Your company has the following debt maturity situation: $20 million in month N8 $60 million in month N15 You want to renegotiate said maturity by paying $14 million in month N11 and a value to be determined in month N13 Use a market rate of 14.5% nominal annual convertible A focal date in month N12 Calculate the value in month N13 Use all decimals

1. Present the debts and payments to the focal date (month N12) using the market rate of 14.5% nominal annual.

2. Debt in month N8 to N12: \text{Amount in N12 from N8} = 20 \times \left(1 + \frac{0.145}{12}\right)^{4}

3. Debt in month N15 to N12: \text{Amount in N12 from N15} = 60 \times \left(1 + \frac{0.145}{12}\right)^{-3}

4. Payment in month N11 to N12: \text{Amount in N12 from N11} = 14 \times \left(1 + \frac{0.145}{12}\right)^{1}

5. Payment in month N13 to N12: Let it be \( X \). So, the present value is: X \times \left(1 + \frac{0.145}{12}\right)^{-1}

6. Set the equation to equate present values of debts and payments at month N12:

20 \times \left(1 + \frac{0.145}{12}\right)^{4} + 60 \times \left(1 + \frac{0.145}{12}\right)^{-3} = 14 \times \left(1 + \frac{0.145}{12}\right)^{1} + X \times \left(1 + \frac{0.145}{12}\right)^{-1}

7. Solve the equation for \( X \) to find the payment in month N13:

X = \frac{ \left(20 \times \left(1 + \frac{0.145}{12}\right)^{4} + 60 \times \left(1 + \frac{0.145}{12}\right)^{-3} - 14 \times \left(1 + \frac{0.145}{12}\right)^{1}\right) }{ \left(1 + \frac{0.145}{12}\right)^{-1}}

8. Compute \( X \) to get the value in month N13.

Answer: X = 65.4733764 \text{ million}