CFA CFA Level 3 Help me understand the WACC/Beta calculations…

# Help me understand the WACC/Beta calculations…

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• I am having a really really tough time with this. The explanation in the book is poor, and I can’t seem to deduce the method from practice questions either.

I’m confused on everything, but one hang-up in particular: why does it seem that Total OPERATING Asset Beta includes pension assets/liabilities? Shouldn’t it just include the operating assets/liabilities? So confused.

Thank you in advance to anyone who can help out.

I did some work on this the other day as it also confused me, but I seemed to get my head around it. What it is saying is that if you exclude pension assets when calculating the beta for a firm, it affects the outcome as the pension assets a implicitly linked to the firm. The pension assets are a future liability to the firm, and should therefore be treated as a liability on the balance sheet.

Scenario 1 (excluding pension assets): assume that the company has an equity Beta of 2, and is funded by £2m equity and £3m debt (total debt + equity of £5m). The Equity + Liabilities side of the balance sheet are therefor as follows:
Debt £3m with Beta 0
Equity £2m with Beta 2
TOTAL FIRM VALUE £5m with Beta 0.8
The firm Beta is a weighted average of the equity Beta and debt Beta (debt beta is equal to 0), and so the company Beta is 0.8.

Because the Beta of Assets and the Beta of Liabilities + Equity is equal, you can conclude that the Beta for the Assets (which at this point consist solely of Operating Assets) is also 0.8. Also, the value of operating assets will equal the value of Liabilities + Equity (£5m).

With me so far?

Scenario 2 (assumes the inclusion of pension assets): let’s now assume we have a £2m pension, and that the pension assets consists of a mix of 50% equity investments (which we will say have a Beta of 1.2) and 50% fixed income (which have a beta of 0). As before, the overall pension asset Beta is a weighted average of the equity and fixed income beta, and is therefore 0.5.

If you now bring the pension assets onto the balance sheet, you have the following:
Operaing Assets £5m with Beta ‘X’
Pension Assets £2m with Beta 0.5
TOTAL VALUE £7m with Beta ‘Y’

We know total beta must equal the existing Beta of the firm. Originally excluding pension assets this was 0.8, however by including the pension on the Assets, we must also include it on the Liabilities & Equity side. Therefor the Equity + Liabilities side of the balance sheet now becomes:
Normal Debt £3m with Beta 0
Pension Liability £2m with Beta 0 (treated just as normal debt)
Equity £2m with Beta 2
TOTAL FIRM VALUE £7m with Beta 0.57

Notice the total firm Beta has now fallen to 0.57. We can therefore plug this back into the Assets side of the balance sheet as follows:
Operaing Assets £5m with Beta ‘X’
Pension Assets £2m with Beta 0.5
TOTAL VALUE £7m with Beta 0.57

We are now in a position to recalculate the Operating Asset Beta so that the Total Asset Beta is 0.57. Rearranging the above numbers provides an Operating Asset Beta of 0.60. This is the actual Operating Asset Beta when taking pension assets into account.

If you then take it a step further. The pension decides to assume more risk by changing the asset allocation to 75% equities and 25% debt. The overall Pension Beta is now therefore 0.75. This changes the balance sheet as follows:
Operaing Assets £5m with Beta 0.60
Pension Assets £2m with Beta 0.75
TOTAL VALUE £7m with Beta 0.64

On the basis that Total Asset Beta equals Total Firm Beta, the Beta of Liabilities and Equity has now also changed to 0.64. On the basis that debt has a Beta of 0, the Equity Beta must therefore have changed. Working backwards, we can calculate that the Equity Beat is now 2.24 (compared to the original value of 2). This makes sense, as there is now more risk in the pension plan which increases the overall risk of the firm.

A common question is then how to change the capital structure of the firm to bring the Equity Beta back down to what it was. The answer here is to issue more equity and use the proceeds to repay debt. This reduces the leverage of the company, and thereby reduces the Equity Beta. So, if the company now issued £0.24m of equity and used it to repay debt, the Equity + Liabilities side would become:
Normal Debt £2.76m with Beta 0
Pension Liability £2m with Beta 0
Equity £2.24m with Beta 2
TOTAL FIRM VALUE £7m with Beta 0.64

Quite long-winded, but hopefully it makes sense! Apologies for any typos too!

Final notes:
Unless told otherwise, assume pension assets a split 50% equities and 50% fixed income. Also, assume debt and pension liabilities have 0 beta.

Forgot to mention, if you use the Operating Asset Beta to calculate WACC then the WACC will be more expensive if you exclude pension assets, as the operating asset beta will be higher. This will lead you to reject potential profitable projects that should actually be accepted.

Formula for WACC = (Risk Free Rate) + [Operating Asset Beta x (Market Risk – Risk Free Rate)]

Hello,
Thank you very much for the explanation.
I have a question regarding the example of what happens if pensions assets risk is increased.

What happens to WACC? I found a question where it says, that the beta for pension assets increase, then the beta for operating asseta increase, and consequently the WACC.

I don’t get it, bc total assets beta increase but not operating assets beta.. I would have said WACC staysmthe same because it is calculated with operating assets beta.

Thx for your help!

Are you able to post the question?

It asks to explain the impact on equity beta and wacc of changing the plan asset allocation to 100% equity.

Equity beta effect is ok, but the wacc?? It says it increases due to increasing operating asset beta.

@MattJuniper, that is BY FAR the best explanation I have seen on this topic. Thank you so much for taking the time to do that. I still have a couple minor questions, but I will run through a couple practice problems today and then post if I am still having trouble.

Thanks again!

Wanted to clarify on “the overall pension asset Beta is a weighted average of the equity and fixed income beta, and is therefore 0.5”
Shouldn’t it be (2/7)*(0.5)*(1.2) = 0.17, instead of 0.5?

Hi I have 2 questions regarding wacc and beta, could someone help me with these:

1. If cash and marketable securities do not have the same risk as debt, show how these assets can be taken into account when calculating WACC. Only a brief answer is necessary.

2. Give a brief explanation for why debt may have a beta above 0, in other words, why the debt fluctuates with the change in the market portfolio. The answer can be brief.

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