1. General Considerations

Having learned what cash flows we have to estimate and how we can forecast them, the next step in our firm valuation journey is to determine the relevant cost of capital (a.k.a. discount rate) for the firm's expected future cash flows. 

 

The basic idea behind the cost of capital is fairly simple:

  • The cost of capital is the rate of return that investors could earn when putting the same amount of money into a different investment with identical risk. 
  • The cost of capital, therefore, is the opportunity cost of making a specific investment: Because the investor puts her money into a specific investment, she cannot invest it elsewhere (at the same risk) and, therefore, foregoes the rate of return that the other project would have promised. In order to attract capital, an investment therefore has to promise at least the same rate of return as the alternative investment (with the same risk).

  

Example

To illustrate this, let's assume that a firm promises a single payout of 1'100 in one year (FCF1). The investor assesses the riskiness of the project and concludes that an alternative investment with the same risk is expected to generate a rate of return of 10% per year. Therefore, the cost of capital, denoted with the letter k, is 10%. Based on this information, how valuable is the firm in question today (present value)?

  • Instead of investing in the firm, the investor could put her money into the "alternative investment" at a rate of return of 10%.
     
  • In order to reach the same payout as the firm in one year, namely 1'100, the investor has to put 1'000 into the alternative investment today. This capital then grows at a rate of return of 10% to 1'100 in one year (future value) and therefore perfectly replicates the cash flow of the firm:

    \( \text{Future value}_1 = \text{Investment} \times (1+k) = 1'000 \times 1.1 = 1'100 \)
     
  • These considerations imply that the present value of the firm's future payment of 1'100 is 1'000:
     
    \( \text{Present value} = \frac{FCF_1}{1+k} = \frac{1'100}{1.1}=1'000 \)
     
  • Put differently, from today's perspective, the value of the firm's future cash flow is 1'000. This is how much the investor is willing to pay today in exchange for the firm's expected future cash flows. 
    • At this purchase price, the investor can expect to earn a fair return that is equal to the cost of capital.
    • If the purchase price is higher than 1'000, the investment will not be able to cover the cost of capital. The investor would be better off putting her money in the alternative investment.
    • In contrast, if the purchase price is lower than 1'000, the firm promises a return that exceeds the cost of capital and therefore constitutes an attractive investment.

  

In competitive markets, where many investors compete for attractive investment opportunities and many investment opportunities seek financing, we can expect that market forces push transaction prices towards their fair values. 

  

The road ahead

While the basic idea behind the cost of capital is, arguably, rather intuitive, there are some implementation issues when it comes to the estimation of the cost of capital (why 10% in the preceding example?). Moreover, since firms are generally financed with debt and equity, we have to discuss the relations between the cost of debt (\( k_D \)), the cost of equity (\( k_E \)), and the firm's overall cost of capital (\( k_A \)).

In most cases, we will rely on the so-called Capital Asset Pricing Model (CAPM) to compute these costs. We will speak alternatively of discount rates, risk-adjusted discount rates, required rates of return, expected rates of return, and cost of capital.