Question
In: Accounting
you are evaluating a new project and need an estimate for your project's beta. You have...
you are evaluating a new project and need an estimate for your project's beta. You have identified the following information about three firms with comparable projects.
| Firm Name | Equity Beta | Debt Beta | Debt to equity ratio |
| Lincoln | 1.25 | 0 | 0.25 |
| Blinkin | 1.6 | 0.2 | 1 |
| Nod | 2.3 | 0.3 | 1.5 |
The unlevered beta for Nod is closest to :
A.1.00
B.0.90
C.0.95
D.1.10
Solutions
Expert Solution
| A | B | C | D | E | F | G | H | I |
| 2 | ||||||||
| 3 | Firm Name | Equity Beta | Debt Beta | Debt to equity ratio | ||||
| 4 | Lincoln | 1.25 | 0 | 0.25 | ||||
| 5 | Blinkin | 1.6 | 0.2 | 1 | ||||
| 6 | Nod | 2.3 | 0.3 | 1.5 | ||||
| 7 | ||||||||
| 8 | Asset (Unlevered) beta for each firm can be calculated using following formula: | |||||||
| 9 | Asset (Unlevered) beta | =βE*W(E)+βD*W(D) | ||||||
| 10 | Where | |||||||
| 11 | βE | is the equity beta | ||||||
| 12 | βD | is the debt beta | ||||||
| 13 | W(E) = 1/(1+ (D/E)) | is the weight of equity | ||||||
| 14 | W(D) | is the weight of debt | ||||||
| 15 | ||||||||
| 16 | Asset unleveread beta of each firm can be calculated as follows: | |||||||
| 17 | ||||||||
| 18 | Firm Name | Equity Beta | Debt Beta | Weight of Equity, W(E) | Weight of Debt, W(D) | Asset (Unlevered) Beta | ||
| 19 | Lincoln | 1.25 | 0 | 0.8 | 0.2 | 1 | ||
| 20 | Blinkin | 1.6 | 0.2 | 0.5 | 0.5 | 0.9 | ||
| 21 | Nod | 2.3 | 0.3 | 0.4 | 0.6 | 1.1 | ||
| 22 | ||||||||
| 23 | Unlevered Beta for Nod will be the average of unlevered beta of comparable firms. | |||||||
| 24 | ||||||||
| 25 | Unlevered Beta for Nod | =(1+0.9+1.1)/3 | ||||||
| 26 | 1.00 | =AVERAGE(H19:H21) | ||||||
| 27 | ||||||||
| 28 | Hence Unlevered Beta for Nod | 1.00 | ||||||
| 29 | Thus the option A is correct. | |||||||
| 30 | ||||||||
Formula sheet
| A | B | C | D | E | F | G | H | I |
| 2 | ||||||||
| 3 | Firm Name | Equity Beta | Debt Beta | Debt to equity ratio | ||||
| 4 | Lincoln | 1.25 | 0 | 0.25 | ||||
| 5 | Blinkin | 1.6 | 0.2 | 1 | ||||
| 6 | Nod | 2.3 | 0.3 | 1.5 | ||||
| 7 | ||||||||
| 8 | Asset (Unlevered) beta for each firm can be calculated using following formula: | |||||||
| 9 | Asset (Unlevered) beta | =βE*W(E)+βD*W(D) | ||||||
| 10 | Where | |||||||
| 11 | βE | is the equity beta | ||||||
| 12 | βD | is the debt beta | ||||||
| 13 | W(E) = 1/(1+ (D/E)) | is the weight of equity | ||||||
| 14 | W(D) | is the weight of debt | ||||||
| 15 | ||||||||
| 16 | Asset unleveread beta of each firm can be calculated as follows: | |||||||
| 17 | ||||||||
| 18 | Firm Name | Equity Beta | Debt Beta | Weight of Equity, W(E) | Weight of Debt, W(D) | Asset (Unlevered) Beta | ||
| 19 | Lincoln | 1.25 | 0 | =1/(1+F4) | =1-F19 | =D19*F19+E19*G19 | ||
| 20 | Blinkin | 1.6 | 0.2 | =1/(1+F5) | =1-F20 | =D20*F20+E20*G20 | ||
| 21 | Nod | 2.3 | 0.3 | =1/(1+F6) | =1-F21 | =D21*F21+E21*G21 | ||
| 22 | ||||||||
| 23 | Unlevered Beta for Nod will be the average of unlevered beta of comparable firms. | |||||||
| 24 | ||||||||
| 25 | Unlevered Beta for Nod | =(1+0.9+1.1)/3 | ||||||
| 26 | =AVERAGE(H19:H21) | =getformula(D26) | ||||||
| 27 | ||||||||
| 28 | Hence Unlevered Beta for Nod | =D26 | ||||||
| 29 | Thus the option A is correct. | |||||||
| 30 | ||||||||
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