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computation of cost of capital

To calculate the total cost of debt for this share issuance, we need to consider the cost of the shares themselves, underwriting costs, brokerage costs, and printing/other expenses. We'll use the formula you provided:

[kdb = \frac{i}{np}]

Where:

  • (kdb) is the total cost of debt.
  • (i) is the interest or dividend rate (8% in this case).
  • (n) is the face value of each share ($100).
  • (p) is the price at which the shares are issued to investors.

Let's break down the calculation step by step:

  1. Calculate the total face value of the shares issued: [ \text{Total Face Value} = \text{Number of Shares} \times \text{Face Value per Share} ] [ \text{Total Face Value} = 2,000 \text{ shares} \times $100/\text{share} = $200,000 ]

  2. Calculate the total underwriting costs: [ \text{Underwriting Costs} = \text{Underwriting Percentage} \times \text{Total Face Value} ] [ \text{Underwriting Costs} = 2% \times $200,000 = $4,000 ]

  3. Calculate the total brokerage costs: [ \text{Brokerage Costs} = \text{Brokerage Percentage} \times \text{Total Face Value} ] [ \text{Brokerage Costs} = 1% \times $200,000 = $2,000 ]

  4. Calculate the total printing and other expenses: [ \text{Printing and Other Expenses} = $2,000 \text{ (given)} ]

  5. Calculate the total cost of shares issued to investors: [ \text{Total Cost of Shares} = \text{Total Face Value} + \text{Underwriting Costs} + \text{Brokerage Costs} + \text{Printing and Other Expenses} ] [ \text{Total Cost of Shares} = $200,000 + $4,000 + $2,000 + $2,000 = $208,000 ]

Now, we have the total cost of shares ((p)) and the interest rate ((i)). Plug these values into the formula to calculate the total cost of debt ((kdb)):

[kdb = \frac{0.08}{$208,000}]

Calculating (kdb):

[kdb = \frac{0.08}{$208,000} \approx 0.0003846]

Now, we can convert this decimal to a percentage by multiplying by 100:

[kdb \approx 0.0003846 \times 100 \approx 0.03846%]

So, the total cost of debt for this share issuance is approximately 0.03846%. -->

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