Removing the brackets, the above expands to:

2.90m – 0.966R + 4.76m – 0.914R + 5.57m – 0.854R +

6.10m – 0.789R + 4.86m – 0.737R= 0

Simplifying this, adding all the $ flows together and R-flows together, gives:

24.19m – 4.26R = 0

$5.68m = R

In percentage = $5.68m/$100m = 5.68%

In practice the receipts and payments of the swap would be netted off such that the company will expect to pay $2.68m ($5.68m – $3.00m) to the bank in year one, and expect to receive $0.84m ($6.52m – $5.68m) from the bank in year three, and so on for the other years. The present values of these n et annual flows, discounted at the yield curve rates, will be zero. The fixed rate of 5.68% is lower than the five-year spot rate of 6.30% because some of the receipts and payments related to the swap contract occur in earlier years when the spot yield curve rate is lower.

Although at the commencement of the contract, the present value of the swap is zero, as interest rates fluctuate, the value of the swap will change. For example, if interest rates increase and the company pays interest at a fixed rate, then the swap’s value to the company will increase. The value of the swap contract will also change as the swap approaches maturity, and the number of receipts and payments reduce.

### Conclusion

The previous article and this article considered the relationship between bonds, interest rates, spot and forward yield curves, culminating with how the forwards rates can be used to determine the equivalent fixed rate of a simple swap contract. The examples used were simplified into annual cash flows and rates, and students undertaking *Advanced Financial Management *should be able to demonstrate their knowledge and understanding of these areas to this extent.

In practice, valuation of bonds and related products is more complicated because of factors such as: cash flows occurring more frequently than once a year, early redemption of products, change in product values, and so on. However, these aspects are beyond the scope of the *Advanced Financial Management* syllabus.

**Written by a member of the ***Advanced Financial Management* examining team