Savings Bonds: Actions Needed to Increase the Reliability of Cost-effectiveness Measures
Released: 2003-07-16T00:00:00

Letter

Background

Savings bonds offer investors the ability to purchase securities with lower minimum denominations than those for marketable Treasury securities. In response to concerns raised regarding the cost-effectiveness of the savings bond program as a funding mechanism for federal government operations, Treasury created a cost-effectiveness model that is now used and maintained by BPD. The model was intended to compare the projected costs for $1 billion of new savings bond borrowing and comparable borrowing through marketable Treasury securities. The model is based on the characteristics of the Series EE and Series I savings bonds and is intended to compare these costs on a present value basis.

Savings Bond Program

Treasury is authorized to borrow money on the credit of the United States to fund federal government operations. Within Treasury, BPD is responsible for prescribing the debt instruments, limiting and restricting the amount and composition of the debt, paying interest to investors, and accounting for the resulting debt. However, Treasury sets the financial terms and conditions of savings bonds and marketable Treasury securities, including denomination and pricing changes.

Savings bonds are an alternative for investors unable or unwilling to pay the minimum denomination of marketable Treasury securities. Table 1 describes several principal differences between Series EE and Series I savings bonds and selected marketable Treasury securities.

In March 2002 the Treasury Assistant Secretary for Financial Markets testified before the House Appropriations Committee, Subcommittee on Treasury, Postal Service, and General Government that Treasury believes that the availability of a savings vehicle with the full faith and credit of the United States should not be limited to those who can afford the minimum $1,000 denominations available in auctions of marketable Treasury securities. The official also said that even though savings bonds are not the most efficient form of borrowing in operational terms, Treasury would continue to offer them to the public.

Treasury is seeking to reduce the operational costs of savings bonds by offering the securities in paperless form. Treasury has started to offer savings bonds that are held in direct Treasury accounts instead of issuing paper certificates for the bonds. The Series EE and Series I savings bonds are available through the new TreasuryDirect system. A BPD planning document describes BPD’s objective as enabling Treasury to stop issuing paper savings bonds and thus begin to realize the long-term cost reductions expected from additional automation and more efficient processing.

Savings Bond Cost- effectiveness Model

In response to concerns raised regarding the cost-effectiveness of the savings bond program as a funding mechanism for federal government operations, Treasury created a cost-effectiveness model. According to a Treasury report to the House Committee on Appropriations and Committee on Financial Services, the savings bond cost-effectiveness model has been used to assess potential changes in the financial terms and conditions for Series EE and Series I savings bonds. According to model documentation, BPD also uses model results to project and trace annual costs and recoveries for distinct cost centers over the life of a savings bond loan.

What is collectively referred to as the savings bond cost-effectiveness model comprises two submodels, Series EE and Series I, with the differences between the two reflecting differences between the two series of savings bonds. The results of each submodel are averaged to estimate the overall cost-effectiveness of the savings bond program. According to a BPD official, the model calculates the value of a single savings bond and its costs to Treasury, and extends this to the total savings bond population in a given year. Subsequently, the model attempts to quantify the differences between the savings bonds and marketable Treasury securities (noted in table 1).

The model was intended to compare the projected costs for $1 billion of new savings bond borrowing and those for $1 billion in marketable Treasury securities on a present value basis, that is, discounting the costs over time to permit a valid comparison. The savings bond cost- effectiveness model utilizes seven key parameters: administrative costs, historic redemption patterns, sales volume, savings bond yields, maturity period, equivalent marketable yield, and tax recovery. Table 2 describes the key parameters of the model in detail.

Conceptual Design for Estimating Savings Bond Cost- effectiveness Is Appropriate, but Model Calculations Contain Errors

OMB guidelines state that a cost-effectiveness analysis is appropriate to use in an analysis of government programs when the benefits of competing alternatives are the same or where a policy decision has been made that the benefits of a program must be provided. A program is cost effective if, on the basis of life cycle cost analysis of competing alternatives, it is determined to have the lowest costs expressed in present value terms for a given amount of benefits. The conceptual design underlying the savings bond cost-effectiveness model reflects this OMB guidance. However, the present value calculations in the model contain errors. As a result, the model’s estimated “present values” do not follow OMB guidance and common financial economics practice, and the model does not provide Treasury with the information it needs to determine whether savings bonds are cost-effective.

Model’s Conceptual Design Follows OMB Guidelines

The model’s conceptual design follows OMB guidelines for cost- effectiveness analysis. Figure 1 shows the conceptual design of the model.

OMB Circular A-94, which is applicable to executive branch agencies, provides that the standard criterion for deciding whether a government program is cost-effective is net present value—a comparison of the discounted monetized value of the expected life cycle costs of alternative means of achieving the same stream of benefits. However, in its comments on this report BPD asserted that the model’s approach follows an alternative OMB method to determine cost-effectiveness. BPD stated that the model measures cost-effectiveness as the “relative financial benefit from two borrowing options whose overall costs are identical. Treasury’s benefit from each alternative is the amount of financing realized at the time borrowing occurs.” We have addressed this comment in the Agency Comments and Our Evaluation section.

A key concept in finance is recognizing that the value associated with funds received or paid at different points changes over time. Funds have a time value because of the opportunity to invest them at different interest rates and in different financial alternatives. Investors demand some compensation for making funds available today in return for future repayment. For example, the interest paid on a loan is a measure of this compensation.

Essentially, a present value calculation measures the value today that would be equivalent to a future payment, or stream of payments, by discounting the future payments (using an appropriate discount rate). For Treasury, this is the value today of the future payments to investors of securities offered for sale which, in the context of the model, is the redemption value of Series EE and Series I savings bonds and the repayment stream of the alternative marketable Treasury security (that is, any coupons plus maturity value). Calculating the present value for each alternative takes the monetary value of costs over time and discounts them at an appropriate discount rate. Discounting transforms costs occurring in different time periods to a common unit of measurement (app. II describes this in greater detail).

As table 1 notes, there are several distinctions between savings bonds and marketable Treasury securities; several of these are relevant to the model. Most notably, the interest rates and the timing of the interest payments are different. Accurate implementation of the conceptual design requires that the model address these issues in order to construct comparable present values for the costs of savings bonds and marketable Treasury securities. The model attempts to address these distinctions by (1) creating an after- tax present value discount factor for the marketable Treasury security from a 6-month average of the constant maturity yield curve, commonly referred to as the “constant maturity Treasury,” or CMT), and (2) reducing the present value of the marketable Treasury security by subtracting its estimated (that is, not paid) “discounted” coupons.

Model Creates Cost- effectiveness Ratio Based on Calculated “Present Values” for Both Alternatives

In general, the model is conceptually designed to create a marketable Treasury security comparable to a savings bond such that the repayment stream (that is, any coupons plus maturity value) to an investor is equal to that of a savings bond’s net cost to Treasury (that is, redemption value adjusted for administrative unit costs and tax revenue implications). The repayment stream of the created marketable Treasury security and the adjusted redemption value of the savings bonds represent costs to Treasury from offering these securities for sale. From this point, the model is intended to compare the costs of these two financing alternatives on a present value basis.

According to model documentation, the present value of the marketable Treasury security is constructed by discounting the savings bond’s redemption value, adjusted for Treasury’s unit cost of redemption and tax revenue implications, at an equivalent after-tax rate for marketable Treasury securities of the same maturity. The model’s calculation of the redemption value of the Series EE and Series I savings bond is similar; changes are due to the different structures of the two series. Table 3 provides additional detail on the redemption value calculation and variables for both the Series EE and Series I savings bond. Appendix III provides examples of redemption value calculations for both the Series EE and Series I savings bond.

The tax revenue implications are reflected in the model as a tax recovery rate. The model assumes that all savings bond tax recoveries are deferred until redemption. Tax recovery—the taxes collected on savings bond earnings that had been deferred until redemption—increases the revenues to Treasury. The model calculates the effect of tax recovery, in terms of life cycle costs for the model, by reducing the amount Treasury pays to an investor at redemption. However, the tax recovery rate is reduced in the model to reflect the education bond program. In general, as shown in table 1, savings bonds are eligible for tax benefits upon redemption when used for qualified education expenses.

The administrative unit cost to Treasury from redeeming savings bonds reduces the revenues to Treasury. The model calculates the effect of administrative unit redemption cost, in terms of life cycle costs for the model, by increasing the amount Treasury pays to an investor at redemption. The model constructs an after-tax “discount factor” based on a 6-month average of the CMT. At the time of our review, the window was the 6-month period ending October 31, 2001.

According to BPD officials, the model is intended to perform an additional step to calculate the “present value” of the marketable Treasury security. This additional step, according to model documentation, is intended to reflect the difference between savings bonds, which do not pay periodic interest, and marketable Treasury securities that do pay such interest in the form of coupons. The model treats the coupon payments that the marketable Treasury security would pay as a separate security in which the tax recovery is simultaneous with the payment. First, the estimated coupons are created based on the savings bond’s redemption value, adjusted for Treasury’s unit cost of redemption and tax revenue estimates. Second, these coupons are “discounted” by an after-tax “discount factor” based on a 6-month average of the CMT.

BPD believes that these coupons would reduce the benefit of the initial marketable Treasury security and therefore its “present value.” According to model documentation, these are subtracted from the “discounted” savings bond final payout, adjusted for Treasury’s unit cost of redemption and tax revenue implications. The model calculations for the “present value” of the marketable Treasury security, however, do not follow model documentation in that the savings bond final payout is not discounted. BPD officials confirmed that the model calculations actually construct the “present value” of the marketable Treasury security as equal to the redemption value of the savings bond, adjusted for Treasury’s unit cost of redemption and tax revenue implications, net of estimated “discounted” coupons.

According to model documentation, the “present value” of the savings bond is its issue price less the unit cost to issue. The model’s calculation returns a value that is equal to Treasury receipts from a savings bond, net of the administrative unit cost of issuance.

As previously mentioned, the model is intended to compare a savings bond and a marketable Treasury security on a present value basis. The difference, according to a BPD official, is then translated to the total savings bond population in a given year and converted to a ratio of millions of dollars in cost per $1 billion borrowed. The model calculation takes the difference between the two “present values” described above, projects the difference across the sales volume for the prior fiscal year, and then converts the difference to a ratio that measures cost savings in millions per $1 billion borrowed. Appendix IV provides a more detailed discussion of the model calculations.

BPD’s Definition of Present Value Does Not Follow OMB Guidance

Although Treasury has presented the model as measuring cost- effectiveness on a present value basis, most notably in a July 2002 report to Congress, the model does not construct a present value comparison in accordance with OMB guidance. Our review indicates that the model does not accurately incorporate all the life cycle costs in the present value calculations for either alternative, does not calculate and apply a true economic discount factor needed to derive present value that would be relevant to the time periods, and ultimately compares values that are not equivalent based on the time value of money. The result is that the model’s calculation of a cost-effectiveness ratio does not provide an accurate present value assessment of the alternatives.

As previously discussed, to create comparable borrowing between the two alternatives, the model is intended to set the repayment stream (that is, any coupons plus maturity value) of the marketable Treasury security equal to that of a savings bond’s net cost to Treasury (that is, redemption value adjusted for administrative unit costs and tax revenue implications). However, the model calculation does not incorporate all the life cycle costs of the savings bond into the marketable Treasury security’s “present value” calculation — the initial administrative cost of issuing the savings bond (that is, unit cost to issue) is not included. In addition, the model calculation does not incorporate all the life cycle costs of the savings bond into the saving bond’s “present value” calculation — the redemption value paid to an investor and the final administrative cost of the savings bond (that is, unit cost to redeem) is not included.

The present value of a bond (or bond price) is equal to the present value of its expected cash flows (that is, any coupons plus maturity value). As noted previously, BPD officials confirmed that the model measures what it terms the “present value” of the marketable Treasury security as equal to the redemption value of the savings bond, adjusted for Treasury’s unit cost of redemption and tax revenue implications, net of estimated “discounted” coupons. However, this calculation implicitly values current and future funds as the same. In addition, as previously discussed, the model treats coupons as if they reduce the benefit of the marketable Treasury security and therefore its “present value.” However, since the CMT already reflects the value of the coupons that Treasury is obligated to pay, reducing the benefit to Treasury essentially counts the coupons twice. Additionally, the construction of the discount factor in the model departs from OMB guidance since the model’s “discount factor” does not create an appropriate time value.

Further, the model treats Treasury receipts from a savings bond, net of the administrative unit cost of issuance, as the “present value” of the savings bond. However, the model does not include or discount over time the savings bond’s redemption value in this calculation, and therefore the model does not reflect a time value associated with these funds, or present value as the term is used in OMB guidance or in general finance usage.

Key Model Parameters and Components May Not Be Reliable

The savings bond cost-effectiveness model utilizes seven key parameters: administrative costs, historic redemption patterns, sales volume, savings bond yields, maturity period, equivalent marketable yield, and tax recovery. Since 1995, when BPD assumed responsibility for the model, it has made four model enhancements in an effort to better reflect changes in the savings bond program, three of which directly affect these parameters. Table 4 presents BPD’s changes to the three key model parameters since 1995. However, despite these enhancements, some of the data used to adjust the model’s parameters have not been updated and do not incorporate historical experience. In addition, the model contains other inaccuracies that could affect its reliability and accuracy. Finally, the model has not been subject to ongoing and periodic reviews by independent external reviewers, a common practice endorsed by OMB.

Despite Enhancements, Model Results May Not Be Accurate

The first enhancement affects a key calculation in the savings bond cost- effectiveness model: the redemption value, or future value, of the savings bond over time. These values form the basis for constructing a marketable Treasury security that is the alternative to savings bonds. The earlier bonds are redeemed, the less administrative costs are offset. Therefore, the accuracy of the model’s cost-effectiveness calculation depends heavily on the accuracy of predicted early redemptions.

The key driver for the redemption values in the model is probability of redemption. The model accounts for redemption probabilities differently than in the original model transferred to BPD in 1995. According to BPD officials, the original model estimated redemption probabilities with the most recent 13 months of Series EE redemption data. When BPD assumed responsibility for the model, staff began estimating redemption probabilities for each denomination of Series EE savings bonds back to 1957. The current model continues to incorporate the historical redemption patterns from 1957 to 1993. However, citing cost concerns, BPD has not updated the probabilities to reflect redemption patterns of the most recent 10 years. Since then, however, a wide variety of financial instruments have become available to investors, which could affect the patterns of redemption. Further, the redemptions do not reflect current interest rates.

As previously discussed, the model also applies the redemption probabilities of Series EE bonds to similarly priced Series I bonds (that is, the redemption probabilities for a $100 Series EE bond and a $50 Series I bond are equal). BPD has not estimated the redemption probabilities of Series I bonds, introduced in 1998, therefore the redemption probabilities applied in the Series I submodel have no direct relation to the Series I bond redemption patterns since 1998.

The second model enhancement deals with the maturity period. The original model assumed the stated maturity date for both securities of 30 years. BPD adjusted the current model to include an additional 20-year horizon beyond the stated maturities of savings bonds and marketable Treasury securities to account for those investors who hold on to the securities past the maturity date. However, according to a statement made by Treasury, the regulations governing savings bonds provide that bonds for which no claims have been filed within 10 years of the maturity date will be presumed to have been properly paid. The 20-year horizon enhancement appears to be inconsistent with this Treasury statement. Further, adding the 20 years appears to be inconsistent with OMB guidance for the alternatives to be compared over their stated life cycles, which for both alternatives should be the 30-year maturity period.

Finally, the third enhancement to the model adjusts the tax recovery rate for savings bonds by 10 percent to account for the education bond program. The 10 percent adjustment was an estimate since there was no program experience to guide the adjustment. The education bond benefit, which allows for the exclusion of interest earned subject to certain rules and limits, applies only to savings bonds. Adjusting the tax recovery rate for savings bonds to reflect this program is appropriate. However, the education bond program was introduced in 1990, providing program experience of at least 12 years. BPD has not analyzed whether the historical experience is consistent with the 10 percent adjustment and thus does not know whether the adjustment improves the model’s accuracy.

Discontinuance of 30-Year Marketable Treasury Bonds Directly Affects the Marketable Yield Model Parameter

A BPD official told us that the equivalent marketable yield, or CMT, has the strongest impact on model results. The CMT is the basis for BPD’s “discount factor” used to derive the “present value” of the alternative marketable Treasury security. Treasury discontinued the issuance of the 30- year Treasury bond in October 2001, however, directly affecting how the discount rate is calculated.

Beginning on February 18, 2002, Treasury ceased publication of the 30-year constant maturity series. Instead, Treasury publishes a Long-Term Average Rate and a linear extrapolation factor that can be added to the Long-Term Average Rate to allow interested parties to compute an estimated 30-year rate. BPD staff told us that BPD is still considering how to reflect this change in the model’s “discount factor.”

Other Model Features Could Affect the Reliability of Model Results

The model coding contains additional inaccuracies that, in comparison to the present value inaccuracy, appear to have a minor impact. Also, the model’s use of older software and lack of controls over changes may allow additional errors to remain undetected.

A coding error in the bonds redeemed calculation occurs in some denominations for both submodels. From the time of issuance through 4 months outstanding, the formula uses the probability of redemption for the month following the correct month. BPD staff told us this error occurred during model maintenance by BPD staff. Additionally, BPD staff told us that this error would be corrected (app. IV describes the correction for this calculation).

Another inaccuracy involves the redemption value calculation in the Series I submodel. The calculation there does not match the savings bond regulations since the redemption value does not reflect the accrued value at the beginning of each semiannual period.

In addition, the savings bond cost-effectiveness model is maintained in older software. Use of the older software can be appropriate, but does increase the difficulty in maintaining and updating the model without introducing errors. As noted above, BPD acknowledged one such error. BPD staff told us that they have not moved the model into current software because of concerns that the software’s features used to calculate the scenario effects of program changes will not function properly.

During the course of our review, we also found that the model contained unlabeled and undocumented data fields. BPD staff told us that these fields were remnants of scenarios that staff had run on the model in the past, which were accidentally left in the model when it was sent to us for review. One aspect of an effective general control and application environment is the protection of data, files, and programs from unauthorized access, modification, and destruction. BPD staff could, by saving scenario data in the master model file, inadvertently add, alter, or delete sensitive data or coding.

BPD Has Not Requested an Independent External Review of the Model

While OMB guidance calls for an independent external review of cost- effectiveness models, as well as assessments of their accuracy and reliability, BPD has not commissioned such analysis. As a result, BPD cannot assess the accuracy and reliability of the model.

OMB guidelines provide elements for a cost-effectiveness analysis and promote subjecting such analyses to independent external reviews. Verification and explicit assumptions are two of the four elements OMB identified for a cost-effectiveness analysis. OMB states that verification through retrospective studies to determine whether anticipated benefits and costs have been realized are potentially valuable. Such studies can be used to determine necessary corrections in existing programs, and to improve future estimates of benefits and costs in these programs. Agencies should have a plan for periodic, results-oriented evaluation of program effectiveness. OMB adds that a cost-effectiveness analysis should be explicit about the underlying assumptions used to arrive at estimates of future benefits and costs and include a statement of the assumptions, the rationale behind them, and a review of their strengths and weaknesses. Key data and results should be reported to promote independent analysis and review.

OMB guidance also acknowledges that estimates are typically uncertain because of imprecision in both underlying data and modeling assumptions and states that analyses should attempt to characterize the sources and nature of uncertainty. In analyzing uncertain data, objective estimates of probabilities, such as those derived from market data, should be used whenever possible. Any limitations of the analysis because of uncertainty or biases surrounding the data or assumptions should be discussed. In addition, major assumptions should be varied and net present value and other outcomes recomputed to determine how sensitive outcomes are to changes in the assumptions. In general, sensitivity analysis should be considered for estimates of benefits and costs, the discount rate, the general inflation rate, and distributional assumptions of probabilities. Models used in the analysis should be well documented and, where possible, available to facilitate independent review.

BPD has not independently verified the cost-effectiveness model. According to BPD officials, a survey and investigations team from the House Committee on Appropriations, which visited BPD’s Parkersburg, West Virginia, location in 1996, conducted the only review of the savings bond cost-effectiveness model. Since the team did not initiate further inquiry, BPD officials said they assumed that the team had found no issues requiring further review and discussion. Although BPD and Treasury officials have maintained in congressional testimonies and in a recent report that the model results are accurate, to date neither BPD nor Treasury has requested an independent external review to validate the savings bond cost-effectiveness model. Further, while BPD has used the model to estimate the potential effects of changes in the savings bond program, it has not sought to conduct any sensitivity analysis that could reveal the model’s limitations.

Conclusions

Our review of BPD’s savings bond cost-effectiveness model indicates that the model’s results do not provide BPD, Treasury, OMB, or Congress appropriate information to assess the relative costs of the savings bond program versus marketable Treasury securities as a source of raising funds. Although the model was intended to compare savings bonds and marketable Treasury securities on a present value basis, the model’s comparison is not based on present values and thus does not follow OMB guidance and common financial economics practice. As previously discussed, a discount factor brings future costs and revenues into present value terms to permit comparisons. While the model calculates a value that BPD terms a “discount factor,” the calculation is incorrect and, as a result, the model does not correctly calculate the present value of the alternatives. In addition, this calculated value is not applied consistent with the model’s conceptual design and OMB guidance. Therefore the cost-effectiveness ratio that the model creates does not provide BPD with the information it needs to assess the relative costs of the savings bond program and marketable Treasury securities to determine which financing approach offers a greater financial benefit to Treasury.

The model also uses data that may not be reliable. In particular, the probabilities of redemption for the Series EE bond are 10 years out of date and BPD has not estimated any probabilities of redemption that have any direct relation to the Series I bond redemption patterns since 1998 when these bonds were first introduced. The model also incorporates a time horizon that extends beyond the life cycles of either security and distorts the cost-effectiveness analysis, allowing a longer time period for the administrative costs of savings bonds to be offset. Finally, the reduction in the tax recovery rate to reflect the education bond program is not based on actual program experience and may be over- or underestimating the financial impact of the program to Treasury.

Given that the model uses data that may not be reliable and BPD has not decided how to reflect the discontinuance of the 30-year constant maturity series in the model’s “discount factor,” we did not make corrections to the model. As a result, we do not know to what degree the present value errors and these data affect the model’s cost-effectiveness ratio.

BPD’s ability to assess the impact of policy changes to the savings bond program, project cost centers for the savings bond program, and determine cost-effectiveness in relation to marketable Treasury securities is hampered by fundamental errors in the present value calculations. When combined with model data that may not be reliable, the need for independent reviews of cost-effectiveness and sensitivity analyses, which are called for in OMB Circular A-94, becomes particularly important.

Recommendations

Because of the importance of measuring the cost-effectiveness of financing mechanisms used to fund the operations of the federal government, we recommend that the Secretary of the Treasury direct that the Commissioner of the Public Debt in conjunction with Treasury’s Office of Domestic Finance revise the savings bond cost-effectiveness model to estimate the relative (or net) present value of the life cycle costs of issuing savings bonds versus marketable Treasury securities.

As part of that revision, the Commissioner should do the following: Update the Series EE probabilities of redemption to capture any changes in redemption patterns caused by the proliferation of financial products or interest rate changes in the last 10 years. At a minimum, Treasury and BPD should collect data for a sample of the more recent time period to test the validity of the 1957-93 data.

Base Series I bond redemption patterns on actual experience with those bonds.

Validate the cost estimate of education bond program participation based on the historical, 12-year data to date.

Replace the 30-year equivalent marketable rate.

Update the software used for the model to enhance BPD’s ability to maintain the model and protect against unauthorized modification.

Put in place a process for ongoing verification, sensitivity analysis, and independent external review of the model.

Agency Comments and Our Evaluation

In a June 4, 2003, letter commenting on a draft of this report, the Commissioner of the Public Debt wrote that the cost-effectiveness model conformed to OMB Circular A-94, sec. 5b, since it “measures Treasury’s relative financial benefit from two borrowing options whose overall costs are identical. Treasury’s benefit from each alternative is the amount of financing realized at the time borrowing occurs.” Noting that the model “is not intended to be a classic present value exercise,” the Commissioner explained that the model “compares the present value of a projected stream of payments associated with the sale of savings bonds with the amount realized from the sale.” BPD suspects it may have inadvertently misused the terms “discount factor” and “present value” in internal Treasury discussions. Further, BPD said that we did not understand the model’s life-cycle duration, the minimum holding period, and the Series I redemption values.

The Commissioner noted that while BPD disagreed with our conclusion that the model’s comparisons were invalid, BPD generally agreed with our recommendations for updating the model. However, the Commissioner also noted that, with Treasury’s goal of moving toward a totally electronic environment for the savings bond program, “we think it's appropriate for us to shelve the existing model, which is based on paper bonds, and focus our attention on the transition to a fully electronic program.”

The model compares the amount of funds raised by selling a given amount of Series EE and I bonds in various denominations and the present value of the future costs to Treasury in connection with issuing the bonds. If the amount raised is greater than the present value of the future costs associated with the bonds, taking into account administrative costs and tax benefits, then the program is deemed to be cost-effective.

While we agree that an approach comparing the benefits of two approaches having identical costs would be a valid alternative to the present value approach that we described in our report, the model’s calculations do not support this analysis. Marketable Treasury securities and savings bonds can be compared by either comparing the costs of raising identical sums using two alternative debt instruments or by comparing the funds raised when the costs of the two instruments are identical. However, if BPD were to base the cost-effectiveness model on a comparison of the “financial benefit from two borrowing options whose overall costs are identical,” the key issue that this approach would have to address is that marketable Treasury securities and savings bonds do not necessarily have identical overall costs.

The challenge of this modeling approach would be to appropriately measure costs over time of the two options in a way that would permit treating the costs as identical. Since the costs vary over time, accurately calculating the present value of the costs of the two options would be an essential step. However, we did not find, for reasons noted in the report, that the model accurately or reliably calculates the present value of the stream of costs associated with the sale of savings bonds. In particular, the report explains that the discount rate used to calculate the present value of the projected stream of costs is inappropriate.

We have changed the report to recognize that BPD allocates a small number of redemptions prior to 6 months to reflect hardship waivers; these waivers are not discussed in BPD’s model documentation. We have not, however, changed the report in response to the Commissioner’s statements regarding life cycle costs and Series I redemption values. As the report notes, the 20-year extension on the life cycle appears to be inconsistent with regulations that provide that bonds for which no claims have been filed within 10 years of the maturity date are presumed to have been properly paid. Our analysis of the Series I savings bond redemption value found that the formula does not correctly recognize the savings bond’s accrued value at the beginning of each semiannual period.

The Commissioner’s letter noted that BPD generally agrees with the recommendations for updating the model, but that BPD believes it appropriate to “shelve” the existing model and focus on the transition to a fully electronic retail securities program. We agree that the importance of many administrative costs will decline if BPD successfully transforms the current paper-based savings bond program to an electronic environment. Further, there may be changes in investors’ purchases and redemptions of savings bonds in an electronic environment.

However, important differences will continue to exist between the costs of savings bonds and marketable Treasury securities, particularly the payment of coupons and the tax treatment of the two debt instruments. A model that accurately recognizes these differences will continue to be as crucial to understanding the relative cost-effectiveness of the two debt instruments as it is in the current paper-based environment. That model, furthermore, will have to be updated regularly to reflect the effect of any changes in investor preferences and behavior on the savings bond program as it moves into this new electronic environment. Our recommendations will remain appropriate for assessing the cost-effectiveness of the savings bond program managed in an electronic environment.

As agreed with your office, unless you publicly announce its contents earlier, we plan no further distribution of this report until 30 days from its date. At that time, we will send copies to the Secretary of the Treasury, the Treasury Under Secretary for Domestic Finance, and the Commissioner of the Public Debt. Copies will be made available to others upon request. In addition, this report is also available at no charge on GAO’s Web site at http://www.gao.gov.

If you have any further questions, please call me at (202) 512-8678 or mccoolt@gao.gov or James M. McDermott, Assistant Director, at (202) 512- 5373 or mcdermottjm@gao.gov.

Objectives, Scope, and Methodology

To assess the savings bond cost-effectiveness model, we obtained an electronic copy of the model as of fiscal year 2001 in addition to hard-copy background and supporting documentation. Given that the model is maintained in older software, Lotus 1-2-3 version 5, we reviewed the model using the same program and version to avoid corruption or translation errors. We then identified and reviewed the various regulations regarding the Series EE and Series I savings bond structure on which the cost- effectiveness model is based. In addition, we reviewed relevant portions of Internal Revenue Service publications regarding the tax implications of the savings bond program. We compared these information sources with the model coding to verify that the calculations reflect the structure of the savings bond program.

To determine if the model constructed a present value comparison, we analyzed the model coding and supplied documentation to determine if (1) the model’s design matched Office of Management and Budget and conventional approaches and (2) the model’s calculations accurately implement the model’s design to arrive at a present value comparison.

Given that the model calculations did not result in a present value comparison, we did not assess the accuracy or completeness of the data input used in the various model parameters and assumptions. As a result, we do not know what effect such data had on the model’s cost- effectiveness calculation.

We conducted our work in Washington, D.C., from September 2002 through April 2003 in accordance with generally accepted government auditing standards.

Present Value Theory and Model Calculations

The present value of a bond (or, bond price) is equal to the present value of its expected cash flows (any coupons plus maturity value). Each cash flow must be discounted at the relevant rate for the time period. ... ... ... ... ... ----------------------------1 +( )

In many explanations of present value, the discount rate is held constant, removing the need for r-1, to vary over time.

0= (coupon + face) = ----------------------------------------------- ---------------------------------------------- , in which ) ) ) )*...* 1 ) for some t >2, for example.

Based on the above table, the following illustrations assume that the periods correspond to years (for example t = 1 represents the end of the first year). ----------------1 r+( )

In the illustrations above, the rate or rates used to discount each component is relevant to the time period.

Model Calculation for the “Present Value” of the Marketable Treasury Based on model documentation, the coupon payments are subtracted to reflect that the coupon payments on the Treasury alternative would reduce the benefit Treasury would receive from the initial security.

Redemption Value1*r1 ------------------------------------------------------- )

Redemption Value2* r2 -------------------------------------------------------- )

Redemption Value2* r2 -------------------------------------------------------- )

Redemption Value3

Redemption Value3* r3 -------------------------------------------------------- )

Redemption Value3* r3 -------------------------------------------------------- )

Redemption Value3* r3 --------------------------------------------------------r2+(r1+() 1) 1 r3+(1 )

The discounting is incorrect in the model, and is carried through for periods two and greater. Appendix IV provides a more detailed discussion of the model calculations, including the monthly after-tax “discount rate” mentioned above.

Future Value Examples for Series EE and Series I Savings Bonds for Bonds 5 Years and Older

Series EE - 31C.F.R. §351.2-(k)(1)(iii); Series I – 31C.F.R. § 359.2-(e)(1)(vi).

Example: An I composite rate of 5.07 percent will result in a newly purchased hypothetical $25 bond increasing in value after 6 months to $25.63, when rounded to the nearest cent.

At the beginning of the first semiannual rate period, the PV is equal to $25 such that Month 1: FV = 25 * {(1/6) = 25.10 Month 2: FV = 25 * {(2/6) = 25.21 Month 3: FV = 25 * {(3/6) = 25.31 Month 4: FV = 25 * {(4/6) = 25.42 Month 5: FV = 25 * {(5/6) = 25.53 Month 6: FV = 25 * {(6/6) = 25.63 Thus, a $5,000 bond purchased at the same time as the hypothetical $25 bond will be worth $5,126 after 6 months ( x $25.63 = $5,126).

The PV variable changes in months 7 through 12 such that the PV is equal to the redemption value at the beginning of the semiannual rate period, which in the above example is equal to month 6 FV such that Month 7: FV = 25.63 * {(1/6) = 25.74 Month 8: FV = 25.63 * {(2/6) = 25.84 Month 9: FV = 25.63 * {(3/6) = 25.95 Month 10: FV = 25.63 * {(4/6) = 26.06 Month 11: FV = 25.63 * {(5/6) = 26.17 Month 12: FV = 25.63 * {(6/6) = 26.28 The PV variable changes in months 13 through 18 such that the PV is equal to the redemption value at the beginning of the semiannual rate period, which in the above example is equal to month 12 FV, and so on.

Model Calculations Detail

The cost-effectiveness calculations in the Series EE and Series I submodels, as well as preceding steps, are similar; coding changes are due to the different structures of the two series, as noted in table 3, and modeling errors, as previously discussed. Though not shown here, both submodel calculations for savings bond redemption value incorporate the 3-month interest penalty for bonds redeemed before 5 years from issue.

Calculations for Marketable Treasury “Present Value” — Five Steps Where n = months outstanding Step 1: Savings bond redemption value respective to denomination (as previously shown in table 3).

Step 2: Savings bond redemption value after unit cost to redeem and tax revenue implications = Adjusted Redemption Value: Redemption Value – ((Redemption Value – savings bond issue price) * savings bond tax recovery rate) + unit cost to redeemStep 3: Algebraic after-tax “present value discount factor”several component calculations): 3a. after-tax semiannual CMT= (6-month average of CMT/2) * (1 – tax recovery rate) 3b. after-tax semiannual CMT expressed as a monthly rate = Y = ((after-tax semiannual CMT + 1) ^ (1/6)) – 1 3c. Y algebraic conversion leading to after-tax “present value 3c.1. S = 1/(1 + Y) 3.c.2 Month 1 FAC (that is, FAC; for all other n, FAC = S * (FACn-1 + 1) 3d. After-tax “present value discount factor” = 1 – (Y * FAC)

Step 4: Algebraic after-tax “present value discount factor”monthly rate: Ie = (((1/FACT) ^ (1/n)) – 1)

Step 5: Treasury “present value” / (1 + Ie) ^ The resulting marketable Treasury “present value” * FACT , which returns the following: Month 1 marketable Treasury “present value” = Adjusted Redemption Value - Adjusted Redemption Value / (1 + Y * Y) + Adjusted Redemption Value / (1 + Y)], and so on.

Savings bond “present value” - marketable Treasury “present value”

Month 0 bonds redeemed = probability of redemption * (savings bond sales volume respective to denomination – bonds redeemed0..n)

Month 0 bonds outstanding = sales volume respective to denomination – bonds redeemed = bonds outstandingn-1 - bonds redeemedStep 6: Cost-effectiveness ratio for each denomination (comprising several 6a. (cumulative projected “present value” difference50 years – pieces outstanding50 years * savings bond unit cost to issue) 6b. (sales volume respective to denomination * savings bond issue price) 6c. (result of 6a. / results of 6b.) * 1,000 The resulting cost-effectiveness calculation returns a ratio of millions saved per $1 billion borrowed.

Additional Calculations That Are Not Relevant to the Model’s Cost- effectiveness Calculation Though not detailed above, the model includes five calculations that do not produce output relevant to the cost-effectiveness calculation.

In addition, the model performs an additional step in the after-tax “present value discount factor” calculation that is not necessary. The model creates an after-tax “present value discount factor” expressed as a monthly rate, shown above as step 4 in the calculations for the marketable Treasury “present value.” Step 5, as shown above in the calculations for the marketable Treasury “present value,” reverses this calculation through the 30-year life cycle of the marketable Treasury alternative.

Comments from the Bureau of the Public Debt

GAO Comments

The following are GAO's comments on the Bureau of the Public Debt's (BPD) letter dated June 4, 2003. 1. As we note in this report's Agency Comments and Our Evaluation section, the approach that BPD outlines here would be an appropriate alternative to the cost-effectiveness model based on a present value analysis described in the report. The description in this report is based on documentation for the cost-effectiveness model that BPD provided in an October 16, 2002, meeting; on a July 2002 report that BPD prepared for the House Committees on Appropriations and on Financial Services; and on March 2002 testimony by the Commissioner of the Public Debt before the House Appropriations Subcommittee on Treasury, Postal Service, and General Government. 2. As we note in the report, the 20-year extension is not consistent with a statement previously made by the Department of the Treasury regarding the presumption of payment 10 years beyond the maturity date.

We agree that all administrative costs are included in the model. As the report notes, however, the model calculation does not accurately incorporate these costs in computing the present value of the marketable Treasury security and the savings bond. 3. Based on BPD's explanation that redemptions within 6 months of a savings bond's issuance are sometimes granted in hardship cases, we have deleted discussion of their inclusion in the model from the report. 4. As we note in the report, the model's compound interest formula for the Series I bonds does not recognize the bond's accrued value at the beginning of each semiannual period. When calculated out over 30 years, the difference between the formula in the regulation and the model's calculation is minor but still exists.

GAO Contacts and Staff Acknowledgments

GAO Contacts

Acknowledgments

In addition to those named above, Heather T. Dignan, Mitchell B. Rachlis, and Barbara M. Roesmann made key contributions to this report.

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