Question

Five years ago, the State of Ohio issued $2,000,000 of 7% coupon, 20-year semiannual payment, tax-exempt bonds. The bonds had 5 years of call protection, but now the state can call the bonds if it chooses to do so. The call premium would be 5% of the face amount. Today 15-year, 5%, semiannual payment bonds can be sold at par, but flotation costs on this issue would be 2%. Note that because these are tax-exempt bonds, taxes are not relevant. What is the NPV of the refunding operation?

Please show work using a financial calculator not excel.

Answer 1

=>Initial Outflow:

Premium on call of bond = $2,000,000 * 5% = $100,000

Flotation cost = $2,000,000 * 2% = $40,000

Total initial outflow = $100,000+$40,000 = $140,000

=> Annual Saving

Saving= Face value * difference in interest rate

Saving = $2,000,000*(7%-5%)

Saving = $40,000 per annum,

However payments are semi annual hence saving will be $20,000 per six months for next 15 years.

Present value of saving = Semi annual saving * PVIFA(r,y)

Where, PVIFA is present value of annuity factor at the rate ''r'' for ''y'' periods

r = 2.5%(5%/2 as it is semi annual), y = 15 years*2(as it is semi annual) = 30

Present value of saving = $20,000 * PVIFA(2.5%,30 period)  

  Present value of saving = $20,000*20.93(rounded off to two decimal points)

  Present value of saving = $418,600

Net Present value = Present value of future saving- Initial outflow as on today

Net Present value = $418,600-$140,000 = $278,600

NPV of refunding will be $278,600