This paper examines the relationship between financial leverage and investment returns, using a straightforward numerical example to show how borrowing transforms an investor's rate of return from 6% to 24% without changing the underlying performance of the investment. Building on this illustration, the paper explains the Modigliani-Miller irrelevance proposition — the theory that a firm's market value depends solely on its ability to generate future income, not on its capital structure or dividend policy. The paper outlines the key assumptions required for the proposition to hold, including neutral taxes, no transaction costs, and equal borrowing and lending rates, before critically noting that these conditions do not exist in practice, limiting the theory's real-world applicability.
The paper demonstrates the technique of using a worked numerical example as a bridge to theoretical exposition. By first calculating the leveraged return step by step in a table, the writer makes an abstract proposition — that capital structure is irrelevant to firm value — immediately intuitive. This approach of moving from the concrete to the abstract is a hallmark of strong applied economics writing.
The paper is organized in three logical stages: (1) a numerical illustration of how borrowing shifts an investor from an unleveraged to a leveraged position; (2) a brief reflection on whether this changes the investment's intrinsic attractiveness; and (3) a full explanation of the Modigliani-Miller irrelevance proposition, including its theoretical conditions and the practical reasons those conditions fail. Each stage builds directly on the previous one, creating a coherent argument arc from example to theory to critique.
The expected rate of return on an investment is calculated by dividing the expected return by the amount invested. For example, if there is a return of $6 on an investment of $100, the rate of return is 6%.
When an investor states they are unhappy with this return and a broker suggests borrowing $90 to help fund the investment at an interest rate of 4%, the broker is recommending a shift from an unleveraged position — where there is no borrowing — to a highly leveraged position, where there is a substantial level of borrowing. Understanding financial leverage and its effect on returns is fundamental to evaluating this suggestion.
The first consideration is the investment itself. If the investor borrows $90 and contributes $10 of their own money, the total investment remains $100 and the gross return is still $6, so the rate of return on the investment itself does not change. However, borrowing affects the net revenue the investor actually receives, since interest must be paid before any income is realized.
This calculation is shown in the table below:
Investment income (a): $6.00
Interest on borrowed money (b): $3.60
Net revenue (a − b) (c): $2.40
As a percentage of $10 invested (c ÷ 10 × 100): 24%
The benefit of moving from an unleveraged to a leveraged position is that it increases the amount available for investment, which in turn increases the investor's marginal rate of return — from 6% to 24% in this example.
At first glance, borrowing to invest appears to increase the attractiveness of the investment, since the calculated rate of return on the investor's own money rises dramatically. However, the underlying investment is still performing in exactly the same way, generating a 6% return. The broker is showing the investor how to maximize their position by increasing the capital deployed, not by improving the investment itself.
There is no different return based on the source of the money. The marginal rate of return for the investor changes as a result of a different investment strategy, not a different investment outcome. Whether this strategy is more attractive depends on the investor's risk tolerance and financial circumstances.
The irrelevance proposition addresses how firms are valued by the market — specifically, whether the level of debt affects that valuation (Miller, 1991). The theory, developed by Modigliani and Miller, states that in efficient markets the market value of a firm should depend solely on its ability to generate future income streams, and not on its capital structure (Miller, 1991). In other words, when assessing the value of a firm, the debt-equity ratio is theoretically irrelevant.
This can be illustrated directly with the example above: the $100 investment generates an income stream of $6 regardless of whether that $100 is equity (owned by the investor) or debt (borrowed). The theory further states that a firm's dividend policy should also be regarded as irrelevant, since the investment will perform the same way whether dividends are distributed or reinvested.
The theory also holds that the level of borrowing is not expected to affect the firm's weighted average cost of capital, and that equity holders should be indifferent to the firm's financial policy — specifically, whether the firm increases or decreases its debt (Miller, 1991).
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