Final answer:
The statement is false because increased leverage, when the rate of return is equal to the cost of debt, leads to higher interest expenses that offset any additional income from invested assets. Other factors like taxes and bankruptcy risk also influence the outcomes of leveraging.
Step-by-step explanation:
The statement that when the rate of return on assets is equal to the cost of debt, and leverage increases, the profits stay constant is false. This is because as leverage—or the amount of debt compared to equity—increases, the firm incurs more interest expenses. If the rate of return on assets is exactly equal to the cost of debt, any increase in debt will lead to increased interest expenses, which in turn will precisely offset any additional income generated from the assets financed with the debt. This is known as the break-even point of leverage, beyond which additional debt will decrease profits, while below which it may increase profits. However, in practice, the effects of taxes, bankruptcy risk, and other factors must be considered, which can affect this break-even point.
Understanding the national saving and investment identity can provide insight into the broader implications of leveraging within an economy. It's essential to analyze both the supply side and the demand side of the financial capital market. An increase in government deficit due to higher interest payments, keeping other spending constant, can influence the national savings and, consequently, the availability of capital for investment. This complex interaction underscores the intricate balance of financial decisions and their impact on national economic indicators such as GDP.