After one year and spending USD 1.

Comprehensive and Detailed In-Depth Explanation:

The recovery rate is the percentage of the original exposure recovered, adjusted for the time value of money and recovery costs. Here, the exposure at default (EAD) is USD 20 million, the gross recovery after one year is USD 10 million, and the recovery cost is USD 1 million. The recovery discount rate is 10%, reflecting the time value of money over one year.

Step-by-step calculation:

Net Recovery Amount:Gross recovery - Recovery costs = USD 10 million - USD 1 million = USD 9 million.

Present Value of Recovery:Since the recovery occurs after one year, discount the net recovery at 10%:PV = USD 9 million / (1 + 0.10) = USD 9 million / 1.1 ≈ USD 8.1818 million.

Recovery Rate:Divide the present value of the recovery by the original exposure:Recovery Rate = (USD 8.1818 million / USD 20 million) × 100 ≈ 40.91%, which rounds to 41%.

This aligns with Basel II/III definitions of Loss Given Default (LGD = 1 - Recovery Rate) and the discounting approach for recovery cash flows in credit risk models.