1. When the business uses debt, the risk of the firm increases. It is because the firm has to make fixed debt interest payments and principal re-payment at regular intervals. This cash outflow at regular intervals increases the burden and hence increases risk of the firm
2. As the risk of the firm increases, investors who invest in the business will require a higher rate of return because of the higher risk being taken. Hence the cost of equity increases.
3. Beta being a measure of the risk the business is calculated as covariance of the return on the stock with market / variance of the return on the market.
4. The numerator "covariance of the return on the stock with market” increases because as pointed in #2, the cost of equity increases. As the numerator increases and the denominator remains constant, the beta of the firm increases.
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