Estimate a project beta financed by 100% debt

In the reading 19"Capital Budgeting", the discount rate error tells “you should use the project’s required rate of return instead of the cost of debt”. Then I suddenly recalled that in Level I, when we use pure-play method to estimate a project’s beta, we use the formula βproject = βu [1+(1-t)D/E]. Here, if a project is 100% financed(E=0), it looks that the formula cannot be applied? and if the cost of debt is not suitable as discount rate, what is the required return here? estimated by CAPM without the assistance of a levered β?

If it’s financed 100% by debt, then equity is zero; you cannot compute beta when equity is zero.

No Equity, no equity beta. Cost of Capital are just interest rate minus tax-shield, i.e. i x (1-t)