Chapter

Annex 3: Debt Securities: Reconciling Market Value with Nominal Value

Author(s):
International Monetary Fund
Published Date:
November 2009
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A3.1 Annex 3 illustrates the relationship between market value and nominal value for positions in debt securities and the recording of the accrual and payment of interest for different types of debt securities, namely (i) a fixed interest rate bond issued at par; (ii) a fixed interest rate bond issued at a discount; (iii) a zero-coupon bond; and (iv) two types of index-linked bonds.

Market value and nominal value

A3.2 Market valuation is the key principle adopted by international statistical standards (2008 SNA 2.59 and BPM6 8.12) for valuing transactions and positions in debt securities. As described in paragraphs 5.19 and 5.20 of the Handbook, the market value is that at which debt securities are acquired or disposed of, between willing parties, on the basis of commercial considerations only, excluding commissions, fees and taxes. In determining market values, trading parties also take account of accrued interest.

A3.3 Nominal valuation of debt securities reflects the sum of funds originally advanced, plus any subsequent advances, less any repayments, plus any accrued interest.48,49 Nominal value is often mistakenly considered to be the same as face value. The Handbook does not recommend the presentation of debt securities at face value, but rather the use of nominal and, in particular, market value.

A3.4 At any specific point in time, the market value of a debt security may deviate from its nominal value due to revaluations arising from market price changes. Movements in market prices arise from general market conditions, such as changes in the market rate of interest;50 specific circumstances, such as changes in the perceived creditworthiness of the issuer; and changes in general market liquidity and in that specific to the debt security.

A3.5 Thus, the following basic equation applies to positions in debt securities:

(i) A fixed interest rate bond issued at par

A3.6 A fixed interest rate bond issued at par (1,000) at the beginning of the first year is repayable at maturity in five years and pays fixed coupons of 100 at the end of each year of its life. Interest accrues on the bond throughout the year and is recorded as being reinvested in the bond, increasing its nominal value from 1,000 to 1,100 at the end of the year, before the coupon is paid. Coupon payments on the existing fixed interest rate bond will not change, although the current market interest rate may change.

A3.7 At issue, the nominal value and the market value are both equal to 1,000. At the end of each year, interest of 100 has accrued and is paid by the bond issuer to the bond holder. The coupon payment of 100 by the debtor at the end of the year is treated as a (partial) redemption of the bond, reducing its nominal value from 1,100 to 1,000.

A3.8 To illustrate the relationship between market value and nominal value and the recording of the flows associated with each of them, Table A3.1 presents (a) the stocks and flows (transactions and revaluations) for the first year of the life of the bond, at the end of each quarter; (b) the market value and related flows during the first year of the life of the bond; and (c) the annual stocks and flows during the life of the bond.

Table A3.1A fixed interest rate bond issued at par

Issue price: 1,000; annual coupon payments: 100; original maturity: 5 years; redemption price: 1,000.

a. Stocks and flows for the first year of the life of the bond

1-Jan.31-Mar.30-June30-Sep.31-Dec.
Nominal value
before coupon payment1,000.01,024.11,048.81,074.11,100.0
after coupon payment at year-end1,000.0
Accrued interest24.148.874.1100.0
Coupon payment–100.0
Market value1,000.0963.41,081.21,175.7969.0
Revaluations arising from market price changes (cumulative)–60.732.4101.6–31.0

b. Market value and its changes during the first year of the life of the bond

Market value at beginning of year1,000.0
Transactions
Accrued interest100.0
Coupon payment–100.0
Revaluations arising from market price changes–31.0
Market value at year-end969.0

c. Stocks and flows during the life of the bond

Start

year 1
End

year 1
End

year 2
End

year 3
End

year 4
End

year 5
Nominal value
before coupon payment1,000.01,100.01,100.01,100.01,100.01,100.0
after coupon payment at year-end1,000.01,000.01,000.01,000.01,000.0
Accrued interest100.0100.0100.0100.0100.0
Coupon payment–100.0–100.0–100.0–100.0–100.0
Market value1,000.0969.01,025.31,054.2982.11,000.0
Revaluations arising from market price changes–31.025.354.2–17.90.0

(ii) A fixed interest rate bond issued below par

A3.9 In this second example, a five-year fixed interest rate bond repayable at maturity is issued at a discount (below par, at 900) and pays annual fixed coupons of 73.6 during its life, which, because of the discount, correspond to a 10% rate of interest. The bond accrues annually two types of interest: (a) a coupon of 73.6; and (b) an annual discount, which is calculated as 19.2 for the first year. At the end of the first year, interest of 92.8 has accrued, but only 73.6 of this accrued interest is paid to the bond holder. This reduces the principal amount outstanding, in nominal value terms, from 992.8 to 919.2. The accrued discount of 100 is only paid at the end of the fifth year as part of the redemption price.

A3.10 As in the previous example, Table A3.2 presents (a) the stocks and flows for the first year of the life of the bond; (b) the market value and related flows during the first year of the life of the bond; and (c) the annual stocks and flows during the life of the bond.

Table A3.2A fixed interest rate bond issued at discount

Issue price: 900; annual coupon payments: 73.6; discount payment at redemption; original maturity: 5 years; redemption price: 1,000.

a. Stocks and flows for the first year of the life of the bond

1-Jan.31-Mar.30-June30-Sep.31-Dec.
Nominal value
before coupon payment900.0922.7945.7969.1992.8
after coupon payment at year–end919.2
Accrued interest
due to coupon17.936.254.773.6
due to discount4.89.514.319.2
Coupon payment–73.6
Market value900.0864.7974.81,062.9887.1
Revaluations arising from market price changes (cumulative)–58.029.193.8–32.1

b. Market value and its changes during the first year of the life of the bond

Market value at beginning of year900.0
Transactions
Accrued interest due to coupon73.6
Accrued interest due to discount19.2
Coupon payment–73.6
Revaluations arising from market price changes–32.1
Market value at year-end887.1

c. Stocks and flows during the life of the bond

Start

year 1
End

year 1
End

year 2
End

year 3
End

year 4
End

year 5
Nominal value
before coupon payment900.0992.81,012.41,032.41,052.81,073.6
after coupon payment919.2938.7958.7979.11,000.0
Accrued interest
due to coupon73.673.673.673.673.6
due to discount19.238.758.779.1100.0
Coupon payment–73.6–73.6–73.6–73.6–73.6
Market value900.0887.1958.51,006.5958.61,000.0
Revaluations arising from market price changes–32.119.847.8–20.50.0

(iii) A zero-coupon bond

A3.11 In the third example, a zero-coupon bond is issued which, by definition, pays no coupons during its life. The bond has a redemption price of 1,000 and an issue price of 620.9. The latter is the present value as at issuance of the final payment at the end of the fifth year, when discounted (on an annual basis) at the current market interest rate of 10%.

A3.12 The only transactions to be recorded for this kind of bond, after its issuance, are the accruing of the discount throughout its life and the payment of the principal at maturity. Changes in market interest rates will affect the bond’s market value in the same direction as in the previous two cases, but with amplified effects owing to the longer duration of the bond.

A3.13 Table A3.3 presents (a) the stocks and flows for the first year of the life of the bond; (b) the market value and related flows during the first year of the life of the bond; and (c) the annual stocks and flows during the life of the bond. At the end of the life of the bond, a transaction of 1,000 is recorded, corresponding to the repayment of 620.9 of principal and the payment of 379.1 of accrued interest.

Table A3.3A zero-coupon bond

Issue price: 620.9; implicit rate of return: 10% per annum; original maturity: 5 years; redemption price: 1,000

a. Stocks and flows for the first year of the life of the bond

1-Jan.31-Mar.30-June30-Sep.31-Dec.
Nominal value620.9635.9651.2666.9683.0
Accrued interest due to discount15.030.346.062.1
Market value620.9588.4676.6746.8658.7
Revaluations arising from market price changes (cumulative)–47.525.479.9–24.3

b. Market value and its changes during the first year of the life of the bond

Market value at beginning of year620.9
Transactions
Accrued interest due to discount62.1
Coupon payment0.0
Revaluations arising from market price changes−24.3
Market value at year-end658.7

c. Stocks and flows during the life of the bond

Start

year 1
End

year 1
End

year 2
End

year 3
End

year 4
End

year 5
Nominal value620.9683.0751.3826.4909.11,000.0
Accrued interest due to discount62.1130.4205.5288.2379.1
Market value620.9658.7772.2873.4892.91,000.0
Revaluations arising from market price changes–24.320.947.0–16.20.0

(iv) Index-linked bonds

(a) Linked to the consumer price index

A3.14 In the fourth example, an index-linked bond, repayable at maturity in five years, with annual coupon payments of 50 (5%) on a principal of 1,000, is indexed to the consumer price index (CPI). The inflation expected over the life of the bond is assumed to be the inflation observed during the last 12 months. Changes in the CPI will affect the market value of the security through changes in its expected redemption price, discounted at the current market interest rate. The same market interest rate and market conditions as in the previous three examples apply to the case of this index-linked bond. At the time of issuance the increase in the CPI during the previous 12 months is 5.5%. The bond is issued at par, with nominal value and market value equal to 1,000.

A3.15 Table A3.4 presents (a) the stocks and flows for the first year of the life of the bond; (b) the market value and related flows during the first year of the life of the bond; and (c) the annual stocks and flows during the life of the bond. As can be seen in this table, the nominal value of the bond increases pari passu with observed inflation, while its market value also reflects expected inflation and displays the same inverse relationship with the market interest rate as in the other examples. As the bond is linked to a broad index, changes in the value of the bond due to indexation are recorded as accrued interest, i.e. as a transaction and not as a revaluation, while changes in its market value are recorded as revaluations.

Table A3.4A bond indexed to the CPI

Issue price: 1,000; annual coupon payments: 50; original maturity: 5 years; redemption price: 1,000; indexed to the CPI.

a. Stocks and flows for the first year of the life of the bond

1-Jan.31-Mar.30-June30-Sep.31-Dec.
Nominal value
before coupon payment1,000.01,022.11,047.01,082.01,120.0
after coupon payment at year-end1,070.0
Accrued interest
due to coupon12.324.737.350.0
due to indexation9.922.344.770.0
Coupon payment–50.0
Market value1,000.0880.81,024.21203.51,079.1
Revaluations arising from market price changes (cumulative)–141.3–22.8121.59.1
CPI (12-month change, %)5.54.04.56.07.0
CPI (index)100.0101.0102.2104.5107.0

b. Market value and its changes during the first year of the life of the bond

Market value at beginning of year1,000.0
Transactions
Accrued interest due to coupon50.0
Accrued interest due to indexation70.0
Coupon payment−50.0
Revaluations arising from market price changes9.1
Market value at year-end1,079.1

c. Stocks and flows during the life of the bond

Start

year 1
End

year 1
End

year 2
End

year 3
End

year 4
End

year 5
Nominal value
before coupon payment1,000.01,120.01,184.21,240.91,294.51,344.3
after coupon payment1,070.01,134.21,190.91,244.51,294.3
Accrued interest
due to coupon50.050.050.050.050.0
due to indexation70.0134.2190.9244.5294.3
Coupon payment–50.0–50.0–50.0–50.0–50.0
Market value1,000.01,079.11,169.71,237.31,205.81,294.3
Revaluations arising from market price changes (cumulative)9.135.546.4–38.70.0
CPI (12-month change, %)5.57.06.05.04.54.0
CPI (index)100.0107.0113.4119.1124.5129.4

(b) Linked to the gold price

3.16 The final example is a five-year bond paying an annual coupon of 100 (10%) on a principal of 1,000, which is indexed to the gold price. The expected redemption price is assumed to reflect the prevailing market price of gold. Changes in the gold price will affect the market value of the security via changes in the expected redemption price of the security, discounted at the prevailing market interest rate. The same market interest rate and market conditions as in the previous four examples apply to this index-linked bond. At the time of issuance the gold price in national currency is 1,000 per troy ounce. The bond is issued at par with nominal value and market value equal to 1,000.

3.17 Table A3.5 presents (a) the stocks and flows for the first year of the life of the bond; (b) the market value and related flows during the first year of the life of the bond; and (c) the annual stocks and flows during the life of the bond. The nominal value of the bond reflects changes in the gold price and also the accrual of interest. The market value of the bond also reflects changes in the gold price and the accrual of interest. In addition, the market value, as in the other cases, is inversely related to the market interest rate. As in the other examples in this annex, the difference between the nominal value and the market value stems from revaluations arising from market price changes. As the bond is linked to a narrow index, changes in the value of the bond due to changes in the gold price are recorded as revaluations and not as transactions.

Table A3.5A bond indexed to the gold price

Issue price: 1,000; annual coupon payments: 100; original maturity: 5 years; redemption price: 1,000, indexed to the gold price.

a. Stocks and flows for the first year of the life of the bond

1-Jan.31-Mar.30-June30-Sep.31-Dec.
Nominal value
before coupon payment1,000.0974.1948.8924.1900.0
after coupon payment at year-end800.0
Accrued interest24.148.874.1100.0
Coupon payment–100.0
Market value1,000.0931.61,010.41,061.3837.2
Revaluations (cumulative)
arising from changes in gold price–50.0–100.0–150.0–200.0
arising from market price changes–42.561.6137.237.2
Gold price (national currency per troy ounce)1000.0950.0900.0850.0800.0

b. Market value and its changes during the first year of the life of the bond

Market value at beginning of year1,000.0
Transactions
Accrued interest due to coupon100.0
Coupon payment–100.0
Revaluations–162.8
arising from changes in gold price–200.0
arising from market price changes37.2
Market value at year-end837.2

c. Stocks and flows during the life of the bond

Start

year 1
End

year 1
End

year 2
End

year 3
End

year 4
End

year 5
Nominal value
before coupon payment1,000.0900.01,050.01,100.01,150.01,200.0
after coupon payment800.0950.01,000.01,050.01,100.0
Accrued interest100.0100.0100.0100.0100.0
Coupon payment;–100.0–100.0–100.0–100.0–100.0
Market value1,000.0837.2986.71,054.21,026.81,100.0
Revaluations (cumulative)
arising from changes in gold price–200.0–50.00.050.0100.0
arising from market price changes37.236.754.2–23.20.0
Gold price (national currency per troy ounce)1,000.0800.0950.01,000.01,050.01,100.0

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