Can you please break down the answers to how they were solved. I want to understand this.

Hoosier Manufacturing, Inc. is a producer of household vacuum cleaning robots. Its current line of cleaning robots are selling excellently. However, in order to cope with the foreseeable competition with other similar cleaning robots, HM spent $6,000,000 to develop a new line of smart vacuum cleaning robots that can automatically adjust to all floor types and return to its dock for Lithium Ion recharging its battery for up to run time of 6 hours. The robot model also has a built-in camera for easier navigation and thus can detect and avoid stairs and other drop-offs. It automatically provides more air power on carpets and rugs. Its lower profile cleans under furniture and bed more efficiently.It has a cleaning path of 4.5 and can clean up to 2,000 sq. ft. per cleaning job. Its enhanced HEPA-style filter can trap more dirt, dust and allergens and as tiny as 0.8 micron. It has a tangle-free extractor that can prevent any hair and debris clog. It is a bagless model with an easy to empty dust cup. Its associated smart phone/tablet application can enable consumers to set their cleaning schedules with their preferences to clean their places from anywhere. The company had also spent a further $1,200,000 to study the marketability of this new line of smart vacuum cleaning robots. HM is able to produce the new vacuum cleaning robots at a variable cost of $570 each. The total fixed costs for the operation are expected to be $8,000,000 per year. HM expects to sell 3,200,000 robots, 2,600,000 robots, 1,600,000 robots, 1,200,000 robots and 1,000,000 robots of the new model per year over the next five years respectively. The new smart vacuum cleaning robots will be selling at a price of $640 each. To launch this new line of production, HM needs to invest $32,000,000 in equipment which will be depreciated on a seven-year MACRS schedule. The value of the used equipment is expected to be worth $4,000,000 as at the end of the 5 year project life. HM is planning to stop producing the existing vacuum cleaning robots entirely in two years. Should HM not introduce the new smart vacuum cleaning robots, sales per year of the existing vacuum cleaning robots will be 1,600,000 robots and 1,250,000 robots for the next two years respectively. The existing vacuum cleaning robot model can be produced at variable costs of $460 each and total fixed costs of $4,500,000 per year. The existing vacuum cleaning robots are selling for $550 each. If HM produces the new smart vacuum cleaning robots, sales of existing vacuum cleaning robots will be eroded by 600,000 robots for next year and 400,000 robots for the year after next. In addition, to promote sales of the existing vacuum cleaning robots alongside with the new smart ones, HM has to reduce the price of the existing vacuum cleaning robots to $500 each. Net working capital for the new smart vacuum cleaning robot project will be 15 percent of sales and will vary with the occurrence of the cash flows. As such, there will be no initial NWC required. The first change in NWC is expected to occur in year 1 according to the sales of the year. HM is currently in the tax bracket of 35 percent and it requires an 18 percent returns on all of its projects. You have just been hired by HM as a financial consultant to advise them on this new smart vacuum cleaning robot project. You are expected to provide answers to the following questions to their management by their next meeting which is scheduled sometime next month.

1. What is/are the sunk cost(s) for this new smart vacuum cleaning robot project? Briefly explain. You have to tell what sunk cost is and the amount of the total sunk cost(s). In addition, you have to advise HM on how to handle such cost(s).

2. What are the cash flows of the project for each year? 3. What is the payback period of the project? Should it be accepted if HM requires a payback of 3 years for all projects?

4. What is the PI (profitability index) of the project?

5. What is the IRR (internal rate of return) of the project?

6. What is the NPV (net present value) of the project?

7. Should the project be accepted based on PI, IRR and NPV? Briefly explain.

1) The sunk costs are:
Cost of development	6000000
Marketability study	1200000
Total sunk costs	7200000
Sunk costs are costs that are already incurred. They are not relevant
for the decision making on hand. In this instance, the above costs
are already incurred and do not affect the decision whether to
produce the new robots or not. Such costs should be excluded from
the analysis.
2) Cash flows:	0	1	2	3	4	5
Cost of equipment	-32000000
Units to be produced & sold		3200000	2600000	1600000	1200000	1000000
Sales-$ (at $640)		2048000000	1664000000	1.024E+09	768000000	640000000
Variable cost (at $570)		1824000000	1482000000	912000000	684000000	570000000
Fixed costs		8000000	8000000	8000000	8000000	8000000
Depreciation % (MACRS)		14.29	24.49	17.49	12.49	8.93	8.92	8.93	4.46
Depreciation-$		4572800	7836800	5596800	3996800	2857600
Operating profit from the new robots		211427200	166163200	98403200	72003200	59142400
Contribution from the existing VCs if the new robot model is not produced.
(at 550-460 = $90 per unit)		144000000	112500000
		(1600000 units)	(1250000 units)
Contribution from the existing VCs if the new robot model is produced.
(at 500-460 = $40 per unit)		24000000	16000000
		(600000 units)	(400000 units)
Loss in contribution if new VC is introduced		120000000	96500000
Incremental operating profit before tax		91427200	69663200	98403200	72003200	59142400
Tax at 35%		31999520	24382120	34441120	25201120	20699840
Incremental after tax profit		59427680	45281080	63962080	46802080	38442560
Add: Depreciation		4572800	7836800	5596800	3996800	2857600
Incremental operating after tax cash flows		64000480	53117880	69558880	50798880	41300160
NWC required (15% of sales)		307200000	249600000	153600000	115200000	96000000
Increase in NWC		307200000	-57600000	-96000000	-38400000	-19200000
Recovery of NWC						96000000
Salvage value of the equipment						4000000
Book value of equipment = 32000000*22.31% = $7139200
Tax shield on loss = 35% of 3139200 =						1098720
Cash flows the project	-32000000	-243199520	110717880	165558880	89198880	161598880
PVIF at 18%	1	0.84746	0.71818	0.60863	0.51579	0.43711
PV at 18%	-32000000	-206101288	79515858	100764246	46007790	70636360	90822965
6) NPV	58822965
PVIF at 30%	1	0.76923	0.59172	0.45517	0.35013	0.26933
PV at 30%	-32000000	-187076554	65513538	75356796	31231007	43523277	-3451936
PVIF at 29%	1	0.7751938	0.600925425	0.4658337	0.361111367	0.27993129
PV at 29%	-32000000	-188526760	66533189	77122899	32210729	45236583	576642
5) IRR = 29+576642/(3451936+576642) =	29.14	%
4) PI = PV of cash inflows/Initial investment = 90822965/32000000 =			2.84
3) Payback period:
Cumulative cash flows		-243199520	-132481640	33077240	122276120	283875000
Payback = 2 + (132481640+32000000)/165558880 =		2.99	years
As the PB is less than 3 years, the project can be accepted.
7) AS NPV is positive, IRR>COC and PI>1, the project can be accepted. Positive NPV projects add to the wealth of the shareholders.