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    A particular firm is fully debt financed (£400,000), but now decides to change its debt-to-value ratio to 0.75 (permanently). Bondholders require a 8% return, whereas SH's require a 12% return. Assuming a corp. tax of 35% (but risk free debt and no distress costs), by how much does the market value of the firm change as it alters its capital structure?

    The answer is MV decreases by 8.8% (less debt = less MV), but I can't work it out. Can you?
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    could you be specific. do you mean debt to total value (debt+equity) or total value as in total market capitalisation?
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    debt to total value (debt+equity)
    so 300000 debt
    100000 equity
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    nothing mentioned about operating income/cash flow?

    All the examples Ive done in seminars mention a cash flow
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    (Original post by neiljeff123)
    nothing mentioned about operating income/cash flow?

    All the examples Ive done in seminars mention a cash flow
    Nope, sorry this is the real past exam question
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    Hi,

    It would be helpful if you also told us about the conditions in which this firm hypothetically operates. I can solve this assuming they're in a modigliani miller perfect world with tax. I think this is probably what you're working with as you mentioned that there's no distress costs (which is one of the conditions of this world also).

    Here's how to solve it:

    In such a MM world, the value of an Unlevered firm (i.e. 100% equity) is = to the value of a leveraged firm. This is because: Debt is cheaper, so one would assume more debt = more firm value (discounted at a lower rate). However, the key assumption here is that as debt is risk free, the equity holders bear all of the firm's risk. And as more (risk-free) debt is added, the firms risk is borne by a smaller proportion of equity holders. This effectively increased risk increases the equity holders required return so as to perfectly offset the value of the cheaper debt. In such instance the firm's value remains the same (i.e. 400,000.)

    However, because there's tax, there's a tax shield of debt, the PV of which is just Debt proportionxtax rate (google for proof, it's quite simple). therefore, the tax shield value has been lost by the reduction in debt, that is, 100,000. (i.e. because they're now only 75% debt). 100,000*0.35= 35,000. 35,000/400,000=0.0875, i.e. 8.8%
 
 
 
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