The IMF's Statistical Systems in Context of Revision of the United Nations' A System of National Accounts
Chapter

27 Treatment of Deep-Discounted and Index-Linked Bonds in the National Accounts

Author(s):
Vicente Galbis
Published Date:
September 1991
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Author(s)
Brian Newson and Soren Brodersen

Index-linked securities and deep-discounted bonds take a variety of forms but have one significant feature in common. In both, the asset carries only a fairly low explicit rate of interest (say 0 percent to 2 percent), but the holder of the security is guaranteed some upward revaluation of the principal invested during or at the end of the term of the security.

I. The Problems Posed

For the United Nations' A System of National Accounts (SNA), the question then is whether this upward revaluation should be shown in the reconciliation account or as interest in the income and outlay account, possibly distributed over the lifetime of the bond.

This paper is based on experience in the European Community (EC) in the 1970s and 1980s, particularly in the United Kingdom and Denmark, where the “imputed” interest payments represented as much as 8 percent of gross domestic product (GDP). The issue, however, would appear to be important for a wide range of countries in conditions of inflation.

Deep-Discounted Bonds

Deep-discounted bonds are bonds with a maturity of several years that are issued at a price substantially below their redemption value, sometimes as little as 50 percent of the redemption price. This arrangement is associated with a very low—or even zero—explicit rate of interest. Investors receive their return mainly from the difference between the issue price and redemption price.

For accounting purposes, treating this gain as interest is attractive for several reasons.

•It seems to be treating this case in the same way as a “normal” bond, which is issued at or around face value with a higher coupon interest.

•It also takes into account the very important point that the increase in the value of the asset (over its complete term, whatever its market value in between) is foreseeable and known to both parties in advance and could almost be said to form part of the contract.

•There is also a direct parallel with short-term bills for which the discount is treated as interest, although in this case, of course, transactions occur mainly within one year.

However, this approach seems to raise many problems when introduced into an integrated system of accounts.

•There are other cases in which differences exist between face value and market value of an asset, hence a risk exists in generalizing this solution.

•It introduces an imputation of interest, whereas both the letter and the spirit of the present SNA and European System of Integrated Economic Accounts (ESA)1 definitions of “actual interest” seem to preclude such imputations.

•It departs from the principle, underlying all financial accounts, of recording transactions as they actually occur.

•For the balance sheets, the implication would be that such assets are always valued at the price at which they were first issued, even at redemption time. This is, of course, necessary to avoid holders' benefiting twice—once from the imputed interest, and once from the capital gain on redemption—but it would seem to require several other imputations to balance a complete system of accounts (for example, there is in fact a redemption at the full price, for which other types of assets are used, such as currency and sight deposits).

Section II of this chapter shows how the discount on deep-discounted bonds can be treated as interest, with support from data for Denmark.

Index-Linked Securities

Various index-linked savings schemes were developed in the United Kingdom in the inflationary conditions of the 1970s.2 They were designed to protect the capital of small investors—indeed, the first example was government savings certificates known as “Granny bonds” that were available only to old-age pensioners. However, index-linked financial assets also exist in other countries and other sectors.

The basic mechanism is that the investor receives a small nominal interest rate (0 percent to 2 percent), but the value of his or her asset increases in line with some price index. Frequently a general retail price index is used, but it could also be an index related to the purposes of the investment, such as an index of housing costs or even of foreign exchange rates. Frequently, too, the whole gain from indexation is only obtained if the investment is maintained for the whole contract period (for example, five years). That is, early redemption is penalized by being granted at a less favorable rate. (This is therefore not the same as actual payment of interest at a rate defined as “2 percent plus the rate of inflation.”)

There is no disagreement about how to record the initial investment and all interest actually received in the period when they do in fact happen (that is, in the same way as for non-index-linked assets of the same type). The problem is how to treat the index-linked increase in the value of the asset itself. Three treatments of the index-linked component seem possible.

•Because there is a revaluation of the principal invested without any transaction occurring, the most obvious solution is to record this upward revaluation only in the reconciliation account.

•The increase in the value of the investment that results from indexation could be counted as a capital transfer. Such a treatment is already accorded to nonrecurrent bonus payments on savings granted by general government to households to reward them for their saving carried out over a number of years.

•The United Kingdom opted to record the increase in value of the asset as interest. This treatment portrays such assets in a way similar to the normal case of high nominal interest. It does, however, add two imputations: of interest paid out to the household, and of reinvestment of the same amount in the asset in order to show in the balance sheet the increasing claim and liability of households and government, respectively.

Time of Recording

For both deep-discounted bonds and index-linked securities, it frequently occurs that the capital revaluation is only available to the creditor at the end of the contract period. However, in both cases the value is known (in advance, for deep-discounted bonds; when the price index is published, for index-linked securities). Thus, the imputed interest could be distributed over the life of the asset.

Most experts advocate showing this gradual increase in the value of the asset and liability. It is true that for individual contracts there frequently is no legal liability for the debtor until the end of the term; indeed, early redemption, if allowed, takes place at much less advantageous terms. However, since only a very small proportion of contracts are prematurely terminated, in general it is probably more reasonable to treat outstanding claims as accruing in line with the price index throughout the period.

The Crucial Argument

In discussions within the EC Working Party on National Accounts in 1984, 1986, and 1988, experts have been fairly equally divided. Roughly half of these advocated recording transactions as they actually occur and so would record all these revaluations in the reconciliation account, but separately identified so that analysts could combine them with actual interest payments for specific analyses.

Other experts considered that these revaluations are a mechanism of equivalent effect to more traditional interest and should be portrayed accordingly. The argument for this behavioral view essentially rests on how creditors and debtors perceive their capital gain. Recording it as interest raises disposable income and saving, although it is not actually available to the household. Do households behave as if their capital gain were interest, a capital transfer, or a revaluation?

One vital characteristic of deep-discounted bonds—and, to some extent, of index-linked securities—is that increases in the value of assets and liabilities are foreseeable, guaranteed, and known to both parties in advance and, thus, could be regarded as part of the initial contract. These gains are therefore different in nature from normal holding gains and losses arising from changes in market prices of assets, which generally do not affect the liability of the debtor.

II. The Concepts in Practice

In both the SNA and the ESA, the transaction date for interest is, as a general rule, the date on which the interest falls due. For discounts and upward revaluations of the nominal values of index-linked bonds, this means that the amounts due are accrued up to the date when the bond is redeemed.

Accrual of Discounts and Index-Linked Revaluations as Interest

Because bonds are issued in series that are often redeemed by being called (or “drawn”) as and when the borrowers pay installments, the discounts and index-linked revaluations have to be divided up over time in line with the installment schedule of the bond series. This is illustrated in Table 1, which shows Danish kroner bonds broken down by borrower sector over the period 1982–86. It can be seen from the table that the special installment schedules for government bonds led to a sharp rise in the interest element between 1982 and 1983. The considerable fluctuations in market rates of interest and bond prices during the period 1982 to 1986 had no noticeable effect on the figures shown. However, the fact that market interest rates and the specified bond interest rate move closer together toward the end of the period will lessen the impact of the distributed discount over a period of years. But because the first index-linked bonds of any importance in Denmark were not issued until 1982, the upward revaluation through indexing has not yet begun to have any significant effect on the redemption of bonds, although it will be of considerable importance in a few years' time. Whether this interest element will be of greater or lesser significance for the Danish economy in the future will depend, among other things, on the future level of inflation.3

Table 1.Discounting and Index-Linked Upward Revaluations of Danish Kroner Bonds, by Installment Periods for Borrower Sectors
Sector19821983198419851986
Billions of kroner
1.Public sector3.79.39.710.09.1
2.Private sector2.62.73.03.13.2
3.Total6.312.012.713.112.3
Percentage
4.Line 1 as a percentage of the public
sector's current expenditure
(including line 1)1323181616
5.Line 1 as a percentage of the public
sector's current expenditure13333
6.Line 3 as a percentage of GNP12222

The following paragraphs show how the overall system of accounts—from opening balance to closing balance via the distribution and use of income accounts, financial account, and revaluation account—may look when two different definitions of interest are used: actual interest payments (the market interest rate based on the date of issue) and nominal interest. Because the interest is computed according to when it falls due, the actual interest in the examples will have a different time schedule from the one it would have had with a purely mathematical computation. This last point may be illustrated by a comparison of lines 13 and 14 in Table 2.

Table 2.Illustrative Calculation of Quoted Value and Interest in Accordance with Varying Definitions over the Five-Year Term of a Serial Bond
12/3112/3112/3112/3112/3112/31
Itemt −1 = 1/1 t0t0 = 1/1t1t1 = 1/1 t2t2 = 1/1 t3t3 = 1/1 t4t4 = 1/1 t5
1. Face value1,000
2. Installments200200200200200
3. Outstanding debt1,0008006004002000
4. Nominal interest (10 percent)10080604020
5. Debt service (lines 2 +4)300280260240220
6. Market interest rate (percent)1515151515
Quoted value300280260240220
1.151.151.151.151.15
280260240220
1.1521.1521.1521.152
260240220
1.1531.1531.153
240220
1.1541.154
220
1.155
7. Total890.15723.67552.22375.05191.300
8. Price (lines [7 ÷ 3] × 100)89.0190.4692.0493.7695.70
9. Price increase
(percentage points)1.451.581.721.94
10. Mathematical adjustment of
residual holdinga11.609.486.883.88
11. Drawing profits following
mathematical price
adjustmentb21.9819.0815.9212.488.6
12. Drawing profits excluding
mathematical price
adjustment (measured in
relation to the issue date)c21.9821.9821.9821.9821.98
13. Drawing profits + nominal
interest (4 +12)d121.98101.9881.9861.9841.98
14. Mathematical price adjustment
+ drawing profits 4 +
nominal interest (4 +10 +
11)e133.58108.5682.8056.3628.60

Price increase (line 9) multiplied by outstanding debt (line 3) divided by 100.

Installments (line 2) minus installment (line 2) multiplied by the price of the bond one year before (line 8).

Installments (line 2) minus installments (line 2) multiplied by the price of the bond at date of issue (December 31, year t − 1).

Actual interest calculated on the basis of when it falls due (total for the period = 409.9).

Actual interest calculated on the basis of mathematical price adjustment (total for the period = 409.9).

Price increase (line 9) multiplied by outstanding debt (line 3) divided by 100.

Installments (line 2) minus installment (line 2) multiplied by the price of the bond one year before (line 8).

Installments (line 2) minus installments (line 2) multiplied by the price of the bond at date of issue (December 31, year t − 1).

Actual interest calculated on the basis of when it falls due (total for the period = 409.9).

Actual interest calculated on the basis of mathematical price adjustment (total for the period = 409.9).

The entries made according to the two definitions of interest are compared, assuming in the one case constant market interest rates over the period under consideration and, in the other, varying market rates. In both cases, the system of accounts is shown one and two years after a bond creditor has acquired a given, newly issued bond holding.

It is assumed in the examples that bond creditors acquire only newly issued bonds for a five-year term, on which installments are paid according to the serial loan principal. It is also assumed that the bonds are issued at an annual nominal interest rate of 10 percent and that the bond holding acquired, 1,000 units (for example, a million kroner), on date t0 is large enough for the actual calling of the bonds to correspond to the theoretical probability of their being called.

In Table 2 the market-determined quoted value (line 7) and the effect of the shortening of the term on the remaining holding (line 10) are calculated for the whole of the period for which the bond series is to run, assuming a constant market interest rate of 15 percent and disregarding risk elements in the quotation. Lines 4, 13, and 14 respectively show the nominal interest, the actual interest calculated on the basis of when it falls due (nominal interest plus drawing profits measured in relation to the issue price), and the actual interest according to the “mathematical” method (nominal interest, plus mathematical price adjustment, plus drawing profits in relation to quoted values mathematically revalued upward). Line 13 corresponds to the definition of interest used for bonds in national accounts; when compared with line 14, it can be seen that this definition results in a certain deferment of interest compared with the mathematical price adjustment system, but that both interest definitions, when totaled over the whole of the bond term, give the same absolute return: 409.9.

The figures in the accounts shown in Tables 3-6 are based on Table 2. In all of them, the accounting system is shown using the actual interest calculated on the basis of when it falls due (on the left-hand side, under main heading A) and nominal interest alone (on the right-hand side, under main heading B). All the figures are rounded, which accounts for minor discrepancies.

Table 3.Illustrative Bond Transactions for the Creditor Sector at Constant Market Rates of Interest, Year 1
A. Actual Interest
Calculation on the Basis of
ItemWhen It Falls DueB. Nominal Interest
Opening balance, year 1
AssetsAssets
NMLiabilitiesNMLiabilities
Bonds1,0008901,000890
Distribution of income account
UsesResourcesUsesResources
Nominal interest100100
Term-shortening effect (due)22
Disposable income122100
Use of income account
Disposable income122100
Consumption8282
Saving4018
Capital account
Saving4018
Investments4040
Net lending (+) or net borrowing (−)0−22
Financial account
Change inChangeChange inChange
assetsinassetsin
BondsNMliabilitiesMliabilities
Drawings−200−200−200
New purchase+200+178+178
Term-shortening effect (due) entered as income22
Net change in financial assets and liabilities00−22
Revaluation account
Bonds
At drawing+22
Residual holding+12+12
+34
BondsClosing balance, year 1
AssetsAssets
NMLiabilitiesNMLiabilities
800724800724
200178200178
1,0009021,000902
Note: N, nominal value; M., market value
Note: N, nominal value; M., market value
Table 4.Illustrative Bond Transactions for the Creditor Sector at Constant Market Rates of Interest, Year 2
A. Actual Interest
Calculation on the Basis of
ItemWhen It Falls DueB. Nominal Interest
Opening balance, year 2
AssetsAssets
NMLiabilitiesNMLiabilities
Bonds800724800724
200178200178
1,0009021,000902
Distribution of income account
InterestUsesResourcesUsesResources
8080
2020
22
Disposable income1264100
Use of income account
Disposable income126100
Consumption8282
Saving4418
Capital account
Saving4418
Investments4040
Net lending (+) or net borrowing (-)4−22
Financial account
Change inChangeChange inChange
assetsinassetsin
NMliabilitiesMliabilities
Bonds
Drawings−200−200−200
−40−40−40
New purchase+200+178+178
+40+36+36
Term-shortening effect (due) entered as income+26
Lending+4+4−4
Net change in financial assets and liabilities44−22
Revaluation account
Change inChangeChange inChange
assetsinassetsin
NMliabilitiesNMliabilities
Bonds
At drawing−319
04
Residual holding99
33
935
Closing balance, year 2
AssetsAssets
BondsNMLiabilitiesNMliabilities
600552600552
160145160145
200178200178
40364036
1,0009111,000911
Lending4444
1,0049151,004915
Note: N, nominal value; M, market value.
Note: N, nominal value; M, market value.
Table 5.Illustrative Bond Transactions for the Creditor Sector with Falling Rates of Interest, Year 1 (Beginning of year = 15 percent; end of year < 15 percent)
A. Actual interest
Calculation on the Basis of
ItemWhen It Falls DueB. Nominal Interest
Opening balance, year 1
AssetsAssets
MMLiabilitiesNMLiabilities
Bonds1,0008901,000890
Distributor: of income account
UsesResourcesUsesResources
Interest100100
22
Disposable income122100
Use of income account
Disposable income122100
Consumption8282
Saving4018
Capital account
Saving4018
Investments4040
Net lending (−) or net borrowing (+)0−22
Financial account
Change inChangeChange inChange
assetsinassetsin
NMliabilitiesNMliabilities
Bonds
Drawings−200−200−200
New purchase+200+180+180
Term-shortening effect (due) entered as income+22
Loans+2+2
Net change in financial assets and liabilities0−22
Revaluation account
Bonds+22
+20+20
42
Closing balance, year 1
AssetsAssets
BondsNMLiabilitiesNMLiabilities
800732800732
200180200180
Loans22
1,00091221,0009122
Note: N, nominal value; M, market value.
Note: N, nominal value; M, market value.
Table 6.Illustrative Bond Transactions for the Creditor Sector with Rising Rates of Interest, Year 2 (Initial rate < 15 percent; final rate = 15 percent)
A. Actual Interest Calculation
on the Basis of When It Falls
ItemDueB. Nominal Interest
Opening balance, year 2
AssetsAssets
NMLiabilitiesNMLiabilities
Bonds800732800732
200180200180
Loans22
1,00091221,0009122
Distribution of income account
UsesResourcesUsesResources
Interest8080
2020
22
4
Disposable Income126100
Note: N, nominal value; M, market value.
A. Actual Interest
Calculation on the Basis of
ItemWhen It Falls DueB. Nominal Interest
Use of income account
Disposable income126100
Consumption8282
Saving4418
Capital account
Saving4418
Investments4040
Net lending (+) or net borrowing (−)4−22
Financial account
Change inChangeChange inChange
assetsinassetsin
NMliabilitiesMliabilities
Bonds
Drawings−200−200−200
−40−40−40
New purchase+200+178−178
+40+36+36
Term-shortening effect (due) entered as income+26
Lending+4+4+4
Net change in financial assets and liabilities−4−22
Revaluation account
Bonds
At drawing−5+17
−0+4
Residual holding+3+3
+1+1
−125
Closing balance, year 2
AssetsAssets
BondsNMLiabilitiesNMLiabilities
600552600552
160145160145
200178200178
40364036
1,0009111,000911
Loans22
Lending+4+4+4+4
1,00491521,0049152
Note: N, nominal value; M, market value.
Note: N, nominal value; M, market value.

The opening and closing balances and financial account show both nominal (N) values and market (M) values in order to make it easier to understand the entries, which in national accounts are assumed to be entered at market values or the actual values of the transactions. The valuation principles in these fields have been discussed many times in connection with the revision of the SNA/ESA and will not be dealt with in this paper.

To make the layout clear, only certain transactions in the accounting system have been shown, and the values shown for interest, consumption, investments, bond transactions, and so on have not been selected as a reflection of the conditions prevailing in the economy of any particular country.

Accounting System for Actual Interest Under Constant Market Rates of Interest

Tables 3 and 4 show the accounting system under a constant market rate of interest. Table 3 shows the opening balance of a newly issued bond holding with a nominal value of 1,000, the issue (market) value of which can be calculated as 890 (compare Table 2, line 7). During the first period, bonds with a nominal value of 200 are called, resulting in a profit of 22 over the issue price, which is included under interest income in the distribution of income account. It can be seen from the financial account that new bonds are bought with the same nominal value as the drawn bonds had, and the closing balance therefore shows an unchanged holding in nominal terms. However, the market value of the bond holding has risen by 12, owing to the unrealized effect of the shortening of the term on the remaining holding (nominally 800; compare Table 2, line 10). No other revaluations are shown because it is assumed that the market rate of interest remains unchanged at 15 percent.

In the financial account, the effect of the shortening of the term4 (+22), which is posted as income, is entered as a special increase in financial assets at market value, and this figure is also included under bonds drawn at market value (−200). The term-shortening effect entered in the financial account is not intended to be an imputed figure but is an accounting device that is necessary because “drawing profits” are to be classified as both interest income and a negative change in assets.

On the right-hand side (under main heading B), it can be seen that drawing profits (measured in relation to the issue price) have to be entered as resources in the revaluation account. The financial closing balance is then shown as the sum of the opening balance, the financial account, and the revaluation account.

In period 2 (Table 4) a loss on bond holdings occurs (under main heading A) in the revaluation account (−3), corresponding to the upward revaluation at the end of the first period of the price of the bonds drawn during the second period. This is because the distributed discount, included under interest in the distribution of income account, is computed to the time of maturity as a drawing profit measured in relation to the issue price (excluding the not-due mathematical upward revaluation as a result of the shortening of the term). The market (mathematical) upward revaluation of the remaining initial holding of period 2 amounts to 9 +3, which is included in the revaluation account under both headings A and B. Under heading B, the drawing profit is also entered, measured in relation to the value of the bond holding in the opening balance (19 +4).

Lending of +4 is also shown in the financial account, since for the purpose of the illustration it was decided to restrict the reacquisition of bonds to exactly what was needed to maintain a constant, nominal bond holding. The total revaluation of 35 under heading B thus corresponds, under main heading A, to the sum of the term-shortening effect entered as income, 26, as shown in the financial account, and the total revaluation of 9.

In connection with national accounts, it is frequently the total earnings on investments, corresponding to 35 in the example, that can be seen, for example, in the accounts of the financial institutions that are most often entered as income together with the nominal interest. Since it is proposed to calculate the drawing profits entered as income in national accounts (corresponding to 26 under main heading A of Table 4), the revaluation entry (corresponding to 9 under main heading A) can be calculated as a residual when the total revaluations (corresponding to 35 under main heading B) are known.

Accounting System for Actual Interest Under Variable Market Rates of Interest

Tables 5 and 6 show the system of accounts when market rates of interest fall during the first period and rise to their initial level during the second period.

In the financial account on the left-hand side of Table 5 (under main heading A), there is a technical set-off to the drawing profits, which in this example is shown both in the distribution of income account as interest (+22) and in the financial account as part of the term-shortening effect (due) entered as income, and is exactly the same as in Table 3 under heading A. It can also be seen that, as a result of the fall in market interest rates, there has been a rise in the price of bonds, since the newly issued bonds with a nominal value of 200 were acquired at a market value of 180, whereas the initial price for the corresponding bonds was 178.

In the revaluation account, the increase in market value is entered for the part of the initial holding that has not been drawn. The market value for bonds with a nominal value of 800 increased from 712 at the start of the period to 732 at the end of the period as a result of the shortening of the term (+12) and the drop in interest rates (+8). The whole of the difference (20) is entered in the revaluation account. In Table 5 under main heading B, further drawing profits (+22) are entered in the revaluation account, since it is only the nominal interest that appears in the distribution of income account.

Under main heading A of Table 6, drawing profits (22+4) are entered as income, measured in relation to the issue price and to the price at the beginning of period 2. As in period 1, a set-off is entered in the financial account—a term-shortening effect of 126 entered as income—since the drawn bonds are assessed at transaction values (−200 −40). This means that there was an indirect discount when the bonds were drawn, which was the difference between the initial market value in period 2 of the drawn amounts and the market value upon issue (−5 − 0). These amounts are entered in the revaluation account together with the market value increase on the part of the initial bond holding that was not drawn during the course of the period. This market value increase (+3 +1) is a combination of the shortening of the term (rising prices) and rising market interest rates (falling prices).

Under main heading B of Table 6, the revaluation account has to include, in addition to the above-mentioned amounts, drawing profits measured in relation to the initial price in period 2 (+17 +4). In this case, the total revaluation remains, with nominal interest, 25, which corresponds to the sum of the balance in the revaluation account and the term-shortening effect entered as income under main heading A of Table 6 (−1 +26). This can also be expressed as the balance in the revaluation account under main heading A being equal to the revaluation under main heading B minus the term-shortening effect entered as income under main heading A.

The closing balance in Table 6 is 2 less than in Table 4 because the reacquisition of bonds at a nominal value of 200 at the close of the first period cost 180 as a result of the drop in interest rates, whereas when market interest rates were constant they cost 178. In the example shown in Table 6, the bond creditor has financed this difference by borrowing 2.

EUROSTAT, European System of Integrated Economic Accounts—ESA,2d ed. (Luxembourg, 1979).

For an excellent discussion, see “The National Accounts Treatment of Index-Linked Bonds,” in Economic Trends (London: Central Statistical Office, February 1984).

The actual procedures used in Danish national accounts for the accrual of discounts as interest are described in “How Discounting on Bonds Is Dealt with in the Danish National Accounts,” Annex to Document B1/CN/59 (Luxembourg: EUROSTAX 1984).

The “term-shortening effect” is another way of phrasing “drawing profits” (see Table 2, lines 11 and 12).

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