Valuing Companies





Kerry Back

Intrinsic value is an all-important concept that offers the only logical approach to evaluating the relative attractiveness of investments and businesses.

Intrinsic value can be defined simply: It is the discounted value of the cash that can be taken out of a business during its remaining life.

Equity value or enterprise value?

  • Can forecast cash flows after net payments to lenders.
    • These are equity cash flows.
    • Discount at an appropriate rate, given stock risk.
  • Or, can forecast total cash flows to shareholders and lenders.
    • Discount at a blended rate, given equity and debt risk.
    • Present value is enterprise value (debt + equity value).
    • Subtract value of debt to get equity value.

Equity cash flow

  • Subtract interest expense in income statement.
  • Forecast future growth in invested capital.
  • Forecast how much of the growth will be debt financed.
  • Subtract change in IC not debt financed and also subtract any net debt redemptions from income to get equity cash flows.

Free cash flow

  • Total cash flows to shareholders and lenders is called free cash flow.
  • Don’t deduct interest expense in income statement.
  • Subtract change in invested capital without worrying aobut how much will be funded by debt or equity.
  • Taxes will be overstated (because interest reduces taxable income). Fix that in cost of capital (more later).

Perpetuities

  • A company has no definite ending date, so a perpetuity model is reasonable.
  • What cash flow will be generated next year?
  • By how much will it grow or decline each year afterwards?
  • If growth is constant at rate \(g\), then value of the company today is \(c_1 / (r-g)\).

Two-stage growth model

  • Instead of constant growth beginning next year, forecast cash flows year-by-year for \(n\) years.
  • Assume constant growth beginning in year \(n+1\).
  • Terminal value at year \(n\) is

\[\text{TV} = \frac{c_{n+1}}{r-g}\]

  • Value of the company today is

\[\frac{c_1}{1+r} + \frac{c_2}{(1+r)^2} + \cdots + \frac{c_n}{(1+r)^n} + \frac{\text{TV}}{(1+r)^n}\]

Example

  • Forecast cash flows \(c_1=100, c_2=150, c_3= 180, c_4=200\).
  • Afterward grow at 5% per year forever.
  • Required rate of return is 12%.
  • \(c_5 = 200 \times 1.05 = 210\), so terminal value at year 4 is \(210/0.07\).

  • Company value is

\[\frac{100}{1.12} + \frac{150}{1.12^2} + \frac{180}{1.12^3} + \frac{200}{1.12^4} + \frac{210/0.07}{1.12^4}\]