Answer: $51,400

The value of the swap to the financial institution is the present value of the yen receipts minus the present value of the dollar payments, expressed in U.S. dollars. ## 1) Value of yen receipts The institution receives: - ¥150 million at the end of year 1 - ¥150 million + ¥1,000 million = ¥1,150 million at the end of year 2 Discounting at the Japanese continuously compounded rate of 2%: \[ PV_{\text{yen}} = 150e^{-0.02} + 1150e^{-0.04} \] \[ PV_{\text{yen}} \approx 150(0.9802) + 1150(0.9608) \approx 1{,}251.9\ \text{million yen} \] Convert to USD at ¥110 per USD: \[ PV_{\text{yen, USD}} \approx \frac{1{,}251.9}{110} \approx 11.381\ \text{million USD} \] ## 2) Value of dollar payments The institution pays: - $1 million at the end of year 1 - $1 million + $10 million = $11 million at the end of year 2 Discounting at the U.S. continuously compounded rate of 3%: \[ PV_{\text{USD payments}} = 1e^{-0.03} + 11e^{-0.06} \] \[ PV_{\text{USD payments}} \approx 0.9704 + 10.3623 = 11.3327\ \text{million USD} \] ## 3) Net swap value \[ V = 11.381 - 11.333 \approx 0.048\ \text{million USD} \] \[ V \approx \$48{,}000 \] The nearest answer is **A: $51,400**.

Author: Manit Arora