A Capital Budgeting Problem
The refunding decision involves outflows in the form of financing costs related to redeeming and reissuing securities, and inflows represented by savings in annual interest costs and tax savings. In the present case, we shall assume the corporation issued $10 million worth of 11.75 percent debt with a 25-year maturity and the debt has been on the books for five years. The corporation now has the opportunity to buy back the old debt at 10 percent above par (the call premium) and to issue new debt at 9.5 percent interest with a 20-year life. The underwriting cost for the old issue was $125,000, and the underwriting cost for the new issue is $200,000. We shall also assume the corporation is in the 35 percent tax bracket and uses a 6 percent discount rate for refunding decisions. Since the savings from a refunding decision are certain—unlike the savings from most other capital budgeting decisions—we use the aftertax cost of new debt as the discount rate, rather than the more generalized cost of capital.3 Actually, in this case, the aftertax cost of new debt is 9.5 percent (1 − Tax rate), or 9.5% × 0.65 = 6.18%. We round to 6 percent. The facts in this example are restated as follows.
Let’s go through the capital budgeting process of defining our outflows and inflows and determining the net present value.
Step A—Outflow Considerations
1. Payment of call premium—The first outflow is the 10 percent call premium on $10 million, or $1 million. This prepayment penalty is necessary to call in the original issue. Being an out-of-pocket tax-deductible expense, the $1 million cash expenditure will cost us only $650,000 on an aftertax basis. We multiply the expense by (1 − Tax rate) to get the aftertax cost.
$1,000,000 (1 − T) = $1,000,000 (1 − 0.35) = $650,000
Net cost of call premium = $650,000
2. Underwriting cost on new issue—The second outflow is the $200,000 underwriting cost on the new issue. The actual cost is somewhat less because the payment is tax-deductible, though the write-off must be spread over the life of the bond. While the actual $200,000 is being spent now, equal tax deductions of $10,000 a year will occur over the next 20 years (in a manner similar to depreciation).
The tax savings from a noncash write-off are equal to the amount times the tax rate. For a company in the 35 percent tax bracket, $10,000 of annual tax deductions will provide $3,500 of tax savings each year for the next 20 years. The present value of these savings is the present value of a $3,500 annuity for 20 years at 6 percent interest, which is approximately $40,145, as shown in the margin.
The net cost of underwriting the new issue is the actual expenditure now, minus the present value of future tax savings as indicated below.
|PV of Annuity|
|− PV of future tax savings||40,145|
|Net cost of underwriting expense on the new issue||$159,855|
Step B—Inflow Considerations
The major inflows in the refunding decision are related to the reduction of annual interest expense and the immediate write-off of the underwriting cost on the old issue.
3. Cost savings in lower interest rates—The corporation will enjoy a 2.25 percentage point drop in interest rates, from 11.75 percent to 9.50 percent, on $10 million of bonds.
|11.75% × $10,000,000||$1,175,000|
|9.50% × $10,000,000||950,000|
|PV of Annuity|
Since we are in the 35 percent tax bracket, this is equivalent to $146,250 of aftertax benefits per year for 20 years. We have taken the savings and multiplied by one minus the tax rate to get the annual aftertax benefits.
$225,000 (1 − T)
$225,000 (1 − 0.35)
Applying a 6 percent discount rate for a 20-year annuity yields an approximate present value of $1,677,476, as shown in the margin.
|Cost savings in lower interest rates||$1,677,476|
4. Underwriting cost on old issue—There is a further cost savings related to immediately writing off the remaining underwriting costs on the old bonds. Note that the initial amount of $125,000 was spent five years ago and was to be written off for tax purposes over 25 years at $5,000 per year. Since five years have passed, $100,000 of old underwriting costs have not been amortized as indicated in the following:
|Written off over five years||25,000|
|Unamortized old underwriting costs||$100,000|
A tax benefit is associated with the immediate write-off of old underwriting costs, which we shall consider shortly.
|PV of Annuity|
Note, however, that this is not a total gain. We would have gotten the $100,000 additional write-off eventually if we had not called in the old bonds. By calling them in now, we simply take the write-off sooner. If we extended the write-off over the remaining life of the bonds, we would have taken $5,000 a year for 20 years. Discounting the 20-year annuity at 6 percent, we get an approximate present value of $57,350, as shown in the margin.
Thus, we are getting a write-off of $100,000 now, rather than a present value of future write-offs of $57,350. The gain in immediate tax write-offs is $42,650. The tax savings from a noncash tax write-off equal the amount times the tax rate. Since we are in the 35 percent tax bracket, our savings from this write-off are $14,928. The following calculations, which were discussed earlier, are necessary to arrive at $14,928.
|− PV of future write-off||57,350|
|Gain from immediate write-off||$ 42,650|
$42,650 (0.35) = $14,928
Net gain from the underwriting on the old issue $14,928