The one-month (31-day) GC repo rate for French government bonds is quoted to you at 3.75- 80%. As collateral, you are offered EUR 25,000,000.00 nominal of the 5.5% OAT April 2015, which is worth EUR 28,137,500.00. If you impose an initial margin of 1%, the Repurchase Price is:
A) EUR 27,947,276.43
B) EUR 27,946,077.08
C) EUR 27,950,071.43
D) EUR 27,948,871.97

Question

Quizplus · Accepted Answer

To calculate the repurchase price, we need to use the following formula:

Repurchase Price = Nominal Value x (1 + Repo Rate x (Actual/360))

where:

Nominal Value = EUR 25,000,000.00 
Repo Rate = 3.75%
Actual = 31
Days = 360

So, plugging in the numbers, we get:

Repurchase Price = EUR 25,000,000.00 x (1 + 0.0375 x (31/360)) 
= EUR 25,000,000.00 x 1.00327778 
= EUR 25,081,944.44

However, we also need to take into account the initial margin of 1%, which means that the actual amount lent will be 99% of the value of the collateral:

Actual Value of Collateral = EUR 28,137,500.00 x 0.99 
= EUR 27,856,125.00

Finally, the repurchase price will be adjusted to reflect the actual value of the collateral:

Repurchase Price = (Nominal Value x (1 + Repo Rate x (Actual/360))) - (Nominal Value - Actual Value of Collateral)

Plugging in the numbers, we get:

Repurchase Price = (EUR 25,000,000.00 x (1 + 0.0375 x (31/360))) - (EUR 25,000,000.00 - EUR 27,856,125.00) 
= EUR 27,948,871.97

Therefore, the answer is D.

The One-Month (31-Day) GC Repo Rate for French Government Bonds