Why does a higher WACC mean lower company value?

The BIWS keeps emphasizing that if a company has a higher WACC it means the company is less valuable as the investor has better options somewhere else, and vice versa. I'm not understanding this. The example used is if a company has a cash flow of 100 and you want a yield (WACC) of 10% you would pay $1000. If you wanted 20% you'd pay $500 today. I understand the math but this isn't making sense to me for some reason, would appreciate if someone could explain.

 
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It's about risk. The WACC is higher because it's riskier.

Edit: Think about what WACC actually is: it's the cost of debt and the cost of equity. If a company is riskier, then they will have to pay higher interest on their debt. At the same time, they will be expected to provide a higher return to their equity holders as an investor would expect to receive a higher return for investing in a riskier company.

So if a company has a high chance at providing $1,000 in the future to an investor, they can "charge" a higher present value for that expected future gain, say $800. On the flip side, if they had a low chance at paying out that $1,000 then nobody in their right mind would pay $800 right now for it, therefore, they company would have to lower what they charge (their present value) to compensate for that additional risk.

 

But why is the company value lower? E.g a start up or small company would probably have a higher WACC right (equity investors would expect more, maybe more expensive to finance via debt bc low creditworthiness) but if we're expecting this start-up to grow in the coming years, shouldn't that be factored into it's price today? BIWS says investors have "better options elsewhere", what exactly does it mean by that? Isn't a 20% WACC (yield) better than 10% even though it's riskier?

 

Important concept that I think you're both missing is that WACC = opportunity cost, and that there is no such thing as a free lunch (arbitrage opportunities don't exist). Every investment can be described by an expected return and a risk level (basically the variance of that return). Consider two investments: investment A has an expected return of 7% with a variance of 2%. Investment B has an expected return of 7% with a variance of 5%. No risk-averse person would invest in B – this is an arbitrage opportunity, and the price of A will adjust upwards to price its higher level of risk appropriately, lowering the expected return. If you were to graph the risk and expected return of every investment in a (perfectly efficient) securities market, the result would be a curve (it looks similar to an indifference curve if you've ever taken a calculus-based econ class) called the efficient frontier. Investments below the curve – that is, investments with lower returns for their levels of risk than other investments available in the market – are, by definition, bad investments.

To relate this to WACC: WACC (in theory) represents the return an investor could get elsewhere in the market by taking the same level of risk that they are taking by investing a marginal dollar in a company with the promise of receiving its free cash flows. If a firm has a 10% WACC, that implies that the company's risk level is akin to that of the investment on the efficient frontier with a 10% return. If a company has a 20% WACC, that doesn't mean that the return you can expect from holding it is higher than a company with a 10% WACC – rather, it means that if you were to purchase the security lying on the efficient frontier at the same level of risk, the return you would expect from that security is 20%.

If an investment exists in the market at the same level of risk as an investment in a company, it's only fair that we compare the potential returns from investing in the company to those from making the equivalently risky investment, for the reasons described above, If that investment has a return of 20%, then we should consider that when valuing the company. If we can grow our initial investment at 20% by taking the same level of risk that we take with an investment in this company, then a dollar in a year is only worth 1/1.2 (0.83x) as much as a dollar today (because by investing it in this company we're not investing it in this equivalent risky investment at 20%).

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That "growth" you're referring to (the higher potential for returns) comes at a higher rate of risk.

Sometimes, it's helpful to take a step back and think about the impact of risk. How much would you be willing to pay for a lottery ticket that has a 25% chance of paying you $100 in 1 year versus the amount you'd be willing to pay for a lottery ticket that has a 75% chance of paying you $100 in 1 year?

Because I have a higher likelihood of receiving a payment, and therefore a lower risk of not receiving a payment, with the second option (75% chance of payoff), I should be willing to pay more for that lottery ticket. Because that lottery ticket represents less risk, there is a higher likelihood I receive payment, so I should be willing to pay up to the amount of the expected payoff.

Similarly, you can think of companies as these sorts of lottery tickets. Some companies are more risky than others. WACC encompasses this risk. Just as I'm willing to pay more for a lottery ticket that has a higher chance of paying off (and lower risk), I should be willing to pay more for a company that has a lower WACC (all else equal).

 

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