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Hello sir,
Pasting a part of a question & its solution on type 3 valuation“….Currently, Anderson Co has an asset beta of 1.25 and Webb Co has an asset beta of 1.60. Assume that the beta of debt is zero.
The current financing of the two companies is:
$million………….. Debt…..Equity
Anderson Co…….50………450
Webb Co…………..20……….80Required:
Calculate the gain in wealth for Anderson Co‘s shareholders if the acquisition goes ahead.
Solution:
The asset beta of the combined company is (1.25 x (500/600)) + (1.60 x (100/600)) = 1.31
Therefore, the equity beta of the combined company is (using the beta formula from formula sheet and assuming the new gearing is 150 debt to 530 equity):
1.31 x (1 + [0.7 x (150/530)]) = 1.57
…”
(Kaplan Study Text, Chapter #15 – Business Valuation, Page# 565)My question: Everything else is clear except how do we assume the new gearing of 150 debt to 530 equity?
I am sorry but unless there is something in the question that you have not typed, then I really have no idea why they have assumed 150 to 530.
I do not have the Kaplan Study Text and so I can’t check what they have done.
Question:
Anderson Co is planning to take over Webb Co, a company in a different business sector, with a different level of risk. Anderson Co’s free cash flows are forecast to be $50m per annum in perpetuity, Webb Co’s free cash flows are forecast to be $10m per annum into perpetuity and there are expected to be annual post-tax cash synergies of $5m if the acquisition goes ahead.
The combined company will pay tax at 30% and will have a pre-tax cost of debt of 5%. The risk free rate is 3% and the equity risk premium is 5.8%.
Currently, Anderson Co has an asset beta of 1.25 and Webb Co has an asset beta of 1.60. Assume that the beta of debt is zero.
The current financing of the two companies is:
$million………….. Debt…..Equity
Anderson Co…….50………450
Webb Co……………20………80Required:
Calculate the gain in wealth for Anderson Co‘s shareholders if the acquisition goes ahead.
Solution:
The asset beta of the combined company is (1.25 x (500/600)) + (1.60 x (100/600)) = 1.31
Therefore, the equity beta of the combined company is (using the asset beta formula from formula sheet and assuming the new gearing is 150 debt to 530 equity):
1.31 x (1 + [0.7 x (150/530)]) = 1.57
Hence, using CAPM, the cost of equity is:
3% + (1.57 x 5.8%) = 12.1%and so the WACC = (12.1% x (530/680)) + (5% x (1 — 0.30%) x (150/680)) = 10.2%
Therefore, the discounted free cash flows of the combined company are (as a perpetuity):
($50m + $10m + $5m)/0.102 = $637m.
The value of equity is then this:
NPV — the value of debt, i.e.$637m — $150m = $487m
Hence the shareholder wealth of the Anderson Co shareholders has increased from $450m to $487m as a consequence of the acquisition.
I think that they have done is this (although it is not really valid and I am guessing (without seeing the study text) that they are trying to illustrate a point:
At the moment the total value of the two companies is Anderson 500 and Webb 100 – a total of 600.
If you ignore the synergy, then adding the two together would result in equity of 530 (450 + 80) and debt of 70 (50 + 20).
However there are two problems. One is that the synergy would increase the total value (and the benefit would go to shareholders and therefore increase the market value of the equity) and the other is that finance would have to be raised in order to pay of the acquisition. It seems that what they have done initially is to ignore the synergy and assume that extra debt of 80 was raised in order to finance the acquisition of the share in Web (which have a market value of 80). This would end up with the equity being 530 and the debt rising to 150.
You are happy with the rest of the calculations and the resulting answer. However the problem is that the end result gives a different value for the equity and therefore a different gearing. So you would then have to rework it all with this new gearing. That would result again with a different gearing which would again mean reworking on this new gearing.
And so on and so on…… However each time you would get close and closer to the final result which would be that eventually the gain would result in the gearing being the same as had been used (I hope that is making some sense).
This is called the iterative approach which you would never have to do in the exam, but you could just be expected to explain the problem that there is. (With a computer you could do it, but not in the exam).
Again I do not have the Kaplan Study Text, but I would be surprised if they have not written after what the problem is and therefore explain this iterative approach.
Thank you for the great explanation sir,
They have a part in the question in the end which I actually missed to type here and also didn’t read properly:
‘Anderson Co is planning to make a cash offer of $80m to buy 100% of the shares of Webb Co. The cash offer will be funded by additional borrowing.’
My apologies and thank you for making it clear.
You’re a great teacher.
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