Doubts

ex. 1 Exercise set 8

ex. 1 Exercise set 8

by Luca Bassotto -
Number of replies: 4

Dear Professor,

I am working through the problem 1) of the exercise set 8 where the company changes its D/E ratio to 0. 

According to the formula for WACC:

WACC=DD+E⋅Rd⋅(1−Tc)+ED+E⋅Re\text{WACC} = \frac{D}{D+E} \cdot R_d \cdot (1 - T_c) + \frac{E}{D+E} \cdot R_e


If D/E = 0, then D = 0, so the first term of the formula becomes 0. The second term becomes EE+0⋅Re\frac{E}{E+0} \cdot R_e​, which simplifies to just ReR_e​, because the weight of equity is 1. Therefore, the WACC should be equal to Re which in this case is 12%.

I have also tried to substitute a random number for EE (say, E=100E = 100). This would result in:

WACC=00+100⋅0.05⋅(1−0.25)+100100+0⋅0.12=0+1⋅0.12=0.12\text{WACC} = \frac{0}{0 + 100} \cdot 0.05 \cdot (1 - 0.25) + \frac{100}{100 + 0} \cdot 0.12 = 0 + 1 \cdot 0.12 = 0.12

So, the WACC would still be equal to ReR_e​, which is 12%.

My question is what I am missing?

Thank for your patience,

Luca

In reply to Luca Bassotto

Re: ex. 1 Exercise set 8

by Alessandro Imbrogno -
From my understanding, what we're seeing here is the fact that the firm is deleveraging and, in particular, is shifting from having some debt to no debt at all. When the firm changes its capital structure — for example, moving from a D/E of 1 to no debt — we can’t assume that the WACC from the original structure remains valid.
In fact, in this new scenario, we'd simply have Ra=Re but we cannot assume Re to be equal to 12% as before because in that 12% we also considered the previous effect of debt, which is now gone. So, starting from the formula:
Re=Ra+D/E*(Ra-Rd) --->MM Proposition 2
we can re-arrange and solve for Ra, and if we do so we obtain 8.5%.

We now see that Ra is = to Re because if D/E is 0, the equation above will bring us to the same result.
We have therefore now calculated the new values to plug into the WACC which gives us: 1*8.5%+0*5%*(1-25%)-->8.5%

From how I see it, by having more debt, the firm becomes more risky and therefore shareholders require a higher Re, and so if we deleverage, we should obtain a lower Re.

I hope this makes sense & that is actually formally correct
In reply to Luca Bassotto

Re: ex. 1 Exercise set 8

by Julio Crego -

Alessandro is correct. When we change the leverage of the firm, we change \(r_E\), even in perfect capital markets. If we have higher debt, equity becomes more risky because investors will get nothing in bad states of the world (high beta).

In perfect capital markets, WACC is independent of leverage. Hence, we always need to compute WACC, and then from WACC (\(r_a\) ), we can obtain the cost of equity or debt. 
In reply to Julio Crego

Re: ex. 1 Exercise set 8

by Roman Lorenz -
I have an additional question for this topic. When we calculate Re in the first step, why aren't we using the formula Re=Ra+D/E*(Ra-Rd)*(1-t) due to the given tax rate of 25%? Is there no necessity to include the taxes in this calculation?

Thanks in advance
In reply to Roman Lorenz

Re: ex. 1 Exercise set 8

by Julio Crego -
If the risk of the ITS is similar to that of assets, we do not include it (e.g. constant debt-to-equity ratio). This is because the equityholders do not change their risk; hence, they do not change their required return

If the risk of ITS is different from that of assets, we include it (e.g., constant debt)