Cash Back / Discount Percentage

[dumbbunny]

Facts:

1. Wash costs $10
2. Customer gets a $25 credit for loading $100
3. Customer gets awarded 10 points for every wash -- 100 points will get him a free wash - customer does not receive points from washes that were free due to accrued points. As soon as enough points are accrued, those points are used for the next wash (rather than using the loaded money)

Question: How much is the customer saving? Our trouble is finding the percentage-- see bottom

Method 1:
With a balance of $125, customer receives 12.5 washes (125/10).
With 10 rewards for every wash, customer accumulates 125 points (10 * 12.5) for an additional 1.25 washes (125/100).
Total washes = 13.75 (12.5 + 1.25)
Value of washes = $137.50 (13.75 * 10)
Customer saves $37.50 for spending $100

Method 2:
Customer uses account balance for 10 washes, after which he accrues 100 loyalty points-- his 11th wash is free.
After which, he has a balance of $25 (bonus credit) and 0 points.
He washes 2 more times.

Summary:
Number of washes = 13 = $130
Free washes from loyalty = 1 = $10
Free washes from $25 bonus = 2 = $20
Balance = $5 (free bonus money) half wash
Points = 25 = $2.50

Customer got $10 + $20 + $5 + $2.50 = $37.50 for FREE
Only spent $100

In percentages does he save:
37.5% (37.50 / 100 * 100)
27.27% (37.50 / 137.5 * 100)
40% (answer from the manufacturer) (40/100 * 100)

Method 3:
($25 cash back for every $100 = 25% (or 20%?!)) + ($1 cash back for every $10 spent = 10% (or 9%?!)) = 35% (or 29%?!)

 

[tkhunny]

Your difficulty is in the number of washes. Each number of washes produces a different percent savings. I get this:

9 Washes - 0%
18 Washes - 19.44%
27 Washes - 25.93%
36 Washes - 29.17%

Seems like it just keeps increasing, doesn't it? That's not the case. It will stabilize in the long run.

45 Washes - 31.11%
54 Washes - 30.56% (Didn't see that coming, did you?)
63 Washes - 31.75%
72 Washes - 31.94%
81 Washes - 31.48% (Another dip.)

Now that we have some in both directions, we should get smaller movement approaching some limit.

100 Washes - 31.50%
120 Washes - 31.25%
140 Washes - 31.79%
160 Washes - 32.19%
180 Washes - 32.50%
200 Washes - 32.75%
220 Washes - 32.95%

Do you see that happening?

I can't guarantee that I have implemented your algorithm exactly as you have intended. Thus, your results may vary.
Rule #1: Every 11th wash is free.
Rule #2: Every 10th wash earns $25, so the next two washes are free and the one after that half price (unless they are already free from Rule #1, then jump to the next non-free.)

The question is, what is it that you want to see? If you don't have customers for a lifetime, perhaps a limit like that shown is unsatisfactory. Maybe you want to stop at some average number of washes before a customer stops coming back.

 

[Steven G]

Suppose a store has a 10% sale today and you go a buy a tv that originally cost $100. Since you get 10% off, ie $10 off, you save $10 off of $100. Well $10/$100 = 10%. That is you got 10% (just like you expected).

Suppose the store instead said that they will give you a $10 off coupon if you spend $100. So you go and but the tv for $100 and they give you a $10 coupon. You promptly purchase that nice $10 sweater you have been looking at for weeks. You pay for the sweater with your coupon. Let's see what really happened. You spent $100 for $110 worth of merchandise. This time you saved $10 off of $110 which equates to 9.09% off.

$25 cash back for every $100 = 25% (or 20%?!). No! You are NOT getting back $25 for every $100. That would mean that when you pay $100 they give you back $25, meaning that you pay $75 for $100. Not so.
You are paying $125 and they (instantly) give you back $25. That is you are paying $100 for $125 worth of washes, ie you are saving $25 for every $125 worth of washes. This is a 20% savings.