The shareholders of DEF Systems Ltd have invested a total of $2 million and have an opportunity cost of 12 per cent.The debtholders of DEF have invested $7 million.If the total return required by the company's capital providers is $1,000,000,how much is the interest rate the company's debtholders are receiving?

Question

Quizplus · Accepted Answer

To find the interest rate of the debtholders, we need to first calculate the cost of equity of the shareholders:

Cost of Equity = Opportunity Cost + Risk Premium
Cost of Equity = 12% + X (let's assume the risk premium as X)

Total Capital Invested = Shareholders' Equity + Debt
$9 million = $2 million + $7 million

Equating the total return required by the capital providers with the cost of equity and cost of debt (let's assume it as Y):

$1,000,000 = ($2 million) (12% + X) + ($7 million)Y

Solving for Y, we get:

Y = ($1,000,000 - $2 million (12% + X)) / $7 million

Y = 10.8% - 0.2857X

We don't know the exact value of X (risk premium), so we can't calculate the exact value of Y. However, we can see that the interest rate of the debtholders (Y) is partially dependent on the risk premium (X) of the shareholders. We also know that the interest rate of the debtholders is lower than the cost of equity of the shareholders, which is 12%. Therefore, the only answer choice that is less than 12% is B) 10.8%.

The Shareholders of DEF Systems Ltd Have Invested a Total