In this workout, we are asked to calculate the size and the direction of payment on the first payment date for the equity swap we are presented with, which has semi-annual reset periods, has the equity leg based on the S&P 500 price return only, and the interest rate leg based on a floating interest rate of six month US dollar LIBOR.

At the beginning of the first payment period, six-month US dollar LIBOR is 3% and the return generated during the first six-month period on the S&P 500 was 8% in terms of price return. And in addition to that 2% dividend yield. The notional principal for the swap is $100 million.

The first thing we will calculate is the payment due on the equity leg, which we'll calculate by taking the notional principal on the swap. And since this is a price return swap only, we only need to include the 8% return on the S&P 500 from a price return basis giving 8 million US dollars.

We then need to also calculate the interest payment due on the floating rate leg. To do this, we take the principal of $100 million dollars and multiply this by the 3% US dollar LIBOR but we also need to multiply this by 0.5 for half a year. It may seem like there is some inconsistency between the equity leg and the interest rate leg. However, the 8% return is within the six-month period as defined in the question, whereas the interest rate, 3%, is always quoted on an annualized basis. So to de-annualize that down to half a year's worth of interest, we need to multiply it by 0.5.

The net payment will then be the net of the two amounts. The 8 million payable on the equity leg and the 1.5 million US dollars payable on the interest rate leg. The net of these two will result in a $6.5 million payment.

So it is not that the whole $8 million is paid in one direction and the 1.5 million paid in the opposite direction but rather, $6.5 million of a cash payment is made from one side of this swap to the other. And the final part of the question is the direction of that payment. This payment we made from the interest rate receiver and made to the equity index receiver.