Cost of Synthetic Borrowing in Cross-Currency Basis Swaps

[Panda]

In the few Cross-Currency Basis Swaps examples given in the Currency Swaps section of the Kaplan Schweser Level III Book, they calculate Cost of Synthetic Borrowing. In the screenshot below, it is the term (1).

I’m not sure how exactly they define the Cost of Synthetic Borrowing, but I am guessing it is supposed to be the net interest payments position, which is the sum of the three terms denoted as (2) on the screenshot.

If my assumption above is correct, I don’t understand how do they get from

    - €42,319,086 x 0.022 x (90/360) (interest paid on the loan)
    + €42,319,086 x 0.014 x (90/360) (interest received on the swap)    
    - $50,000,000 x 0.019 x (90/360) (interest paid on the swap)

---

    - €42,319,086 x 0.08 x (90/360)
    - $50,000,000 x 0.019 x (90/360)

to

- $50,000,000 x (0.019 + 0.08) x (90/360)?

It seems like they are assuming that

 €42,319,086 = $50,000,000 

at second settlement date, but surely the FX rate can change from the initiation of the swap to second settlement date to literally anything? How is the currency risk eliminated if the Canadian firm still needs to pay floating $?

[MikeyF]

I don’t have kaplan notes.
Do you want to post full question and answer

[Panda]

Not sure why, but I cannot see the Edit link for my initial post so I’m just replying to it with the full Question and the Answer of the Example

I don’t understand the Cost of Synthetic Borrowing calculations in the example - more precisely, how do they end up netting off EUR and USD assuming the FX rate from the initiation of the swap, although these payments are happening 3 and 6 months after the initiation.

Thanks

[MikeyF]

Sorry I can’t read any of that

[Panda]

Here it is:

Example: Cross-currency basis swap

Boivis Patisseries Sarl is a French chain of patisseries that has an extensive network of shops in continental Europe. As part of their expansion strategy, they are looking to set up shops in the United States. Boivis estimates that it will initially require $50 million to set up shops and cover working capital requirements. The finance directors at Boivis have looked at directly borrowing in USD but have found that costs would be the U.S. dollar reference floating rate + 100 bp. The decision is made to borrow for four years in euros at a rate of the euro reference floating rate + 60 bp with interest paid quarterly and enter a currency swap to exchange euros for dollars. Basis on the Eurodollar swap is being quoted at –20 basis points (–20 bp). The swap pays variable interest on both legs on a quarterly settlement basis. The current $/€ exchange rate is $1.1815.

The three-month euro reference rate is 1.5% and U.S. dollar reference rate is 2.0% at swap initiation. Three months later at the first settlement date, the three-month euro reference rate is 1.6% and the U.S. dollar reference rate is 1.9%.

Compute the principal flows exchanged at the start and end of the swap’s tenor. Compute the interest payments at the first and second settlement dates on the swap and the cost to Boivis for its synthetic dollar loan.

Answer:

Principal flows:

$50,000,000 / $1.1815 = €42,319,086

Boivis will need to borrow €42,319,086 and exchange it for $50,000,000. These amounts will be swapped back at the maturity of the swap.

Interest payment at first settlement date

Pays:

€ interest on the loan: €42,319,086 × (0.015 + 0.006) × 90 / 360 = €222,175

$ interest on the swap: $50,000,000 × 0.02 × 90 / 360 = $250,000

Receives:

€ interest on the swap: €42,319,086 × (0.015 − 0.002) × 90 / 360 = €137,537

Cost of $ financing:

Cost of borrowing $ direct: $50,000,000 × (0.02 + 0.01) × 90 / 360 = $375,000 (U.S. dollar reference rate + 100 bp)

Cost of synthetic $ borrowing: $50,000,000 × (0.02 + 0.006 + 0.002) × 90 / 360 = $350,000 (U.S. dollar reference rate + 80 bp)

Net benefit of swap: $375,000 − $350,000 = $25,000

Net benefit of swap: $50,000,000 (1% − 0.8%) × 90 / 360 = $25,000

Interest payment at second settlement date

Pays:

€ interest on the loan: €42,319,086 × (0.016 + 0.006) × 90 / 360 = €232,755

$ interest on the swap: $50,000,000 × 0.019 × 90 / 360 = $237,500

Receives:

€ interest on the swap: €42,319,086 × (0.016 − 0.002) × 90 / 360 = €148,117

Cost of $ financing:

Cost of borrowing $ direct: $50,000,000 × (0.019 + 0.01) × 90 / 360 = $362,500 (U.S. dollar reference rate + 100 bp)

Cost of synthetic $ borrowing: $50,000,000 × (0.019 + 0.006 + 0.002) × 90 / 360 = $337,500 (U.S. dollar reference rate + 80 bp)

Net benefit of swap: $362,500 − $337,500 = $25,000

Net benefit of swap: $50,000,000 (1% − 0.8%) × 90 / 360 = $25,000

Conclusion:

By borrowing in euros and entering a currency swap, Boivis has locked into a cost of the U.S. dollar reference rate + 80 bp for their USD borrowing, reflecting the 60 bp spread above the euro reference rate on the loan and the –20 bp on the swap.

Thanks

[guest]

It’s been a long time since I sat L3, and this material wasn’t in there when I sat L3 anyway.

Nor do I have either the underlying text or the study notes covering this material. If there are formal definitions of these things in the text/notes, just learn them so you can spew them out during the exam.

You seem to be correct about the variations in the FX rate, but it’s a very small effect, and the answer they give is an approximation which is correct at first order.
The FX variations would make a big difference when exchanging the principal, but those rates are locked in in the contract.
The FX variations make a much smaller difference when considering the interest payments.

For the interest payments:
On the first settlement date, as you say, there’s an 8% net payment (times 90/360) in Euros which they carry over into USD.
If there were a 5% swing in the FX rate, that 8% could be 7.6% or 8.4% when converted to USD,
so the 80 basis points would be 76 basis points or 84 basis points.
And the 20 basis point advantage of synthetic borrowing over direct borrowing (100 less 80) would be 16 or 24. There’s still an advantage but slightly less.
As I said, their answer is correct to first order.

If there are formal definitions of these things in the text/notes, learn them and use them in the exam.

[MikeyF]

You are correct in that is structural difference in the payments after the swap.

Previously payments were purely in USD
Now we have a net EUR payment and USD payment.

There is no risk on the principal at payment. - This provides fx hedging as the firm is not exposred to fx chnage on the principal.

But as the EUR loan and EUR leg don’t match you have some fx risk.

I estimate if fx rate moves to around 1.5 then payments in USD terms would be higher.

But you could argue that the company feels loess exposed to the USD as the size of the USD payments are lower than previously