Explanation

Step 1: Calculate Cash Inflow at Repo Start

The cash inflow at the beginning of the repo transaction is calculated as: $\text{Cash Inflow} = [(\text{Notional Amount} \times \text{Bond Price}) + (\text{Notional Amount} \times \text{Coupon Rate} \times \text{Time Period})] \times (1 - \text{Haircut})$

Given:

• Notional Amount = USD 100,000
• Bond Price = 97% = 0.97
• Coupon Rate = 6% semi-annual = 3% per 6 months
• Time Period = 3 months = 0.25 years
• Haircut = 10% = 0.10

$\text{Cash Inflow} = [(100,000 \times 0.97) + (100,000 \times 0.06 \times 0.25)] \times (1 - 0.10)$ $\text{Cash Inflow} = [(97,000) + (1,500)] \times 0.90$ $\text{Cash Inflow} = 98,500 \times 0.90 = \text{USD 88,650}$

Step 2: Calculate Cash Outflow at Repo End

The cash outflow at the end of the repo reflects the interest earned at the repo rate over the 6-month period: $\text{Cash Outflow} = \text{Cash Inflow} \times [1 + (\text{Repo Rate} \times \text{Time Period})]$

$\text{Cash Outflow} = 88,650 \times [1 + (0.04 \times 0.5)]$ $\text{Cash Outflow} = 88,650 \times 1.02 = \text{USD 90,423}$

Why Other Options Are Incorrect:

• A (USD 89,046): Omits the accrued interest of USD 1,500 in calculating the cash inflow
• C (USD 93,177): Uses 1 instead of 97% for price in calculating the cash inflow
• D (USD 100,470): Omits the haircut of 10% in calculating the cash inflow

Key Learning Points:

• Repo transactions involve lending securities in exchange for cash with an agreement to repurchase them later
• Haircuts provide protection to the cash lender against market price fluctuations
• Accrued interest must be included when valuing bonds between coupon payment dates
• The repo rate represents the interest cost for borrowing cash against collateral