Debt Issuance with Placement Fee — Sizing to Target Net Proceeds

The company plans to raise R$ 11.342 million in net proceeds from a bond issue sold at par, but must pay a placement fee of 1.85% of the total face value issued.

Because the fee is deducted from the proceeds, the company must issue more than the target amount to achieve its goal. The required face value is found by dividing the target net proceeds by \((1 - \text{fee})\):

\(\text{Face value} = \frac{\text{Target Net Proceeds}}{1 - \text{fee}}\)

1. How much face value (million R$) must be issued to net the target?

2. How much is the total fee paid (million R$)?

3a. Face to issue (R$ million):

✅ \(\text{Face} = \frac{\text{Target Net}}{1 - \text{fee}} =\) 11.56 million.

3b. Total fee (R$ million):

✅ Fee paid = Face × fee = 0.21 million.