Some pitfalls in loan subsidy valuation.

The purpose of this cautionary note on Jennergren's (2005) comprehensive compendium of loan subsidy valuation methods is to emphasize the loan structure specificity of his paper. Only bond-type arrangements are considered; i.e., only interest payments are made at the end of each year and the repayment of the entire principal occurs at the loan's maturity date.

Needless to say, there are other loan arrangements that are popular in financial markets; e.g., mortgage-type arrangements that entail equal annual debt service payments comprised of a changing blend of interest payment and principal repayment and arrangements that require equal annual repayment of principal and that therefore imply annual interest payments that decline monotonically throughout the life of the debt. These two alternative loan arrangements are broached in the next two sections of this note in the context of Jennergren's first method of loan subsidy valuation, employing numerical examples similar to that cited by him. His two interpretations of his first method are shown to be inconsistent with each other for the mortgage-type arrangement but consistent for loans that specify equal annual principal repayment. It is argued that a requirement must be satisfied to ensure consistency of Jennergren's two interpretations, namely, both the subsidized or entering loan and the benchmark unsubsidized or exiting loan must entail identical principal repayment schedules. Absent this restriction, the two interpretations of his first method produce different valuations. This note concludes by emphasizing the required focus for future research in loan subsidy valuation methods.

EQUAL ANNUAL DEBT SERVICE EXAMPLE

Consider the same numerical example cited by Jennergren (2005) with solely one difference. A firm whose tax rate is 35% obtains a loan of $100,000 with a maturity of 5 years at the subsidized rate of 5% rather than at the unsubsidized rate of 13%. The debt contract specifies equal annual debt service payments; i.e., this is a mortgage-type arrangement that contrasts with the bond-type arrangement Jennergren considers.

The subsidized or entering loan entails a constant annual debt service payment of $23,097.48, whereas the benchmark unsubsidized or exiting loan entails a constant debt service payment of $28,431.45. In Jennergren's (2005) first method of loan subsidy valuation, both entering and exiting debt involve the same original loan principal that equals $100,000 in this numerical example.

Table 1 details the interest payments and principal repayments associated with these two loans, the subsidized or entering and the benchmark unsubsidized or exiting loans, during their common 5-year life.

Consider the dual interpretations Jennergren (2005)presents of his first loan subsidy valuation method. The first interpretation states that the value of the loan subsidy involves the following three components: the loan subsidy without consideration of tax shields minus the loss of tax shields on the exiting or unsubsidized loan plus the gain of tax shields on the entering or subsidized loan. Jennergren's first method is characterized by the assumption that both exiting and entering loans share a common initial principal that equals $100,000 for the example at hand. Invoking this first interpretation, the value of the loan subsidy equals $18,760.82 minus $11,101.73 plus $4,103.93, resulting in a value of $11,763.02.

The $18,760.82 value of the first component equals $100,000, the amount of subsidized financing obtained, minus the value of the before-tax subsidized loan debt service payments discounted to the present at the unsubsidized interest rate of 13% that equals $81,239.18. This first component may be interpreted as the extra financing obtained by the firm as a result of its ability to tap a financing source that charges only 5%, rather than its unsubsidized interest cost of 13%. Whereas the firm is able to elicit $100,000 in subsidized financing, with the same before-tax debt service payments as the subsidized loan, the firm would be able to elicit merely $81,239.18 from its unsubsidized source.

The second component equals the 35% tax rate times the unsubsidized loan interest payments, discounted to the present using the unsubsidized interest rate of 13%. These are the interest tax shields lost as a result of not obtaining the benchmark unsubsidized loan. The third component equals the 35% tax rate times the subsidized loan interest payments, discounted to the present using the same discount rate. These pertain to the interest tax shields gained as a result of accessing the subsidized or entering loan.

Jennergren's (2005) second interpretation of his first method of loan subsidy valuation is articulated as the present value of the after-tax differences in annual interest payments discounted to the present at the before-tax unsubsidized interest rate. Pursuing this interpretation, the annual differences in interest payments between the unsubsidized and subsidized loans (refer to the interest payment lines in Table 1) are multiplied by one minus the 35% tax rate and these resulting amounts are discounted to the present employing the before-tax unsubsidized rate of 13%. This interpretation yields a loan subsidy value of $12,995.91, which differs from the value of $11,763.02 calculated earlier. Clearly, the two interpretations of the putatively identical loan subsidy valuation method are inconsistent. Observe that the subsidized and the unsubsidized loans detailed in the cited table entail different principal repayment schedules. It will be argued in the next section that consistency of Jennergren's two interpretations requires that these principal repayment schedules be identical.

EQUAL ANNUAL PRINCIPAL REPAYMENT EXAMPLE

Consider an alternative loan structure that entails equal annual principal repayments and that therefore requires monotonically declining annual interest payments due to the declining loan principal. All other facets of the loan are identical to both Jennergren's (2005) example as well as the earlier loan considered. The table analogous to Table 1 is the following, Table 2.

Observe that the principal repayment schedules of the subsidized or entering loan and the unsubsidized or exiting loan are identical. As suggested in the previous section, this guarantees consistency of Jennergren's (2005) dual interpretations of his first method.

Invoking the first interpretation, the value of the loan subsidy equals the first component (the extra financing elicited from a subsidized financing source compared with an unsubsidized financing source when the common schedule of debt service payments assumed is that of the subsidized loan and when tax considerations are ignored), whose value is $18,249.46, minus the second component (the present value of the interest tax shields lost on the benchmark unsubsidized or exiting loan discounted at the before-tax unsubsidized rate), whose value is $10,379.36, plus the third component (the present value of the interest tax shields generated on the subsidized or entering loan discounted at the before-tax unsubsidized rate), whose value is $3,992.07. This calculation yields a loan subsidy value of $11,862.15.

Invoking the second interpretation--i.e., the present value at the unsubsidized rate of 13% of the after-tax differences in interest payments saved as a result accessing the subsidized loan--the loan subsidy value likewise equals $11,862.15. Thus, in contrast to the example presented in the previous section, the current example yields consistent interpretations of Jennergren's (2005) first method of loan subsidy valuation. It is easy to see that consistency of the two interpretations requires that the principal repayment schedules of the entering and exiting loans be identical.

CONCLUSION

This brief addendum to Jennergren's (2005) comprehensive treatment of loan subsidy valuation methods has emphasized the role of loan structure; i.e., the specific arrangement for paying interest and repaying principal on the debt. Specifically, it was shown that his two interpretations of his first method of loan subsidy valuation are inconsistent if the subsidized loan and the benchmark unsubsidized loan entail different principal repayment schedules.

Future research must develop loan subsidy valuation methods that are valid across the wide gamut of possible loan types. This is merely one facet of the more fundamental question that remains unresolved, namely, how to calculate the amount of the unsubsidized loan that is replaced by the subsidized loan. Possible answers to the latter that have been articulated in Jennergren (2005), Pierru (2006), and Babusiaux and Pierru (2007) are the book value of the unsubsidized loan, defined as the sum of the before-tax subsidized loan cash flows discounted at the subsidized rate, and the economic value of the subsidized loan, defined as the sum of the after-tax subsidized loan cash flows discounted at the after-tax unsubsidized rate.

REFERENCES

Babusiaux, D. and Pierru, A. (2007) Adjustment of the standard WACC method to subsidized loans: a clarification. Estudios en Economia Aplicada, 25, 341-364.

Jennergren, L.P. (2005) Loan subsidy valuation. The Engineering Economist, 50, 6986.

Pierru, A. (2006) Loan subsidy valuation: an alternative approach. The Engineering Economist, 51, 297-306.

Jacques Schnabel

School of Business and Economics, Wilfrid Laurier University, Waterloo, Ontario, Canada

BIOGRAPHICAL SKETCH

JACQUES SCHNABEL is a Professor in the School of Business at Wilfrid Laurier University, where he teaches and researches in the areas of Corporate and International Finance and Derivative Studies.

Address correspondence to Jacques Schnabel, School of Business and Economics, Wilfrid Laurier University, 75 University Ave., Waterloo, Ontario, N2L 3C5, Canada. E-mail: jsehnabel@wlu.ca

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