Project cost of capital capital

slackeranalyst

Hello, AF!

I've got here one tricky EOC question from the CFAI textbook - Reading 45, Cost of capital, N. 16 (page 80).

The company considers expansion to China. The current capital structure of the company is as follows: D = 0.9 billion; E = 2.4 billion USD. The project requires additional 0.1 billion financing: 0.08 billion as debt and 0.02 as equity. The asset beta of the company is 1.053. If the China project has the same asset risk as the company, the estimated project beta for the China project, if it is financed 80 percent with debt, is closest to:

A. 1.300
B. 2.635
C. 3.686

The right answer is C and that's what I can't understand. In the solution the D/E = 4 is used for levering beta:
Project beta = 1.053*[1+(1-0.375)*0.08/0.02]
This "project" beta is further used to calculate the cost of capital using CAPM. Then expected CFs from the project are discounted using this cost of capital to arrive at NPV.

But shouldn't we use the whole company's capital structure:
Project beta = 1.053*[1+(1-0.375)*0.98/2.42]

Am I wrong?

thommo77

The project is 80% financed by debt and 20% with equity and to calculate the risk associated with the project (Beta) I think we'll use the project's capital structure in spite of taking the whole company's capital structure. We are asked in the question to estimate the project beta for China project so we'll use that capital structure.

pawn

Well, I can see your point. But the project shares its financing risks with the company, doesn't it?

Consider the same situation but the project being financed 100% with debt. Then following this approach the beta and cost of equity will be infinitely large.

SkipE99

The project does shares the risk with the company but the company's asset beta is given which I think includes the effect of the overall debt and equity financing. I think the question straight away asks about the project beta and the asset beta, which already has the effect of company's financing, is used to calculate it so we'd use the project financing. Again it's my opinion according to my understanding which could be wrong.

willsucceed

Thank you for you opinion!

Actually as I understand, company's asset beta does not include any financing risks. That's why we need to re-lever it.
I agree that this particular question is fairly straightforward. But it raised doubts im my mind concerning my understanding of the subject.

So I will restate the question and I hope someone will help me with this:
What's the appropriate discount rate for FCFFs of the project similar to the main business of the company?

ba736

Deimon Wrote:
-------------------------------------------------------
> Thank you for you opinion!
>
> Actually as I understand, company's asset beta
> does not include any financing risks. That's why
> we need to re-lever it.
> I agree that this particular question is fairly
> straightforward. But it raised doubts im my mind
> concerning my understanding of the subject.
>
> So I will restate the question and I hope someone
> will help me with this:
> What's the appropriate discount rate for FCFFs of
> the project similar to the main business of the
> company?


wacc

MarginofSafety

WACC of the whole company (including the project) or WACC of the project itself (as though it was a separate company)?

hw0799

wacc of the whole company if project risk = company risk.

wacc of the project itself if project risk <> company risk.

hw0799

Well, it defenitely makes sense.
But frankly saying, I'm still confused a little bit about all this.

Please consider the situation that I've already referred to:

the project is slightly less risky than the company business (project risk <> company risk), for example the company asset beta is 1 and the project asset beta is 0.9;

the 1-mln project is fully financed with a new debt issuance (D = 1 mln, E = 0 mln);

Then if we try to calculate levered beta for the project using project capital structure we get:
proj.equity.beta = proj.asset.beta * ( 1 + (1 - T) * D/E ) = 0.9 * (1 + (1 - T) * 1/0 ) = Inf

Notice that it's all right if we calculate the project equity beta using the whole company weights.

Please clarify. I trust this hint can help me fully grasp the concept.

SkipE99

wacc of the whole company if project risk = company risk AND project capital structure = company capital structure.

wacc of the project itself if project risk <> company risk.

Since project is less risky that company risk, wacc of project should be less than company wacc.

You have to use the capital structure of project and not the whole company's capital structure. You use the capital structure that's relevant to the project.