Mullet Technologies is considering whether or not to refund a $100 million, 14% coupon, 30-year bond...

The complete bond refunding analysis will have three components. Let's calculate them one by one:

1. Figure out total investment outlay
2. Figure out annual cash flows:
   1. Figure out total amortization tax effects
   2. Figure out net post tax interest savings
3. Use total investment outlay and annual cash flows to calculate NPV of bond refunding

Part 1: Figure out the total initial investment outlay to refund the old issue

• Pre tax call premium to be paid on refund = Call premium rate x face value of old issue = 13% x 100,000,000 = 13,000,000
• Post tax call premium to be paid = Pre tax call premium to be paid x (1 - tax rate) = 13,000,000 x (1 - 40%) = 7,800,000
• Floatation cost on new issue = 4,000,000
• Balance old floatation cost = (Old floatation cost / Life of the old bond) x balance life = 3,000,000 / 30 x (30 - 5) = 2,500,000
• Since we are retiring the old bonds, we will get the tax benefit by expensing the balance floatation cost immediately. Tax benefit on expensing the balance floatation cost = Balance floatation cost x tax rate = 2,500,000 x 40% = 1,000,000
• Since there is a time gap of 1 month between the new bond issue and retiral of old bonds, we will have to continue to pay the interest on the old bond issue for this one month. However this interest will also give us an interest tax shield. Hence, post tax interest on old bonds for 1 month = Face Value x interest rate of old bond x 1 / 12 x (1 - Tax rate) = 100,000,000 x 14% x 1 / 12 x (1 - 40%) = 700,000
• New bonds issued will be invested in short-term government securities returning 6% annually during the interim period of 1 month.

  However this interest income will be subjected to tax as well. Hence, post tax interest income = Face value of new bond issue x short term government securities interest rate x 1 / 12 x (1 - Tax rate) = 100,000,000 x 6% x 1/12 x (1 - 40%) = 300,000

Thus, total initial investment outlay = Post tax call premium paid + New floatation cost - Tax savings by expensing the balance floatation costs on old bonds + post tax interest paid on old bonds in the interim period of 1 month - post tax interest earned on proceeds from new bond issue invested in short-term government securities during the interim period of 1 month = 7,800,000 + 4,000,000 - 1,000,000 + 700,000 - 300,000 = 11,200,000. Please note that this is an outlay i.e. a cash outflow .

Part 2: Figure out annual cash flows. This comprises of two sub parts:

• Figure out total amortization tax effects
  • Annual floatation cost on new issue = Total floatation cost of new issue / Life of new issue = 4,000,000 / 25 = 160,000
  • Annual floatation cost foregone on old issue = Total floatation cost of old issue / Life of old issue = 3,000,000 / 30 = 100,000
  • Incremental annual floatation cost that will be amortised = 160,000 - 100,000 = 60,000
  • Total amortization tax effect = Tax saved due to incremental annual floatation cost amortisation= 60,000 x Tax rate = 60,000 x 40% = 24,000
• Figure out net post tax interest savings
  • Annual interest on old bonds = 100,000,000 x 14% = 14,000,000
  • Annual interest on new bonds = 100,000,000 x 9% = 9,000,000
  • Annual interest saved = 14,000,000 - 9,000,000 = 5,000,000
  • Net Post tax interest saving = Pre tax interest saving x (1 - Tax rate) = 5,000,000 x (1 - 40%) = 3,000,000

Thus annual cash flow = total amortization tax effects + Net Post tax interest saving = 24,000 + 3,000,000 = 3,024,000

Part 3: We are now ready to calculate NPV

Initial investment outlay (as calculated in part 1 above) = 11,200,000

Annual post tax cash inflows = 3,204,000 (as calculated in part 2 above)

NPV = - Initial investment + PV of all the future annual post tax cash inflows

For PV of all the future annual post tax cash inflows:

Discount Rate = short-term government securities rate = 6%

Period = 25 years

Payment = 3,204,000

Use excel function "PV" to calculate the PV of all the future annual post tax cash inflows = PV (Rate, Period, Payment, FV) = PV(6%, 25, -3204000,0) =  38,656,869.02

Hence, NPV = - Initial investment + PV of all the future annual post tax cash inflows = -11,200,000 + 38,656,869.02 =  $ 27,456,869.02

Hence, the bond refunding's NPV = $ 27,456,869.02