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Calculus in SaaS (causal.app)
56 points by Lukas1994 on Sept 25, 2020 | hide | past | favorite | 21 comments


How are people not up to their eyeballs in monthly subscriptions at this point? I've always been wary of adding subscriptions, but it feels like there's got to be some breaking point when there's one too many Netflix/Disney/Hulu/Apple One/Peloton subscriptions to handle for your average consumer.


One way to think about subscriptions is to translate them into additional-years-to-retirement. How much capital would you need to accumulate to generate enough investment income to pay for the recurring expense? How many years of extra work would you need to accumulate that amount of extra capital from savings?

For example: suppose we're considering a recurring expense of $10 / month = $120 / year. How much capital K would we need to generate income to pay for this expense? Assuming a 4% real annual return on invested capital [+], we'd need K = $120/0.04 = $3k.

How many years of work does it take to accumulate savings of $K capital to invest?

Assume a median US individual annual income of around $30k and an optimistic savings rate of 5%.

Savings per year = $30k * 0.05 = $1.5k / year. Years of work required to accumulate enough capital to cover a $10 / month recurring expense: $3k / ($1.5k / year) = 2 years [#].

In this scenario, avoiding the $10 / month recurring expense is roughly equivalent to retiring 2 years earlier than otherwise.

[+] i.e. the long-run annual real return from investing 100% into the stock market given current market conditions

[#] this over-estimates the amount of work required by a few percent as it neglects that we can start investing our savings while we are accumulating it


I also wonder how many people aren't realizing just how much they're devoting to subscriptions, especially those with dark patterns where they sign you up for a 1-3 month introductory rate and then jack up the price significantly after that.

I review my monthly charges every few months and cut anything that isn't giving me enough joy, but I also imagine I'm a rarity.


> dark patterns

I was pleasantly surprised by Netflix recently. After avoiding using the service until recently, I was motivated enough to subscribe by one particular film I wanted to watch.

Initially, they automatically upgraded me to the Premium subscription level on a trial basis. When that trial time period ended I received an email saying, "do nothing and we'll downgrade you to the Standard subscription level."

That was truly a pleasant surprise.

I did nothing.


On the opposite note, amazon goes out of the way to make sure you don't unsubscribe.


I tend to cancel the subscription as soon as I've purchased it so that I can't possibly forget in the future. You'll still have the 1-3 months you initially paid for, and if it winds up being a service that's worth continuing then you can subscribe for longer (I'll usually pay for a year and immediately cancel at that point).


A ton of SaaS is business facing. Not much more beyond what you listed is aimed at consumers. Businesses already think of expenses in terms of time period and even prior to SaaS being normal they'd be paying for customer support, maintenance, custom development, etc as a service on top of their software purchase anyway.


For some people I know, everything as a subscription is a lifestyle.

House as a Service (renting), movies galore, MacBook with 0% interest 24 month financing (basically a subscription), phones with 2-year payments (also a subscription), cars with loans (subscription)...

Basically, if you view everything as no ownership, all subscription... it's a very weird dystopian way of "owning" things.


All of those can potentially be the best financial choice. Especially the 0% loans.


Many of them are also deferred payment on something that is eventually owned, which is different than SaaS


In principle it's not much different than any one time purchase. Each consumer can afford a certain amount and they prioritize which to buy that month.

The rich just subscribe to everything, others who are at their limit have to prioritize and draw the line somewhere.


> The rich just subscribe to everything

I’m pretty rich and I pirate things rather than having a million separate streaming accounts - out of moral concern as much as convenience.


> If y = 10x where y = ARR and x = time in months, then after two months ARR = $20. After 12 months, ARR = $120 (assuming we start from $0 of ARR)

I don't think this makes sense, because the time is in months yet you're calculating a yearly value. Time should be in years, because otherwise you're calculating forecasted values.

> So at the end of a year, the business has grown from $0 to $120 in ARR. But what is the recognized revenue? The complex answer is that it's the integral of 10x from 0 to 12 months

(Recognized revenue = $720 in this example)

Again, this doesn't make sense due to the fact that your calculated ARR values are forecasted.

If your projected ARR has grown throughout the year, it's intuitive that your recognized revenue must be lower than your ARR.

It's not possible to recognize $720 in revenue when your ARR is only $120, it should be $60.

I think the issue here is using ARR, since ARR grows quadratically given a linear increase in MRR. This math would make sense if you used MRR instead, or modelled actual ARR instead of forecasted ARR.


LOL @ myself: I thought "Calculus in SaaS" meant that they had an app like Wolfram Alpha or something. But, idk, with more features ¯\_(ツ)_/¯


It seems that a simple analogy with cars can make any topic completely intuitive.


As noted in other comments, the $720 of recognized revenue is off and should instead be $60.

Assuming $10 of ARR is added each month:

> y = 10x where y = ARR and x = time in months

needs to instead be

> y = (10/12)x where y = MRR and x = time in months

ARR is increasing 10 per month but MRR is increasing 10/12 per month.

The height of the triangle is 10 at the end of the year since the height is MRR.


isn't the 'recognized' revenue in the example 60M not 720M?


How do you get that? 5 * 122 =720


y is annual RR and x is in months.


can someone help me - they went from 10M ARR (annual) to 10M integrated month over month for a year, why?


I guess answering myself - they point out that this equation isn't applicable, but darn I had a hard time getting past that.

ARR growth comes from sales, but that's a huge broad word and it's quite fun to watch a startup grow and see how they start to make money from a number of areas that aren't just direct inbound/outbound sales.




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