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The formula is as follows:
?a = Ve/((Ve +Vd (1?T ))*?e+Vd/(Ve +Vd (1?T ))*?d?a is the asset or ungeared ?
?e is the equity or geared ?
?d is the ? of debt in the geared company
Ve is the market value of equity in the geared company
Vd is the market value of debt in the geared company
T is the rate of corporation taxI am wondering why tax rate applied to the whole Vd if actual impact of tax is 6% instead of 30%.
As example 10% annual interest rate (average approximate) * 2 years (for instance) * 30% tax rate (for example) = 6%.It depends on long term or short term loan, interest rate and etc. But simply apply (1-T) is very rough calculation.
Or other conclusions are used in formula?
I assume that you have watched my free lectures in which case you will know that Vd is the PV of the interest payments in perpetuity discounted at the investors required return (which is pre-tax).
The tax saving in perpetuity will be T x the interest payment each year, and therefore the net cost to the company each year will be (1-T) x the interest payment.
Since the PV of the interest payments in perpetuity is Vd, the PV of the net cost in perpetuity will be (1-T) x Vd.
(I also hope you realise – and I explain in my lectures – that the second term in the formula is always irrelevant in the exam because we always assume that the debt is risk free and that therefore the beta of debt is zero.)
If you haven’t watched the lectures then I do suggest that you watch them – they are a complete free course for Paper FM and cover everything needed to be able to pass the exam well.
In future, if you want me to answer then please ask in the Ask the Tutor Forum – this forum is for students to help each other 🙂 )
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