Why the Dividend Platinum Card is Not For You, Unless You Are a Rich Bastard

2004-06-11

Recently I acquired a Dividend VISA Card from CIBC. Essentially, the card offers, as a perk, up to 1% cash back on annual net purchases, and has no service charge.

This seemed like a good move, since at the time I had only a Classic VISA, which is essentially the same thing but with no cash back. So I signed up for a Dividend Card. Afterwards, though, I wondered if perhaps the Dividend Platinum was the way to go. Its obvious benefit was up to 2% cash back, but a more detailed comparison was in order.

Of course there's a bit of fine print behind that 'up to'. Here are the specifics on both cards, as explained by CIBC:

Card Annual Fee Cash Back Rate
Dividend $0
  • Tier one - 0.25% for amounts up to $1,500.
  • Tier two - 0.50% for amounts $1,500.01 to $3,000.
  • Tier three - 1% for amounts over $3,000.
Dividend Platinum $79
  • Tier one - 0.5% rebate on your first $3,000 in annual net purchases.
  • Tier two - 1% rebate on your next $12,000 in annual net purchases. (Between $3,000 and $15,000)
  • Tier three - 1.5% rebate on your next $20,000 in annual net purchases. (Between $15,000 and $35,000)
  • Tier four - 2% rebate on your next $15,000 in annual net purchases. (Between $35,000 and $50,000)

Now, Dividend Platinum's rate only exceeds 1%, the maximum rate of the Dividend Card, after you've spent $15000. This already makes Platinum a bit out of reach. But the slightly more interesting question is: how much do you have to spend using Dividend Platinum before it becomes a better deal than plain Dividend, given Platinum's $79 annual fee?

I decided to do this in Maple. Here are Maple procedures which compute the cash back in a year for each of the two cards, given money spent. Note the initial values of 0 and -79 respectively, and also notice that DividendPlatinumCard returns unknown past $50000, since CIBC's description curiously doesn't give the rate in that case1.

Dividend Card Dividend Platinum Card 
DividendCard := proc(x)
    local C;
    C := 0;
    if x > 0 then
        C := C + 0.0025 * min(x, 1500)
    end if;
    if x > 1500 then
        C := C + 0.0050 * (min(x, 3000)-1500)
    end if;
    if x > 3000 then
        C := C + 0.0100 * (x-3000)
    end if;
    C
end proc:
 
DividendPlatinumCard := proc(x)
    local C;
    C := -79;
    if x > 0 then
        C := C + 0.0050 * min(x, 3000)
    end if;
    if x > 3000 then
        C := C + 0.0100 * (min(x, 15000)-3000)
    end if;
    if x > 15000 then
        C := C + 0.0150 * (min(x, 35000)-15000)
    end if;
    if x > 35000 then
        C := C + 0.0200 * (min(x, 50000)-35000)
    end if;
    if x > 50000 then
        C := unknown;
    end if;
    C
end proc:

Plotting these procedures along with the difference function f(x)=DividendPlatinumCard(x)-DividendCard(x) along the interval [0, 40000], we get the following results:


(Note DividendCard(x) is in red, DividendPlatinumCard(x) is in green, and f(x) is in blue)

Solving exactly for the point at which the nondecreasing function f(x) hits the origin, we find it is x=30050. So, it seems that the Dividend Platinum Card is worthwhile2 if you plan to spend more than $30050 in credit card purchases in a given year.

I would tentatively offer that this qualifies you for Rich Bastard status. Not being rich3, I'll stick with my plain old Dividend Card.

1. You'll see the maximum credit limit for the Dividend Platinum is $50000, but obviously someone can spend more than eir credit limit in a year. It would be very strange if CIBC didn't give any cash back to someone spending >$50000, particularly since the 'lesser' Dividend Card has no equivalent ceiling4. But if there is cash back, at what rate?

2. I realize there are more perks with the cards than just the cash back. But they aren't quantifiable, so I'm ignoring them.

3. I realize how incredibly bourgeois this sounds. Well, at least I'm half of a rich bastard.

4. You might wonder: assuming the Dividend Platinum gives no cash back after $50000, how much do you have to spend before using the plain Dividend Card is again the best option? The answer is $67475. So perhaps I should have said that the Dividend Platinum Card is Not For You, Unless You Are a Rich Bastard Yet Not a Filthy Rich Bastard.