Question

You have just run a regression of monthly returns on MAD, a newspaper and magazine publisher, against returns on the S&P 500, and arrived at the following result.

                                        Intercept: -0.005% ; Slope: 1.950; R2: 45. 0%.

You now realize that MAD went through a major restructuring at the end of last month (which was the last month of your regression), and made the following changes.

• The firm sold off its magazine division, which had an unlevered beta of 0.55, for 39 million.

• It borrowed an additional 18 million and bought back stock worth 57 million. After the sale of the division and the share repurchase, MAD had 43 million in debt and 148 million in equity outstanding. If the firm’s tax rate is 40.00% percent, re-estimate the beta after these changes.

1.

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The value of equity before the sale of the division and stock buyback is equal to: (please enter your numbers in millions (i.e., 100 million is 100, not 100,000,000)

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2

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The value of debt before the sale of the division and stock buyback is equal to

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3

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The unlevered beta of the firm prior to the sale of the division and stock buyback is equal to

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4

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The weight (proportion of selling unit divided by total firm value) of the selling unit is equal to (hint: please enter your answer in decimal format. i.e., 25% is 0.25)

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5

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The weight of the remaining unit is equal to

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6

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The unlevered beta of the remaining unit is equal to

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7

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The levered beta after the sale of the division and stock buyback is equal to

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Answer 1

SOLUTION:

1. The value of equity before the sale of the division and stock buyback is equal to: (please enter your numbers in millions (i.e., 100 million is 100, not 100,000,000)

E = Current equity + stock bought back + sale value of magazine division

E = 148 + 57 + 39

E = $ 244 million

Hence The value of equity before the sale of the division and stock buyback is equal to $ 244 million

2. The value of debt before the sale of the division and stock buyback is equal to

D = Current debt - incremental borrowing

D = 43 - 18

D = $ 25 million

Hence The value of debt before the sale of the division and stock buyback is equal to $ 25 million

3. The unlevered beta of the firm prior to the sale of the division and stock buyback is equal to

Unlevered beta = Levered Beta / [1 + D / E x (1 - tax rate)]

Levered beta = slope of the regression line = 1.950

D = 25 (part (2) above)

E = 244 (part (1) above)

Tax rate = 40%

Hence, unlevered beta = 1.950 / [1 + 25 / 244 x (1 - 40%)]

= 1.8371

Hence The unlevered beta of the firm prior to the sale of the division and stock buyback is equal to 1.8371

4. The weight (proportion of selling unit divided by total firm value) of the selling unit is equal to (hint: please enter your answer in decimal format. i.e., 25% is 0.25)

Weight, W = selling unit divided by total firm value

= 39 / (D + E)

= 39 / (25 + 244)

= 14%

= 0.14

Hence The weight (proportion of selling unit divided by total firm value) of the selling unit is equal to 0.14

5. The weight of the remaining unit is equal to = 1 - 0.14

= 0.86

Hence The weight of the remaining unit is equal to 0.86.

6. The unlevered beta of the remaining unit is equal to:

If B is the unlevered beta of the remaining unit then,

Unlevered beta of the whole firm = W x Unlevered beta of the selling division + (1 - W) x B

Or, 1.8371 = 0.14 x 0.55 + 0.86 x B

Hence, The unlevered beta of the remaining unit = B = (1.8371 - 0.14 x 0.55) / 0.86 = 2.06

Hence The unlevered beta of the remaining unit is 2.06

7. The levered beta after the sale of the division and stock buyback is equal to

Levered beta = Unleverd beta x [1 + New D / E x (1 - tax rate)]

= 2.06 x [1 + 43 / 148 x (1 - 40%)]

= 2.41

Hence The levered beta after the sale of the division and stock buyback is equal to 2.41