Explanation

Step 1: Calculate the cash inflow at the beginning of the repo transaction

The bond price is 98% of face value, and there is 3 months (0.25 years) of accrued interest since the last coupon payment. The repo haircut is 5%.

• Bond value = Face value × Price = 100,000 × 98% = 98,000
• Accrued interest = Face value × Coupon rate × Time = 100,000 × 5% × 0.25 = 1,250
• Total bond value = 98,000 + 1,250 = 99,250
• Cash inflow after haircut = Total bond value × (1 - Haircut) = 99,250 × (1 - 5%) = 99,250 × 0.95 = 94,287.50 ≈ 94,288

Step 2: Calculate the cash outflow at the end of the repo transaction

The repo interest rate is 3% for 6 months (0.5 years).

• Cash outflow = Cash inflow × (1 + Repo rate × Time) = 94,288 × (1 + 3% × 0.5) = 94,288 × (1 + 0.015) = 94,288 × 1.015 = 95,702.32 ≈ 95,702

Why other options are incorrect:

• A: Left out the accrued interest of 5% × 0.25 in the correct equation for cash inflow
• C: Used 1 instead of 98% for price in the correct equation for cash inflow
• D: Left out haircut of 5% in the correct equation for cash inflow

Learning Objective: Describe the mechanics of repurchase agreements (repos) and calculate the settlement for a repo transaction.