Winner: Chad - Perpetuity Formulas

Congrats to the winner: Chad!

The answer to last night's question is: Infinite

If you calculated the value using the Gordon Growth model (or cash flow perpetuity model), you would get -20.11 (which is what Darshan got).

[Solution - Finance Answer]
If your cash flows grow faster than you discount, each cash flow continues to contribute more and more in terms of present value when calculating the price. With a perpetuity, you are adding an infinite number of values which don't converge.

The perpetuity formula is calculated by using a geometric series of cash flows which include the growth rate and discount rate.

[Solution - Calculus Answer]
Another way to look at this question is what happens when the cost of capital (k) is equal to the growth rate (g). If you use Gordon's Growth model, you get a divide by zero. Or if you look at values of g which are trivially smaller than k, you get astronomical prices (if k = 8% and g = 7.99999%). If you take values of k and g such that g incrementally approaches k in the manner shown above, you can see the astronomical effect it has on the stock price.

If you graph price as a function of g (holding k constant), you can see that there is some crazy behaviour when g is close to k (take the limit as g approaches k).

[Why this question is tricky]
Most people could understand that the numbers didn't look right, but let's look at why.
k is usually pegged at about 8% to reflect the opportunity cost of capital (traditionally it is pegged at historical year-over-year returns in the stock market).

g is usually pegged at inflation or GDP growth and is realistcally 2% (for those of us doing Womack's homework yesterday, he had us do a sensitivity test with ranges between 1 to 4%). Even if a company has phenominal growth, you have to remember that a perpetuity formula is the company's performance ever after. And over time, everyone starts to look "the same". Basic economic theory says that over time overly profitable industries will have entry and become more competitive and you have to consider this when doing a terminal value calculation.

Therefore, the best criticism of the problem I've got is that the growth rate is too high. But the reason it's too high is because most people will only use a growth rate of 3% (at most).

Also, note that ke and kd are both less than g so there is no weighting of capital such that WACC is greater than g (no calculation needed to solve this problem).

Chad: Let me know when you want to go eat!