One of the things I’ve been thinking about lately is the cost of capital. Given the inflationary environment we’re in currently, I’m sure I’m not the only one. What started me on this path was thinking about the mechanics of the weighted average cost of capital calculation (WACC). WACC is probably familiar to many, but as a brief refresher, the formula is:

WACC=(E/V×R_{e})+(D/V×R_{d}×(1−T_{c}))

Where:

- E = Market value of the firm’s equity
- D = Market value of the firm’s debt
- V = E+D
- R
_{e}= Cost of equity - R
_{d}= Cost of debt - T
_{c}= Corporate tax rate

As the name suggests, we’re taking the cost of equity and the cost of debt, and creating a weighted average based on the market value of each source of capital. Generally speaking, debt is cheaper (i.e. has a lower cost) than equity. This is because in a liquidation event, debt gets paid off first. In financial theory it would be impossible to have a cost of debt of 7% and a cost of equity of 5%. That would violate one of the fundamental laws of finance and Ben Graham would rise from the grave and destroy Wall Street.

As I began thinking through that premise, it occurred to me that the way to achieve the lowest cost of capital then would be to finance a company with 100% debt. Since the cost of debt will always be lower than the cost of equity, it makes sense to increase leverage as much as possible.

The issue with the above is that a company that is financed 100% with debt is absolutely more risky than a company financed 100% with equity because the debt holders expect payments periodically and can force the company into bankruptcy if the company doesn’t make those payments whereas equity owners can typically only fire management and have no guaranteed payments^{1}.

Of course the idea that a 100% debt financed company should have a lower cost of capital than a 100% equity financed company is absurd. As I spent time thinking about this, I realized two things that are probably rudimentary for many people but were just shy of epiphanies for me. The first thing I realized is that WACC is not a static number. It is constantly evolving, based on the performance of a company, macroeconomic forces, and market psychology. This is easy to see when looking at public companies. The market value of their equity changes many times each hour and thus, their cost of capital would change as well. In normal times, the change in equity weight will not change the cost of capital in a material way.

The second realization I had is that cost of equity and cost of debt are not independent. As a company accrues more debt, the marginal debt will become more expensive, and as a company becomes more highly leveraged, the cost of equity will increase.

This leads me to believe that for each company there is probably an optimal capital structure that results in the lowest cost of capital possible and since the cost of debt influences the cost of equity, that optimal capital structure is related to the current risk-free rate, quality of the management, age and stability of the company, macroeconomic factors, market psychology, etc.

I’m still thinking through whether there is a way to calculate an optimal capital structure as a business manager, but that will come another time.

**Effect on Valuation**

Why, you might ask yourself, is this useful beyond an academic exercise? Because one of the other fundamental laws of finance is that the value of something is the present value of future cash flows. The formula is:

PV=FV/(1+r)^{n}

Where:

- PV = Present Value
- FV = Future Value
- r = Required Rate of Return (i.e. Cost of Capital)
- n = Number of periods

As you can see, the cost of capital has a significant effect on the present value, especially if the future cash flows remain constant. As an example, let’s look at a fictional business that generates $1,000 of cash flow per year for ten years.

Cost of Capital | Present Value |

2% | $8,982.59 |

5% | $7,721.73 |

7% | $7,023.58 |

10% | $6,144.57 |

12% | $5,650.22 |

So if I am estimating a consistent cost of capital of 7% when it is really 10%, then the valuation I arrive at for this business may be off by ~14%. That’s a small dollar amount when we’re talking about $1,000 per year of cash flows, but a large dollar amount when we’re talking about $1,000,000 or $100,000,000 per year of cash flows.

If we incorporate my first realization about cost of capital not being a constant, we can see how this effects our valuation as well. Using a constant 7% cost of capital from above, our present value is $7,023.58. However, if our cost of capital changes over time, we can still have an average cost of capital over the ten years of 7%, but a present value of $7,339.83^{2}. That’s a 4.5% difference in value.

I subscribe to the general idea that valuations should not be precise, but rather tell us whether the currently offered price of something is unrealistically high or low, so having a 4.5% swing in valuation isn’t necessarily bad. However, a 15% or more swing in valuation may not be precise enough to make a good decision. And that is assuming you have more or less accurately predicted future cash flows.

**Conclusion**

For quite some time now, most companies have had a very low cost of capital, and that is at least a partial reason that valuations have been so rich. When doing valuation exercises, either academically or professionally, remember to adjust your cost of capital as well as your future cash flow predictions to the best of your abilities in order to get a more accurate valuation estimate.

**Notes and Further Reading**

I recommend this presentation by Aswath Damodaran as well as the entire section of his website devoted to cost of capital.

1 – When discussing equity here, I am speaking of common equity and not preferred equity which can have a dividend payable and operates as a hybrid between debt and common equity.

2 – For the series of 10 years, I used the following discount rates: 7%, 7%, 7%, 10%, 10%, 10%, 10%, 5%, 2%, 2%. The average of these is 7%.