My Decade-Long Journey To Five Million

I’ve been going through the Corporate Finance practice questions, many of which are about calculating Weighted Average Cost of Capital (WACC), a.k.a.: Marginal Cost of Capital (MCC).

The formula is simple:

WACC = w_d[k_d(1 - t)] + w_psk_ps + w_cek_ce

So just like its name, it’s basically a weighted average of the 3 capital components: debt, preferred stock, and common equity.

In some questions, the weights are given as percentage numbers, e.g.: 30% debt, and 70% equity. This is straightforward. We just use 30 and 70 as the weights. 

But sometimes, they are given as debt-to-equity ratio, e.g.: target debt/equity ratio = 0.4. Then Schweser usually explains how to calculate w_d and w_e  from this given ratio in greater details:

First, calculate the weights for debt and equity 
w_d + w_e = 1
w_e = 1 − w_d
w_d / w_e = 0.40
w_d = 0.40 × (1 − w_d)
w_d = 0.40 − 0.40w_d
1.40w_d = 0.40
w_d = 0.286, w_e = 0.714

Dropping unnecessary calculations

This is not necessary–it’s too slow. We don’t need to perform this calculation at all. 

The key point here is that what matters about weights is really their proportion relative to one another, instead of the actual values we use as weights.

That is, if debt/equity ratio is 0.4, it doesn’t matter whether we enter 

w_d = 0.286, w_e = 0.714 

after doing that calculation above, or

w_d = 0.4, w_e = 1 

As long as the d/e ratio is 0.4, we can use 4 and 10. Or 40 and 100. 2 and 5. Or whatever two numbers has that ratio–the most obvious of which is of course 0.4 and 1. So whatever debt/equity ratio is given, just enter that ratio for w_d, and 1 for w_e. Easier, yes?

And of course, here’s the way we do weighted average in HP12c:

1. Clear the statistics registers: f – CLEAR – ∑
2. <Enter value> – Enter – <Enter weight> - ∑+ (an easy way to remember to enter value before weight, is to remember that v comes before w in the alphabet)
3. Repeat step 2 as many times as necessary
4. Display the result: g – 6 (that is, g, and then number 6 key–that’ll give you the weighted average.)

March 15th, 2009 | Category: CFA, Level 1 | Subscribe to comments | Leave a comment | Trackback URL