Question

You are the engineering representative on a team for a new product introduction. The proposed manufacturing process uses a semi-automated machine along with people. Components for each unit of the product cost $8. The semi-automated machine costs $1,500,000, and it has a 7-year MACRS recovery period. The salvage value is $0 for this specially designed machine. This machine can manufacture 175 finished parts per hour.

Table 29-1 Production Volume (1000’s)

Year: 1 2 3 4 5 6 7 8 9

Production Volume (1000’s): 195  275 385 550 625 695 630 550 295

The normal manufacturing operation runs 8 hours per shift per day. Initial production would begin with one shift, 5 days a week. The machine placed in the facility must support this plan. Each working year has 50 weeks (250 regular working days) to allow for vacations. The total labor cost is $50 for each regular time hour that the machine operates and $65 for overtime (these costs include benefits). Assume that employees can be shifted between production of this new product and other products already in manufacturing. This assumption means that this product is charged with only those hours used and not with one or two full 8-hour shifts. The production operation can operate a maximum of 8 extra hours/week, if needed to meet the demand without adding an extra shift. This may be a 6th day or some hours added at the end of the regular shift. Many employees like to earn “some” overtime. Thus, the overtime option is more desirable than adding a second shift if overtime can meet the demand. Other required information: Corporate MARR 12% (after tax) Cost of borrowing 9% Effective tax rate 35% Maintenance cost 12% of raw material cost Overhead cost 2% of raw material cost(utilities, supervision, marketing, etc.)

1) If required Annual production volume is Y units, raw material cost per unit is $8, selling price is $10.5 per unit and After-Tax MARR is 12%, what is the value of Y at which After-Tax Net Present Value (ATNPV) is 0 ?

Answer 1

Please note that MACRS depreciation asset is fully depreciated in 8 years. So we will have to project P&L and cashflows till year 8 and not beyond.

The 7 years MACRS depreciation rate will be as below:

	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Year 7	Year 8
MACRS Depreciation rate	14.29%	24.49%	17.49%	12.49%	8.93%	8.92%	8.93%	4.46%

You start with the given quantity (production) and sales price per unit of $10.5 to arrive at sales. Sales = 10.5* production for the year. You will then calculate raw material cost = $8 * production

You then calculate Maintenance cost, overhead cost as a percentage of above raw material cost.

For labour cost, divide the production by 175 to get the number of hours in a year. Now labour cost of $50 per hour,  you have 8 hours a day, 5 days a week and 50 weeks a year, so in a year you can work for 8*5*50 = 2000 hours at $50 / hour labor cost. So for upto 2000 hours a year, you will pay $50 per hour as labor cost and above that will be at $65 per hour.

Use $1500,000 as base and calculate depreciation as per the above precent values given.

You will arrive at PBT and then apply taxes and caculate PAT. Then draw out cash flows as below:

For year 0, capex is - $1,500,000 and from year 1 you will have inflow of PAT + depreciation

You calculate NPV using MARR of 12%. Using Goal seek in excel, you calculate the production such that NPV becomes zero.

The final calculations are shown as below: