The pay floating counterparty is effectively receiving fixed, so:

$$\text{Swap value} = PV(\text{fixed leg}) - PV(\text{floating leg})$$

1) Discount factors

Flat continuously compounded rate = 4.0%.

Remaining cash-flow dates are approximately:

• 2 months = $2/12$ years
• 8 months = $8/12$ years
• 14 months = $14/12$ years

So:

• $P(0,2/12)=e^{-0.04\cdot 2/12}\approx 0.993356$
• $P(0,8/12)=e^{-0.04\cdot 8/12}\approx 0.973686$
• $P(0,14/12)=e^{-0.04\cdot 14/12}\approx 0.954084$

2) Fixed leg

A 5.0% fixed rate with semiannual compounding gives a 6-month coupon of:

$$50,000,000 \times 0.05 \times 0.5 = 1.25\text{ million}$$

With three remaining payment dates, the fixed-leg PV is approximately:

$$PV_{fixed} = 1.25P_1 + 1.25P_2 + 51.25P_3$$ $$PV_{fixed} \approx 1.25(0.993356) + 1.25(0.973686) + 51.25(0.954084) \approx 51.35\text{ million}$$

3) Floating leg

The next floating coupon was set four months ago at 4.0%, so the next coupon is:

$$50,000,000 \times 0.04 \times 0.5 = 1.0\text{ million}$$

With the curve flat at 4.0%, the following floating coupons are also effectively priced at 4.0%:

$$PV_{float} \approx 1.0P_1 + 1.0P_2 + 51.0P_3 \approx 50.63\text{ million}$$

4) Swap value

$$V = PV_{fixed} - PV_{float} \approx 0.71\text{ million}$$

So the value to the pay-floating counterparty is positive, about $710,950.