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Hi
I am wondering if you can help understand an answer in b) i) of Cigno Co question in the exam kit.We are calculating the cost of capital for acquisition of a company by method of degearing and re-gearing asset beta.
We know that asset beta of Anatra Co is 0.68 and have calculated asset beta of Cigno Co as 0.72.Tax rate is 22%.
In the answer, we have calculated that MV Equity of Cigno Co is 36,000 million and Anatra Co is 21,000m.
But to get the equity beta the formula is given in answer as:
Equity beta = (0.68 x 21,000 + 0.72 x 36,000) / (21,000 + 36,000)The asset beta formula uses MV debt which I dont see above? I might be being silly here but I can’t work out why we’ve used two MV of equity and no MV debt information? And also why have we taken MV Equity after tax? (0.72 x 36,000).
Apologies if unclear, quite hard to explain on this with the length of these questions!
Thanks in advance
You have written:
“But to get the equity beta the formula is given in answer as:
Equity beta = (0.68 x 21,000 + 0.72 x 36,000) / (21,000 + 36,000)”However that is not correct and is not what the answer says. That equation is calculating the overall asset beta (0.71), which is the weighted average of the two individual asset betas (0.68 and 0.72), weighted by the market values of the two company’s equities (21,000M and 36,000M).
It is only after having calculated the overall asset beta that we then use the asset beta formula to calculate the overall equity beta (by bringing in the gearing).
I do explain in my free lectures on CAPM, that when two streams with different betas are combined, then the overall beta is the weighted average of the two individual betas.
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