Service tax and tips

This came about because I don’t like ++’s behind prices. If you tell me the price of the food is \$14.90, then when I’m paying, it’d better be just \$14.90. I don’t like doing mental arithmetic gymnastics. I also don’t like whipping out my phone to use the calculator.

It’s probably the main reason why I don’t go to fancy restaurants. It’s not so much the high price (though it’s a big factor), but that I feel deceived about the price. The listed price is not the price I have to pay.

Consumption tax

The Goods and Service Tax (GST) was established in Singapore, 1994. It started out as 3% in April 1994, then 4% in January 2003, then 5% January 2004, and is currently 7% from July 2007 onwards.

This caused some confusion because what used to be “round” prices now became weird. \$5 became \$5.15, and pray you had a human calculator with you if a price was something weird, like \$4.95.

Because the GST is a consumption tax, it generally applies to everything. From food to clothes to electronic gadgets. Almost every price is affected.

The progression from 3% to 7% made things worse. I remember having to design and code a software system to deal with taxes. Based on the date of the transaction, a different tax rate had to be used. For example, in December 2002 it would be 3%, but January 2003 it would be 4%.

Because it generally confused the Singapore consumer, most shops simply incorporated the GST into their prices. Instead of saying an item costs \$4.95 with 7% GST, the listed price is \$5.30 (actual is \$5.2965). The consumer doesn’t have to do any mental calculations.

It is also particularly fortunate that the Singapore 1 cent is no longer issued, because then businesses forced their prices to be rounded to the nearest 5 cents. Apparently, even 5 cent coins are no longer issued, we might see prices rounded to 10 cents. This rounding will come into play later on.

Also, if you’re in America, death to pennies… It costs more to produce a penny than a penny is worth.

Waiting tips

It is not common in Singapore (or Asia in general) to tip a waiter or waitress. I think East Asians and South-East Asians believe that it’s their job. Any tips are a bonus, not a given.

I’ve read that in Western countries, particularly in America, the wage for waiters and waitresses are lousy. Some wait staff survive a month because they had tips.

The tip is another unknown factor in my calculation of payment. How much to tip? I would much rather you work everything I have to pay into the price, and I decide beforehand whether I want to consume food and beverage at your eating establishment.

While I’m against exploitative wages, I also don’t want to fire up the neurons needed to calculate the appropriate tip amount.

Besides, the tips given to the waiter or waitress probably don’t even go directly to them. The tips go to a general pool, where it’s either spent on something for all the wait staff, or divided evenly amongst the wait staff. This also generally discourages staff not to be extra attentive to customers, since all their colleagues gain at their expense.

One lump price

So for most Singapore businesses, the GST is included in the price. The consumer is charged at one price, and the business has to calculate the correct GST to pay the Singapore government. Remember, tax evasion is a criminal offense.

However, there are 2 ways to calculate the GST. One is to calculate the GST portion first, the other is to calculate the sales price first.

For example, \$14.90 with GST included. Using 7% as the GST, we divide \$14.90 by 107 (because \$14.90 is 107% of the sales price) and then multiply by 7 to get the GST amount. Which is \$0.97 (rounded from \$0.9748). So the sales price is \$14.95 – \$0.97 = \$13.93.

In the second case, the sales price is \$14.90 / 107 * 100 = \$13.93 (rounded from 13.925). And so the GST amount is \$14.90 – \$13.93 = \$0.97

So far that seemed fine. Both calculations give the same results. Aahhh, but what if the government don’t care to accept values not in multiples of 5 cents? Or what if the business fudges the calculations a bit?

If you round the GST amount \$0.97 to \$1, then the final sales price is \$13.90.

If you round the sales price \$13.93 to \$13.95, then the GST amount is \$0.95, which makes the GST rate as \$0.95/\$14.90 * 100 = 6.38%. Not quite the 7%.

I’m not saying businesses do this manipulation (which is easy if you have transaction history and just tilt calculations in your favour), but rounding is the bane of financial applications.

10% service tax

Because Singapore (or Asia in general) don’t have a practice of tipping the wait staff, I think that’s why businesses set a 10% flat service charge. Basically, 10% of the meal price work as tips.

While I don’t have a complaint about this, I do complain that a \$14.90 meal can become \$17.45 (rounded from \$17.433). How? Because the service tax and GST weren’t included. Thus the final price is \$14.90 * (10% + 7%)

I don’t care if there’s a big asterisk or ++ at the end of your price. I hate reading footnotes directed from asterisks. And ++’s? They just scream clever/obnoxious/brilliant/crafty to me. Why do you think programmers prefer pre-increment (++i) than post-increment (i++) for readability?

Making it easier for me

I was telling this to my mom, and she had an answer (she’s a sales person). Businesses don’t include all those taxes into one price because it’s easier for them to calculate their service tax and GST.

If \$17.45 was the listed price, they’d have to back-calculate. The GST amount would be \$17.45 / 117 * 7 = \$1.04. The service tax would be \$17.45 / 117 * 10 = \$1.49.

If they only work with \$14.90 as the only price, then it’s a “simple” matter of \$14.90 * 10% = \$1.49 for service tax, and \$14.90 * 7% = \$1.04 (or \$1.05?).

I don’t really care. Your business probably handles hundreds and thousands of transactions every day. You’re not going to do this by hand. You have a fancy financial application that does it for you. Your financial application doesn’t care if it needs to do one more arithmetic operation per transaction. Computers crunch numbers for breakfast. Your financial revenue report will still look pretty.

You know, I don’t really know the point of this article. Probably a rant. Make it easier for me, ok? Or at least be more honest with your prices. I might just patronise your eating establishment more frequently.

Negative sales targets and percentage commissions

A while ago, I received an email from a distraught salesman. He believed his sales commissions were wrongly calculated, and asked me to shed some light.

Note that I’m not using the exact numbers he gave in his email.

The story goes that Michael (as I’ll call him) and his colleagues were given sales targets that were negative. How could sales targets be negative? Shouldn’t you be trying to sell something? The reason given was that the current economy was disastrous, and basically each sales person was trying to not lose sales.

You’re gonna bleed. It’s how much you bled.

Anyway, given Michael’s negative sales target, he managed to exceed it. He didn’t manage to bring in sales (positive sales numbers), but he didn’t lose too much money (slight negative sales numbers). But his sales commissions didn’t reflect that.

Now I’m not going to discuss how that works out. I can’t presume to understand the business logic behind the sales commission in this case, but I’ll discuss the mathematics behind the numbers.

The normal sales targets and commission

Let’s say your sales target for this month is \$1000. This means you’re expected to sell about \$1000 worth of products or services. We’ll ignore the condition that you will get some commission based on what you sell, regardless of how much you sold (my brother’s a sales person), as well as other types of commissions.

Let’s say the sales commission is based on how much extra you sold beyond your sales target. Makes sense, right? Let’s use simple percentages.

If you sold \$1100 worth of products or services, then your percentage commission might be calculated as follows:

Or (\$1100 – \$1000) / (\$1000) = 10% commission.

This is assuming that your sales amount exceeded the sales target, of course.

The case of negative sales targets

Now if the sales target is negative, as in Michael’s case, the mathematical formula still applies. But you have to note the negative sign. For some reason, “business” people (no offense to business people) tend to see -4567 as larger than 12, even though 12 > -4567. They see the magnitude first, not the value itself. (It’s also why I get emails about calculations involving negative numbers… anyway…)

Let’s say the sales target is -\$1000. Everyone’s expected to lose money, but you try not to lose more than \$1000. At least that’s what I’m interpreting it as.

Let’s say Michael managed to lose only \$50. Or -\$50 to be clear. The formula

have to be modified to this

In maths and programming terms, the “magnitude” part refers to the absolute function. Meaning you ignore any negative signs. Actually, the modified version works for the normal case too (which is why you should use it for the normal version anyway to take care of weird cases like this but I digress…).

So, we get (-\$50 – [-\$1000]) / abs(-\$1000) = \$950 / \$1000
= 95%

Actually, you should use this:

That’s the “foolproof” version. Consider it a bonus for reading this far. Frankly speaking, any competent programmer should be able to come up with that formula, even without much maths background. You just need to think about the situation a little carefully (ask “what if?” more often).

Michael’s calculated commission

When Michael wrote to me, he said his commission was calculated as follows (given that he only lost \$50):
-\$50 / -\$1000 = 5%

Let’s say someone else lost -\$900 that month. With the above calculation, that person gets:
-\$900 / -\$1000 = 90%

Clearly it makes more sense to lose more money! This was why Michael wrote to me.

I don’t propose the method I gave is correct, business-logic-wise. Michael didn’t give me any details on what he’s selling, or what his company is (or even why it’s acceptable to have negative sales targets, regardless of the economy). So I cannot give any help other than from a pure mathematical point of view. But I hope it’ll at least give Michael a fairer commission amount.

Questions

Given Michael’s situation, what do you think is an appropriate calculation formula?

Can you think of (or know of) a realistic situation where a negative sales target is acceptable? I say “acceptable”, but seriously, no company should “accept” that they lose money every month.