Modigilani and Miller Explained….

Thought of writing a blog post about this based on my experience lecturing for the subject of ‘Financial Strategy (F3)’ for CIMA. Seemingly many students and academics a like, go through the theoretical stuff of MM without a simplified understanding and rationale behind the theory it self. However given the engineering background I come from, I refuse to accept a theory as it is without atleast a simplified rationale or explanation to it. This blog post is an attempt to provide a simplified rationale to the theory it self and it is the exact same explanation that I use in my class room as well. This blog post is part of a blog series where I intend to share with the wider student community some of the CIMA F3 explanations that I use in the class room. So here we go.

Value of a Geared Company = Value of an Un-geared Company + Tax Benefit

Before we get in to the above let us consider the following illustration of three companies with differed levels of gearing.

Let us assume that these companies are identical in all aspects, except their capital structures. A is ungeared, B has a gearing of 30:70, and C has a gearing of 40:60 as observed by their Debt and Equity values. Given that the companies are identical in all aspects the PBIT is 10,000 for all three of them, however the interest changes based on the level of Debt (for simplification purposes I am assuming that the market value of Debt is the same as its book value). Understandably the Tax also changes due to interest given that interest is tax deductible.

Let us observe the respective Equity and Debt values of the three companies now.

Equity at end of year 1 =Equity at beginning + PAIT

Company A — Given that PAIT is 7000 is the total value created solely for the Equity providers, the Equity value has increased to 107,000 at the end of 1 year.

Company B — Equity value increases to 75,950. (i.e. 70,000 + 5,950).

Company C — Equity value increases to 65,600. (i.e. 60,000 + 5,600).

Debt at end of year 1 = Debt at beginning + Interest

The equivalent of PAIT, from Debt perspective is Interest. In other words, whilst Equity providers get ‘PAIT’ in return of their investment, what Debt providers get is ‘Interest’.

Total Value = Equity Value + Debt Value

The total value of a company is understandably, the total value of its funders. i.e. the summation of Equity Providers Value and Debt Providers Value. The interesting thing we note now is that despite all three companies starting off with the same Total Value of 100,000; their respective values at the end of the year is now different. The observation is that the company with the highest gearing also happens to have the highest value.

So why do geared companies have a higher value?

As observed by the table above, the explanation is simple. Given that interest is tax deductible Company C pays the lowest tax, whilst Company A suffers as a result of not having any interest what so ever. So the difference between company values is solely attributed towards the tax saving due to interest.

Tax Saving on Interest = Total Interest * Tax

Let us continue this further. Imagine this benefit getting compounded further as the years go by. This implies that every single year Company Cs value increase by 600 (i.e. Interest of 2,000 multiplied by the tax rate of 30%).

So when comparing values of companies assuming a going concern, this saving is equivalent to a perpetuity. If we take the Present Value of this Perpetual Tax Saving, we should effectively end up with the total value difference between an Ungeared Company and a Geared Company.

So how do we calculate this perpetual tax saving?

Tax Saving per year = Total Interest * Tax = Debt * Interest Rate * Tax (**understandably the Total Interest = Debt x Interest Rate)

Assuming Irredeemable Debt this Tax Saving will be a perpetuity. Thus,

Present Value of Total Tax Saving = Tax Saving per year * 1/r

r is the discount rate here, and given that we are considering debt, the discount rate of ‘r’ here can be simply assumed to be the ‘Interest Rate’. Thus,

PV of Tax Saving = [Debt * Interest Rate * Tax] * 1/[Interest Rate]

PV of Tax Saving = Debt * Tax

The above result is basically the difference in value between a Geared Company and an Ungeared Company. In other words it is the ‘Present Value of the Total Tax Benefit due to Interest’ of a Geared Company assuming a going concern. Voilah and that is how we end up with MMs first equation

Value of a Geared Company = Value of an Ungeared Company + Debt*Tax

You might wonder, so what if we have redeemable debt. Well the explanation is still the same. Now you’d be having an ‘Annuity of Tax Savings’ instead of a perpetuity. You can still obtain the tax benefit using the Tax Saving per Year and multiplying that by the respective Annuity Factor based on the Debt period.

What about other two equations of MM

Well the other 2 equations are basic mathematics of multiplication and cross multiplication derived on the basis that WACC is inversely proportional to Value. I hope to uncover this in my next blog post.

Shemal Mustapha (Snail)