It is because the answer is calculating the APV (because there is a substantial change in the level of gearing).
With APV, for the base case NPV we always discount at the cost of equity if it was all equity financed (and then adjust later for the effect of the gearing). If a company is all equity financed then the equity beta will always be equal to the asset beta.
I do explain all of this in my free lectures 🙂
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