This workout tells us that we work on the equity structuring desk of a bank and are structuring a single stock equity principle protected participation note for a client.

We need to calculate the participation rate for a five-year PPPN using firstly a participation level of 100% of the initial stock price, and then a participation level of 110% of the initial stock price.

We need to use the information below and assume an investment size of 100.

Looking at the information below, we've got a five year bank funding rate of 4.15%.

The bank's markup in percentage of notional of 0.25%, so that's the bank's fee.

Then we've got the premium for a five year, 100% call in percentage of option size of 21.54%, and then the premium for a five year, 110% call of 16.98%.

Let's start by capturing the investment size, which we know is 100 and the maturity of the note, which is five years.

We then need to work out what the zero coupon bond will cost, because remember, this is what the bank will buy to ensure that the principle can be returned to the investor at maturity.

So this is a simple present value calculation.

We take the 100 that we need to end up with in five years, and we present value this by dividing it by one plus the discount rate, which in this case is the five year bank funding rate of 4.15%, and we put that to the power of five years.

So the cost of the zero coupon bond that the bank would need to buy today is 81.6.

Next, let's work out the bank's markup or fee, which is a quarter of a percent on the 100 investment size.

So that's 0.25.

And now we can work out how much money we've got left to buy the call option.

We start with the 100.

We then take off what we use to buy the zero coupon bond, which is 81.6, and then we also need to take off the bank's fee of 0.25.

And so we are left with 18.15 to buy the call option.

So now we need to work out the size of the option that can be purchased and that will inform the participation rate.

If we have $18.15 to buy the option worth, we need to divide that by the option premium to work out the size of the option that can be purchased.

So we take the 18.15 and for scenario A, we divide by the option premium of 21.54, and that means that the size of the option we can buy is $84.25, and as a participation rate that is 84.25 out of the 100, which gives us 84.25% participation.

So that means the investor will receive 84.25% of any increase in the stocks price above the initial level.

Moving on to scenario B, the size of the option that can be purchased is exactly the same calculation.

So we take the 18.15 and we divide that by the option premium, which is 16.98%, and that gives us 1 0 6 0.88.

So we can buy a bigger option and achieve a higher participation rate.

So the participation rate is 1 0 6 0.88 divided by 100, which gives us 106.88% participation.

Now, why is the participation rate higher? Well, that's because the option premium is lower.

It's a cheaper option, and the reason is because it has a higher strike price, it's got a strike of 110% of the initial stocks level.

So what this means is that the investor will participate in 106.88% of any increase in the stock's price, but only after it has increased by 10% from the initial level.