## A2 Problem Definition

About 40 minutes later, Dave and Xaomi were most of the way through their main courses. Dave suggested that they get started. He took a pad from his briefcase and said that he would take notes. Xaomi agreed to let him do that.

Dave started. "OK. A\ nat are our options?"

"Well, I did a bit of arithmetic on my calculator while you were on the phone before lunch. It looks as though, even if the demand growth rate is only 5%, a single small former will not have enough capacity to see us through 10 years. This means that there are four options. The first is a sequence of two low-capacity formers. The second is just a high-capacity former. The third, which would kick in only if the growth rate is high, would be a sequence of three low-capacity formers. The fourth is a low-capacity and a high-capacity. I'm not sure of the sequence for that."

Dave thought for a bit. "I don't think so. I assume that, even if we put in our own former, we could contract out requirements that our own shop couldn't handle. That might be the way to go. That is, you wouldn't want to add to capacity if there was only one year left in the 10-year horizon. There probably would not be enough unsatisfied output requirement to amortize the first cost of a second small former."

"That sounds as though there are a whole bunch of options. It looks like we're in for a couple of long nights." Xaomi sounded dejected.

"Well, maybe not."

"Maybe not what?"

"Maybe we won't have to spend those long nights. I think we can look at just three options at the start. We could look at a sequence of two small formers. We could look at a small former followed by outsourcing when capacity is exhausted. And we could look at a large former, possibly followed by outsourcing if capacity is exhausted. If we can rule out the two-small-formers option, we can certainlv rule out three small formers or a big former combined with a small one."

"Smart, Dave. How should we proceed?"

"Well, there are a couple of ways of doing this. But, given that we have only 10 years to look at,

1. Businesses are required to pay tax on their earnings. Determining the effect of taxes on before-tax earnings may involve extensive computation. Managers frequently approximate the effect of taxes on decisions by increasing the MARR. However, it is good practice to do precise calculations before actually making a decision.

it's probably easiest to use a spreadsheet to develop cash flow sequences for the three options. The two options in which only a single machine is bought at time zero are pretty straightforward. The one with a sequence of two small formers is a bit more complicated. One of us can do the two easy ones. The other can do the sequence. For each option we need to look at, say, nine outcomes: three possible demand growth rates—5%, 10%, and 15%— times three possible prices—3c, 3.5c, and 4c—for selling excess capacity. That should be enough to show us what's happening. What part do you want to do?"

"I'll take the hard one, the sequence of two. I'd like the practice. I'll let you check my analysis when I'm finished."

"OK. That's fine. But notice that the two-low-capacity-formers sequence is not a simple investment, so let's stick with present worths at this stage. Also, we are going to have to make some decision about how we record the timing of the purchase of the second former if we run out of capacity during a year. I suggest that we assume the second former is bought at the end of the year before we run out of capacity." "OK."

Dave continued, "We need to put together a simple table on the specifications for these two machines. I'll do that, since you are doing the hard job with cash flows. Why don't we go back to the plant. I'll make up the table. I'll get you a copy later this afternoon."

A. 3 Crunch Time

Xaomi was sitting in her office thinking about structuring the cash flows for the two-small-machines sequence. Dave knocked and came in.

He handed Xaomi a sheet of paper.

"Here's the table. Shall we meet tomorrow morning to compare results?" (See Table A.l.)

Xaomi glanced at the sheet of paper, and motioned for Dave to stay. "This is a bit new to me. Would it be okay if we get all of our assumptions down before we go too far?"

"Sure, we can do that," replied Dave as he grabbed a seat beside Xaomi's desk. Xaomi already had a pad and pencil out.

Dave went on, "OK, first, what's our goal?"

"Well, right now we are faced with a 'make or buy' decision," suggested Xaomi. "We need to find out if it is cheaper to make these parts or to continue to buy them, and if making them is cheaper we need to choose which machine or machines we should buy."

"Pretty close, Xaomi, but I think that may be more than we need at this point. Remember, Clem is primarily interested in whether this project is worth pursuing as a full-blown proposal to top management. So we can use a greatly simplified model now to answer that question, and get into the details if Clem decides it's worth pursuing."

"Right. If we look at the present worths of the three options we came up with at lunch, we should see quickly enough if investing in our own machines is feasible. Positive present worths

Table A.l

Specifications for the Two Cold Formers

Characteristics First cost (S)

Hourly operating cost (\$) Average number of pieces/hour Hours/year

Model El (Small) 125 000 35.00 1000 3600

Model E2 (Large) 225 000 61.25 2000 3600

Depreciation 20%/year declining balance, for both machines

Market facts Buying price: S0.05/piece plus cost of metal

Selling price: SO.03 to SO.04 per piece plus metal Demand growth: 5% to 15%

indicate buying machines is the best course; negative values would suggest it's probably not worth pursuing further."

Dave nodded. "OK," continued Xaomi, "so we want to do a 'first approximation' calculation of present worths of each of our three options. Xow, what assumptions should we use?"

"Let's see. We want to consider only a 10-year study period for the moment. I think we can assume the machines will have no salvage value at the end of the study period, so we don't have to worn7 about estimating depreciation and salvage values. This will be a consenative estimate in any case.

"Next," Dave continued, "we will ignore tax implications, and use a before-tax MARR of 25%. The 'sequence of machines' option has a complex cash flow, but by only considering present worths we can avoid dealing with possible multiple IRRs."

"You know," interjected Naomi, "it just occurred to me that the small machine makes 1000 pieces per hour at an operating cost of S35."

"And this is news to you?" said a bemused Dave.

"No, Dave. What I mean is that the operating cost is SO.03 5 per part on this machine, while one scenario calls for our selling excess capacity at only \$0.03. We'll be losing half a cent on every part made for sale."

"Hmmm. You know, you're right. And look at this. Even the bigger machine's operating cost is S0.030625 per piece. We'd be losing money on that one too."

"When we run the different cases, it looks like we'll have to consider whether excess capacity will be sold or whether the machine will just be shut down. Just when I thought this was going to be easy . . . ," trailed Naomi.

"Maybe, but maybe not. Look at this another way. If the small machine sells its excess capacity at a loss of half a cent per piece, that comes to five bucks per hour. On the other hand, if the machine is shut down, we'll have an operator standing around at a cost of a lot more than that."

"But can't an idle operator be given other work to do?"

"Again, maybe, but maybe not. With the job security clause the union has now, if we lay the operator off for any period of time, the company has to pay most of the wages anyway, so there isn't much savings that way. On the other hand, the operator would probably be idled at unpredictable times, so other departments would have a difficult job of scheduling work for him or her to do. I'm not saying it's impossible, but it's a job in itself to figure out if we can place the operator in productive work when trying to idle the machine."

"Boy, they didn't talk about these problems in engineering school!"

"Welcome to the real world, Naomi, where nothing is simple."

"Then how about if we do this?" Naomi continued. "We assume that since an idle operator is probably more costly to the company than \$5 per hour, the machines will run a full 3600 hours per year each regardless of whether the excess capacity is being sold at a price above operating costs or not."

"Sounds good, Naomi. In fact, we could claim an indirect benefit of this othenvise unprofitable operation since our operators will gain more experience with doing quick setups and statistical process control. That should make the brass happy," Dave said with a quick wink.

"I guess we can also assume that a machine is purchased and paid for at the beginning of a year while savings and operating costs accrue at the end of the year," continued Naomi. "And that the demand for parts is constant for each month within a year but grows by a fixed proportion from one year to the next."

Naomi finished scribbling down the assumptions, including the ones they had discussed with Clem earlier that day. Turning to Dave, she said, "So, how does this look?"

"Looks fine to me. Should we get together tomorrow and compare results?" "OK. What time?"

"Why don't we exchange results first thing in the morning and then meet about nine-thirty in my office?"

"That's fine. See you then."

As Dave left, Naomi looked more closely at the table he had given her (Table A.l). "Time to crunch those numbers," she said to herself.