CAPM debt to equity calculation of proxy comp and investing company

Hi there first and foremost thanks for the amazing lectures, they really help sink in the info I’ve previously learnt.

however this bit isn’t quite sinking in for me and I’m getting myself confused and just want to clarify his for the exam.

so I understand the capm model but keep getting confused with the calc part, so for example:

tax is 30% lets say and proxy comp say it has 25% debt, 75% equity and its beta equity is say 0.8. from the online lecture i think i learnt that you do .8 * (100/100+(.7*25) = .8(100/117.5) = .6809 (4dp). this gives me the beta asset and then i re gear using investment companies debt to equity ratio, which i understand but the calculation aspect is confusing me somewhat.

or i could do it this way = 25% means debt to equity ratio is 1/.25 = 4, so 1:4. so i could do if im right, 0.8*(4/4+(1*.7) = .8(4/4.7) = 0.6809 so either way i get the same answer.

but on the acca tech article i just read they calculated the above question as 0.8*(75/75+(.7*25) = 0.8(75/92.5) = 0.6486 which is obviously a different answer?

i’m confused as to which technique is correct or have i made a silly mistake somewhere. because some questions say the debt to equity is 1:4 where other questions might say like the above question, debt is 25% and equity is 75%.

Thank you in advance as always !

Hoping to nail this exam and get part qualified , fingers crossed !

Martin