3. 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?

Answer all of the question above. Be sure to show your work and explain your methods.

Answer 1

There are 3 condition for analysis infront od Rainbow

1) Buying the machine

2) Servicing the machine

3) Internal Capacity building

Rainbow should go for 2nd option ie "Good as New" service contact as the net cash flow is nore than the other two option.

1)Option one of buying new machine

NPV is $14946

IRR is 6.70% and payback period is 4 years and 2 months.

Condition 1- Buying new machine
Additional cash	5000
Machine cost	35000
Machine life	15
cost of capital	12%
year	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Saving in cost	5000	5000	5000	5000	5000	5000	5000	5000	5000	5000	5000	5000	5000	5000	5000
Add:Depreciation	2333.3	2333.3	2333.3	2333.3	2333.3	2333.3	2333.3	2333.3	2333.3	2333.3	2333.3	2333.3	2333.3	2333.3	2333.333333	B4/15
Free acsh flow from operation	7333.3	7333.3	7333.3	7333.3	7333.3	7333.3	7333.3	7333.3	7333.3	7333.3	7333.3	7333.3	7333.3	7333.3	7333.333333	P9+P10
Discounted cash flow	6548	5846	5220	4660	4161	3715	3317	2962	2644	2361	2108	1882	1681	1501	1340	P11/(1+$B$6)^P8
Total Discounted cash flow															49946	sum(B12:P12)
Total initial investmet	35000
NPV=	total cash inflow- total cash outflow
	14946	P13-B14
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Cash flow	-35000	6548	5846	5220	4660	4161	3715	3317	2962	2644	2361	2108	1882	1681	1501	1340
Irr	6.70%	irr(B18:Q18)
Payback
Cummulative cashflow	0	7333.3	14666.6	21999.9	29333.2	36666.5	43999.8	51333.1	58666.4	65999.7	73333.0	80666.3	87999.6	95332.9	102666.2	109999.6
					5666.8	0.1545487438
					B14-F21	F22/G21
						4 years and 2 months

Please refer to the attched file for step explanation and calculation along with formula and cell referred.

2) "Good as new " Service the net cash flow from this option is $37500

and formula used is perpetuity cash flow/cost of capital

=>4500/12%

=> $37500

3) Self engineers option give and net cash flow of $31250 which is more than purchase option but less than service option.

Here formula used is perpetuity cash flow/(cost of capital-growth rate)

=>5000/(20%-4%)

=>$31250

In this condition required cost of capital is 20%

and growth rate till perpetuity is 4%

Please refer to the attched file for step explanation and calculation along with formula and cell referred.