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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.

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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.

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