The State of Idaho issued $2,000,000 of seven percent coupon, 20-year semiannual payment, tax-exempt bonds five years ago. The bonds had five years of call protection, but now the state can call the bonds if it chooses to do so. The call premium would be five percent of the face amount. Today 15-year, five percent, semiannual payment bonds can be sold at par, but flotation costs on this issue would be two percent. What is the net present value of the refunding? Because these are tax-exempt bonds, taxes are not relevant

(a) $278,606

To calculate the net present value (NPV) of the refunding, we need to compare the cash flows of the current bonds with the cash flows of the new bonds. Here are the steps to calculate the NPV:

1. Calculate the current bond's cash flows:
- The current bond has a $2,000,000 face value and a 7% coupon rate. The semiannual coupon payment is $2,000,000 * 7% / 2 = $70,000.
- The current bond has 20 years remaining, but it has already been 5 years, so the remaining life is 20 - 5 = 15 years.
- This means there will be 15 * 2 = 30 semiannual payment periods in total.

2. Calculate the present value of the current bond's cash flows:
- To calculate the present value, we need to discount each semiannual payment using an appropriate discount rate.
- Since these are tax-exempt bonds and taxes are not relevant, we can use a discount rate equal to the yield to maturity (YTM) of the new bonds.

3. Calculate the new bond's cash flows:
- The new bond has a 15-year maturity with a 5% coupon rate. The semiannual coupon payment is $2,000,000 * 5% / 2 = $50,000.
- The new bond will have 15 * 2 = 30 semiannual payment periods in total.

4. Take into account the flotation costs:
- The flotation costs for issuing the new bonds are 2% of the face value, which is $2,000,000 * 2% = $40,000.

5. Calculate the present value of the new bond's cash flows:
- Similar to step 2, we need to discount each semiannual payment using the YTM of the new bonds.

6. Calculate the call premium:
- The call premium is 5% of the face amount, which is $2,000,000 * 5% = $100,000.

7. Calculate the net present value:
- NPV = Present value of the current bond's cash flows - Present value of the new bond's cash flows - Flotation costs + Call premium.

By following these steps, you can calculate the net present value of the refunding.