| Here are some examples of how to calculate Beta. You can use these formulas for |
| other calculations after you understand how they work. |
| Exercise: | (From the Cost of Capital Workbook - Pratt, Shannon 2nd edition) |
| The following are known: |
| Risk Free rate as of the valuation date (Rf) | | | 6% |
| Beta for Security XYZ (B) | | | 1.50 |
| Equity Risk Premium for the market as a whole (RPm) | | | 0.08 |
| Compute the equity risk premium for security XYZ |
| The equity risk premium for security XYZ Rpi is equal to beta times the equity risk premium |
| for the market as a whole: |
| Beta XYZ | 1.5 | | 1.50 |
| RPm | x8% | | 8% |
| RPi | 12% | | 12% | Excel solution: | | 0.12 |
| | | | | | or | 12% |
| Compute the expected return (cost of capital) for security XYZ based on the CAPM |
| The formula for computing the cost of equity based on CAPM is: |
| | E(Ri) = | = Rf + B X (RPm) |
| | | =0.06 + (1.5 X 0.08) |
| | | =0.06 + 0.12 |
| | | =0.18 or 18% | | Excel solution: | | 0.18 |
| | | | | | or | 18.00% |
| The expected return in excess of the risk-free rate for security ABC is 12% and the equity risk |
| premium for the market as a whole is 8%. |
| Compute the beta for security XYZ. |
| Drectly, from the CAPM formula: | E(Ri) - Rf = B X (RPm) |
| Take this formula and use your algebra from Junior High - divide each side by RPm and you get: |
| =(E(Ri) - Rf) / RPm | =(0.18-0.06)/0.8 = 0.12/0.08 = | | | 1.5 |
| | | | | Excel solution: | | 1.5 |
| We know the following about Company ABC: |
| | Raw Numbers | Notation | Input Numbers |
| Unlevered Beta | 1.25 | B(u) | 1.25 |
| Debt | $75million | Wd | 0.75 |
| Equity | $25million | We | 0.25 |
| Tax rate | 40% | t | 40% |
| Question: Compute the levered beta for Company ABC |
| Formula: B(L) = | B(U) x (1 + (1-r) x Wd/We) | | | | Excel Help: |
| Answer: | =1.25 x (1 + 1-0.40) x 0.75/0.25) | | | | 3.5 |
| | =1.25 x (1 +0.60 X 3) |
| | =1.25 x (2.8) |
| | =3.5 |
| We know the following about private Company XYZ: |
| | Raw Numbers | Notation |
| Unlevered Beta | 0.5 | B(U) |
| Levered Beta | 1.4 | B(L) |
| Tax Rate | 40% | t |
| Total market value of capital: | $100million |
| Question: What is the market value of the EQUITY for Company XYZ? |
| Answer: | Use elementary algebra to modify each side of the equation |
| | =1 + (1 - t) Wd/We | | = | B(L) |
| | | | | B(U) |
| | =(1 + t)Wd/We = | | = | B(L) | -1 |
| | | | | B(U) |
| | =0.60 x Wd/We = 2.8 - 1 |
| | =Wd/We = 1.8/0.6 |
| | =Wd/We = 3 OR D / E = 3 OR D = 3E |
| Excel Help: This one is better worked by hand. |
| Since we know that total capital equals $100million therefore: |
| | D + E = $100,000,000 |
| | 4E = 100,000,000 |
| | E = $25,000,000 |
| | D = 3E = $75,000,000 |
| | The estimated equity value is therefore $25,000,000. |
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example.xlsx
