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Hi,
I am struggling to understand how the answer for Step 1 in this question is calculated.
The answer I get is “2” for step one. My working is from the inside brackets to outside brackets and then x / + – , could you please help with where I’m going wrong, I can’t get the answer 1.304.
Question:
South Co is a private company that wants to establish its cost of equity in order to evaluate a new investment proposal. North Co is a listed company that is very similar to South Co.
South Co has a debt:equity ratio of 1:3
North Co has a debt:equity ratio of 1:4
North Co’s equity beta is 1.50
Corporation tax is 40%
Calculate an appropriate beta for South Co to use in its cost of equity calculation to 2 decimal places.Answer:
Step 1 – estimate an ungeared (asset) beta from North
Co’s equity beta
Assuming a debt beta of zero:
Ba = Be (Ve/(Ve+ Vd(1-T))
Ve = value of equity
Vd = Value of debt
T = rate of tax
Ba = 1.50 x 4/(4 + 1 (1-0.40)) = 1.304Step 2 – estimate the geared (equity) beta for South Co
Be = Ba (Ve+ Vd(1-T)Ve)
= 1.304 × (3+1 (1-0.40)/3)
=1.56The answer is beta asset = beta equity * ( E / ( E * D(adj for tax))
So in other words it is Ba = 1.50 * (4 / 4.6) as you must work out Debt first then add it to equity – so 1 * 0.6 + 4 = 4.6
That gives you the bottom part of the formula
Then 4 / 4.6 gives you 0.8695 then multiply by 1.25 which results in 1.304
Hope that answers your question
You have to work out D (adj for tax), then calculate D+EThen divide E by (E + D(adj for tax))
Then multiply by Be to get Ba
Hi, thank you so much for the response, makes sense. I will keep practicing 🙂
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