Hey all,
I received a rather interesting technical question during my interviews recently on what the discount rate would be for a gift card at, say Starbucks, that gave you $5 into perpetuity. Alas, I struggled because I had no idea where to begin, but the interviewer suggested a few options:
- Inflation
- Looking more into the solvency of the company itself, and it's likelihood to operate into perpetuity
My question for everyone is, how do you go about thinking about these problems? What if we swap out a gift card for an Apple tree? Or a table manufacturer that delivers tables to you ever day (say each table cost $400)? Any heuristics on approaching these problems? Thanks in advance.
Not sure, but I'll take a stab.... My thought process was as follows: A Starbucks gift card paying $5 over some period into perpetuity sounds like a bond. It's not paying cash that can be reinvested elsewhere and can only be spent at Starbucks so discount rate as inflation is a good start. I did a distressed debt internship so I know that gift cards are technically unsecured liabilities and in Ch11, gift cards are usually honored because the business doesn't want to screw customers but in Ch7, gift card holders will (likely) be wiped out which justifies the inclusion of an additional risk premium.
I'd love to get feedback on whether that approach is correct.
Appreciate the help, thank you.
The most practical answer would be to explain that the gift card face value is different from a cash value but that is not the exercise.
So instead, next time just explain PV = PMT / R and that you understand a perpetuity cannot be infinite unless the company can sustain itself.
The following is only meant to help you think about the problem in more complex terms;
Thanks for the help, this is very helpful.
Will take a stab at this.
The discount rate should incorporate four things:
1) Your cost of capital
2) Your view on the term structure of interest rates
3) Your view on the Starbucks credit itself
4) Liquidity
1) Because the interviewer is presumably trying to understand what value YOU would place on the gift card, the discount rate here should incorporate your cost of capital (cost of capital = the discount rate used in corp finance). For example, the cost of capital for a broke recent college grad is going to be much higher than for a wealthy and successful individual close to retirement. This translates to the recent college grad being able to pay comparatively less for the gift card (they'll need a more leveraged return for their scarcity of funds). So what's your cost of capital (what return do you need)?
2) The rate should also incorporate some view on the term structure of interest rates going forward. For example, interest rates are on the rise; if you expect this trend to continue well into the future then your discount rate should reflect this. If you fail to account for this and rates go up by 200bps you're going to take a sizeable PNL loss on the value of your gift card.
3) It's hard to imagine Starbucks going out of business, but it's certainly not a risk free credit. You'll need to incorporate some credit premium (additional discount) for the implicit risk that Starbucks falls down on its commitment to refill and honor the card every year. How much faith do you have in the brand?
4) Liquidity. How easily can you sell the card if you needed to? Would you have to offer a discount to find a buyer? If so, better bake that into your discount rate too.
Hope this helps.
Discount rate is related to risk - the question is, how risky is the value of a $5 card?
The trick is that in a bankruptcy proceeding, gift card holders are treated more senior than most forms of debt - it is one of the first liabilities to be paid out in the waterfall, if I recall correctly.
So probably something similar to whatever the risk free rate is, given that it's got a static cash value and that said value would likely be paid out in a bankruptcy proceeding.
I'd attack it as:
First principles:
1. Note the math of a perpetuity; PV = CF / r
2. Note perpetuities have a natural limit based on whatever discount rate you use (i.e. there is a 'finite' value that spits out despite it going on forever), and practically speaking the 'value' of the perpetuity decreases as time goes on (such that the $5, 210 years into the future is worth about 1c on a discount of 3%)
Attack specifics
3. Gift Card ranks as what - debt, equity, or somewhere in between? Take a stab at it, but it is a liability, not equity, so theoretically should be lower than the cost of equity (there's your ceiling), is it secured senior debt? (no so should be higher than this discount, which already has inflation implied in it technically). But if you were to draw a line between the rights of an equity vs. debt holder, gift card could reasonably be put closer to the equity side (especially considering it's perpetuity credit risk), think of it like a CoCo bond or AT1 capital, or a 100 year bond.
4. Starbucks - how long have these guys existed for? Will they exist and be able to honour for 100, 200, 300 years? Because that's really what you're betting on.
Be cheeky
5. Finally if you have the rapport, ask if you are buying or selling it. If you are buying, then jack up the discount rate to something like 20%+ based on the fact the company may not last forever and you basically have no rights if they turn around and decide to stop paying you. If you are selling, argue for it to be priced at the inflation rate (but call it around the long-term average of 2-3%).
Apologize if this is a dumb question, what explains the asymmetry in the cost of capital? Shouldn't it be agnostic of whether you are the buyer or seller (if it isn't symmetrical, how can they come to a price consensus)? The rest of everything you explained makes perfect sense, thank you very much.
This is why I put it under the 'cheeky' headline.
Because assets are bought and sold by two different parties, in the 'real world' most people play games around the discount rate (never usually the cashflows as much) to get an appropriate price. (that's why things always have a bid/ask spread)
If you're a buyer, you want the lowest price possible, this means highest discount, if you're a seller you want the highest price possible, which means the lowest discount. Where the ACTUAL transaction occurs that is the 'true' but only observable in hindsight discount rate that 'the market' sees for the asset. (and from a further cheeky point - people pay about 100x more attention to market-led prices than intrinsic ones).
Second final layer of cheeky is that technically whatever rate you use is not going to be 'flat', it will have a curve, trend and volatility (i.e. it won't be 3%,3%,3%, more like 3%, 3.5%, 2% etc), which also can influence the value of the asset in the short-term (read for the first 100 years of the asset).
Final layer is how are you funding the purchase of the asset - is it with debt or equity or something in between? What's the cost of that (as you just learned, if you're funding with equity you're in fact going to be ripped off because Cost of Equity is higher than your discount rate, or at best the same, so it doesn't make sense to purchase), so you'd be funding with a mix of Equity and Debt, but then depends on that mix (which ALSO then begs the question about what discount rate YOU are subject to for your funding arrangements, including CSA risk and the like).
The thought process I described is pretty normal for valuing / viewing long-term derivatives.
Remember that the inflation used should be that of Starbucks' own products and that the card is only redeemable in Starbucks. So a better analogy would be sovereign debt rather than a corporate bond because Starbucks can change the price & quality of its products (which is all you can get with the gift card) and it could go broke. There is also a lot of subjective value.
You're missing the big picture.
Correct answer is 100% because a Starbucks giftcard is worthless. BB chads drink Blue Bottle.
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