# Interest Rate Swap Termination Valuation ## Problem Restatement - **Swap start:** 2 years ago, 5-year term —> **3 years remain** - **Notional principal:** €10,000,000 - **Fixed rate (paid by company):** 5.75% p.a. (annual payments) - **Floating rate (received by company):** 12M EURIBOR (currently 4.6% p.a.) - **Latest cash flow just paid** - **Current market rates:** - **12M EURIBOR:** 4.60% p.a. - **2-year bond:** 4.90% yield, 4% coupon (annual, TTM = 2y) - **3-year bond:** 5.40% yield, 5% coupon (annual, TTM = 3y) We are to find the **fair value of the swap** (the "closeout" amount) and **who pays whom**. --- ## Step 1: Identify Remaining Cash Flows **Company pays fixed:** - 3 remaining annual payments of €10m × 5.75% = **€575,000** each, at \( t = 1, 2, 3 \) years from now. **Company receives floating:** - Typically, the next floating payment is set equal to today’s 12M EURIBOR, i.e., 4.60% × €10m = **€460,000** at \( t = 1 \). - For \( t = 2 \) and \( t = 3 \), the future floating rates are unknown, so we use the expectation from the swap market (par swap rates, bond yields). --- ## Step 2: Discount Factors from Zero-Coupon Yields ### Calculate Discount Factors #### For \( t = 1 \): No direct bond, but since yield curve is upward sloping, we can interpolate between EURIBOR (4.6%) and 2-year bond (4.90%): \[ DF(1) = \frac{1}{1 + 0.046} \approx 0.956 \] #### For \( t = 2 \): \[ DF(2) = \frac{1}{(1 + 0.049)^2} \approx \frac{1}{1.1001} \approx 0.909 \] #### For \( t = 3 \): \[ DF(3) = \frac{1}{(1 + 0.054)^3} \approx \frac{1}{1.1716} \approx 0.854 \] --- ## Step 3: Estimate Expected Floating Payments - **\( t = 1 \):** Already set, €460,000 (from 4.6%) - **\( t = 2, 3 \):** Use swap market to estimate the forward rates (or, since the swap is at fixed 5.75%, and current market swap rates are lower, the market expects lower floating payments than the fixed leg). However, for valuation, **the floating leg is valued at par** (notional) after payment date, so its value is approximately equal to the notional principal. But since the floating rate resets annually, the value of future floating cash flows is approximately the notional amount minus the present value of the next floating payment. Since the next reset just occurred, the floating leg can be valued as the notional (no accrued interest). --- ## Step 4: Value Both Legs ### Present Value of Fixed Leg (Outflows) \[ PV_\text{fixed} = 575{,}000 \times DF(1) + 575{,}000 \times DF(2) + 10{,}575{,}000 \times DF(3) \] The last payment includes the notional principal. But **for a plain vanilla interest rate swap, the notional is not exchanged**, so only the coupons are considered. So: \[ PV_\text{fixed} = 575{,}000 \times DF(1) + 575{,}000 \times DF(2) + 575{,}000 \times DF(3) \] \[ PV_\text{fixed} = 575{,}000 \times (DF(1) + DF(2) + DF(3)) \] \[ PV_\text{fixed} = 575{,}000 \times (0.956 + 0.909 + 0.854) = 575{,}000 \times 2.719 = €1,564,425 \] ### Present Value of Floating Leg (Inflows) At reset date, the value of the floating leg is **par** (no accrued interest), so the present value is approximately the notional principal: **€10,000,000**. But to be precise, since the next floating payment is €460,000 in 1 year, we calculate: \[ PV_\text{float} = 460{,}000 \times DF(1) + \text{(expected floating payments at t = 2, 3)} \] But as per standard swap valuation, after reset, the floating leg's value is the notional. --- ## Step 5: Net Swap Value The swap value to the company is: \[ \text{Swap Value} = PV_\text{float} - PV_\text{fixed} \] But since both legs have notional principal, the value is only the difference in present values of the remaining fixed and expected floating coupons. Given that the fixed coupons are much higher than current floating rates and swap rates, the fixed payer side (the company) is at a loss (the fixed leg is "expensive"). --- ## Step 6: Estimate Market Value of the Swap Alternatively, the **market swap rate** for 3 years (from bond yields) is about **5.40%** (from 3-year bond yield). - The company is paying 5.75%, while the current 3-year swap rate is 5.40%. - The swap has negative value to the company: to terminate, the company must compensate the counterparty for the difference. \[ \text{Difference in annual payments} = 0.0575 - 0.0540 = 0.0035 \text{ (35 bps)} \] \[ \text{Annual difference} = €10,000,000 \times 0.0035 = €35,000 \] \[ \text{PV of this difference over 3 years} = 35,000 \times (DF(1) + DF(2) + DF(3)) \] \[ = 35,000 \times 2.719 = €95,165 \] **Who pays whom?** - The company pays fixed above-market rate → must pay the present value of 35,000 per year for 3 years. - **The company must pay the counterparty approximately €95,165 to terminate the swap.** --- ## Step 7: Summary Table | Year | Fixed Paid (€) | Discount Factor | PV (€) | |------|:-------------:|:--------------:|---------:| | 1 | 575,000 | 0.956 | 549,700 | | 2 | 575,000 | 0.909 | 522,675 | | 3 | 575,000 | 0.854 | 491,050 | | | **Total** | | 1,563,425| --- ## Final Answers ### Fair Price - **The fair price for terminating the swap is approximately €95,000 (rounded), payable by the company to the counterparty.** ### Cash Flow Direction - **The company pays the counterparty to exit the swap.** --- ## Key Points - **Swap market value** is the difference between the fixed rate paid and the current market swap rate, discounted over the remaining payments. - **Negative value** for the fixed payer if market rates have fallen. - **Fair termination price** ≈ present value of the excess fixed payments over market rates. --- ## Summary > **To withdraw from the swap, the company must pay the counterparty approximately €95,000.** > **This is because the fixed rate on the swap (5.75%) is higher than current market rates (about 5.40%), so the swap has negative value for the company.**