How does Enterprise Value change when Debt-to-Equity changes?

einy's picture
Rank: Chimp | 15

Hey guys!

I've been confused lately by the way experts interpret the way Enterprise Value changes when Debt-to-Equity ratio changes.

Some of them say that since D/E changes, tax shields are expected, so EV is going up.

But if you think of it this way:
D/E going up drives Beta(levered) to go up. Higher Beta leads to higher cost of equity, which also makes WACC higher. Since WACC is becoming higher, EV goes down.

This may be a simple question for some of you guys out there, can you please shed some light on it?

Thanks!

And a small follow-up:

Do we calculate WACC using D/E or D/V (where V = Enterprise Value, i.e. D+E), because I've seen both versions?

Comments (7)

Aug 13, 2012

weighting on cost of debt in your wacc will increase, so wacc does not necessarily increase when beta increases, in fact, I'm pretty sure the relationship is inverse.

Aug 13, 2012

WACC = [D/E * r(debt) * (1 - t)] + [(1 - D/E) * r(equity)]

take a partial derivative of WACC wrt D/E and get:

dWACC/d(D/E) = [r(debt)(1 - t)] - r(equity) = r(debt) - r(equity) - r(debt)(1-t)

Since under normal circumstances cost of equity is more than the cost of debt, [r(debt) - r(equity)] < 0; the second term is obviously less than zero as well. Thus, the change in D/E provokes and inverse change in WACC, and therefore a same-direction change in EV (as dEV / dWACC < 0 as well).

This is simple calculus, however, some structural factors might come into play that will alter it the other way (my guess)

Aug 13, 2012

More simply put, it depends. Each dollar of debt has a lower cost than equity due to the benefits of the tax shield. Each dollar of debt however, also increases the company's risk of bankruptcy.

Up to a certain point, an additional dollar of debt will lower one's WACC and effectively maximize its EV. Beyond that point however, an additional dollar of debt threaten's the company's livelihood and the prospect of bankruptcy outweighs the benefits of the tax shield. Thus, the WACC increases and EV decreases. The theoretical optimal capital structure is the point which minimizes the cost of WACC.

If you want to learn more look up the static theory of capital structure.

    • 1
Aug 13, 2012
evergumptious:

More simply put, it depends. Each dollar of debt has a lower cost than equity due to the benefits of the tax shield. Each dollar of debt however, also increases the company's risk of bankruptcy.

Up to a certain point, an additional dollar of debt will lower one's WACC and effectively maximize its EV. Beyond that point however, an additional dollar of debt threaten's the company's livelihood and the prospect of bankruptcy outweighs the benefits of the tax shield. Thus, the WACC increases and EV decreases. The theoretical optimal capital structure is the point which minimizes the cost of WACC.

If you want to learn more look up the static theory of capital structure.

I just gave out my last SB but you answered his question beautifully: Optimal/Capital Structure

Here to learn and hopefully pass on some knowledge as well. SB if I helped.

Aug 13, 2012

Thanks, that clears the things up a bit!)

But in terms of the EV and WACC formula how can we interpret this?

WACC = Ke * (1-D/E) + Kd * D/E * (1-T)

Aug 13, 2012

I just shown that before, einy. evergumptious is right - look up Brealey / Myers corporate finance. At some point cost of debt will be larger than the tax shield and cost of equity. Bell-shaped curve

Aug 13, 2012
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