Chapter

Annex 1. Comparing Market Value and Nominal Value for Debt Securities

Author(s):
Jose Cartas, and Qi He
Published Date:
June 2015
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A1.1Annex 1 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 security, namely (1) a fixed interest rate bond issued at par; (2) a fixed interest rate bond issued at a discount; (3) a zero-coupon bond; and (4) two types of index-linked bond.

Market Value and Nominal Value

A1.2Market valuation is the key principle adopted by the 2008 SNA for valuing transactions and positions in debt securities. 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 value, trading parties also take account of accrued interest.

A1.3Nominal valuation of debt securities reflects the sum of funds originally advanced, plus any subsequent advances, less any repayments, plus any accrued interest.

A1.4 At any specific point in time, the market value of a debt security may deviate from its nominal value owing to revaluations arising from market price changes. Movements in market prices arise from general market conditions, such as changes in the market interest rate; or specific circumstances, such as changes in the perceived creditworthiness of the issuer. For the following examples, it is assumed that all valuation changes are due to changes in the market interest rate, or in the prices of the underlying assets to which the bonds are linked.

A1.5 Thus, the following basic equation applies to positions in debt securities: Market value = Nominal value + Cumulative revaluations arising from market price changes.

A Fixed Interest Rate Bond Issued at Par

A1.6 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.

A1.7 At issue, the nominal value and the market value are both equal to 1,000, implying the market yield to be 10 percent. At the end of each year, interest of 100 has accrued and is paid by the bond issuer to the bondholder. The coupon payment of 100 by the debtor at the end of the year is treated as (partial) redemption of the bond, reducing its nominal value from 1,100 to 1,000.

A1.8 To illustrate the relationship between market value and nominal value and the recording of the flows associated with each of them, Table A.1.1 presents the annual stocks and flows during the life of the bond.

Table A.1.1-A Fixed Interest Rate Bond Issued at ParIssue price: 1,000; annual coupon payments: 100; original maturity: 5 years; redemption price: 1,000. Stocks and flows during the life of the bond
Start year 1End year 1End year 2End year 3End year 4End year 5
Nominal value at year-end
before coupon payment1,000.01,100.01,100.01,100.01,100.01,100.0
after coupon payment1,000.01,000.01,000.01,000.01,000.0
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
Interest rate (per annum)10.011.09.07.012.08.0
Cumulative revaluations arising from market price changes−31.025.354.2−17.90.0

A Fixed Interest Rate Bond Issued Below Par

A1.9 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 percent rate of interest. This discount bond accrues interest on its nominal value of 10 percent, which is the market interest rate at the time of issuance. Part of the accrued interest (73.6) is paid to the bondholders as coupon at the end of each year, with the difference increasing the nominal value of the bond. At the end of the fifth year, the accrued interest due to the discount will add up to 100 and will be paid as part of the redemption price.

A1.10 As in the previous example, Table A.1.2 presents the annual stocks and flows during the life of the bond.

Table A.1.2A Fixed Interest Rate Bond Issued at DiscountIssue price: 900; annual coupon payments: 73.6; discount payment at redemption; original maturity: 5 years; redemption price: 1,000. Stocks and flows during the life of the bond
Start year 1End year 1End year 2End year 3End year 4End year 5
Nominal value at year-end
before coupon payment900.0990.01,008.01,027.81,049.61,073.6
after coupon payment916.4934.4954.2976.01,000.0
Accrued interest90.091.693.495.497.6
Due to coupon73.673.673.673.673.6
Due to discount16.434.454.276.0100.0
Coupon payment−73.6−73.6−73.6−73.6−73.6
Market value900.0887.1958.51,006.5958.61,000.0
Interest rate (per annum)10.011.09.07.012.08.0
Cumulative revaluations arising from market price changes−29.224.152.3−17.40.0

A Zero-coupon Bond

A1.11 In the third example, a zero-coupon bond which, by definition, pays no coupons during its life, is issued at a redemption price of 1,000, with an issue price of 620.9. The latter is the present value 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 percent.

A1.12 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 examples, but with amplified effects owing to the longer duration of the bond.

A1.13Table A.1.3 presents 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 A.1.3A Zero-coupon BondIssue price: 620.9; implicit rate of return: 10 percent per annum; original maturity: 5 years; redemption price: 1,000. Stocks and flows during the life of the bond
Start year 1End year 1End year 2End year 3End year 4End year 5
Nominal value at year-end620.9683.0751.3826.4909.11,000.0
Accrued interest due to discount62.1130.4205.5289.2379.1
Market value620.9658.7772.2873.4892.91,000.0
Interest rate (per annum)10.011.09.07.012.08.0
Cumulative revaluations arising from market price changes−24.320.947.0−16.20.0

Index-linked Bonds

Linked to the Consumer Price Index

A1.14 In the fourth example, an index-linked bond, repayable at maturity in five years, with annual coupon payments of 50 (five percent) 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 was 5.5 percent. The bond is issued at par, with nominal value and market value equal to 1,000.

A1.15Table A.1.4 presents 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 attributable to indexation are recorded as accrued interest, that is, as a transaction and not as a revaluation, while changes in its market value are recorded as revaluations.

Table A.1.4A Bond Indexed to the Consumer Price IndexIssue price: 1,000; annual coupon payments: 50; original maturity: 5 years; redemption price: 1,000; indexed to the CPI. Stocks and flows during the life of the bond
Start year 1End year 1End year 2End year 3End year 4End year 5
Nominal value at year-end
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 interest120.0184.2240.9294.5344.3
due to coupon50.050.050.050.050.0
due to indexation70.0134.2190.9244.5294.3
Coupon Payment5050505050
Market value1,000.01,079.11,169.71,237.31,205.81,294.3
Interest rate (per annum)10.011.09.07.012.08.0
CPI (12-month changes, percentages)5.57.06.05.04.54.0
CPI (index with year 1 as the base year)100.0107.0113.4119.1124.5129.4
Cumulative revaluations arising from market price changes9.135.546.3−38.70.0

Linked to the Gold Price

A1.16 The final example is a five-year bond paying an annual coupon of 100 (10 percent) 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 domestic currency is 1,000 per troy ounce. The bond is issued at par with nominal value and market value equal to 1,000.

A1.17Table A.1.5 presents the annual stocks and flows during the life of the bond. The nominal value of the bond reflects changes in the gold price and the accrual of interest. The market value of the bond reflects changes in the gold price and also the accrual of interest. In addition, the market value, as in the other examples, is inversely related to the market interest rate. 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 attributable to changes in the gold price are recorded as revaluations and not as transactions.

Table A.1.5A Bond Indexed to the Gold PriceIssue price: 1,000; annual coupon payments: 100; original maturity: 5 years; redemption price: 1,000, indexed to the gold price Stocks and flows during the life of the bond
Start year 1End year 1End year 2End year 3End year 4End year 5
Nominal value at year-end
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
Interest rate (per annum)10.011.09.07.012.08.0
Gold price (domestic currency per troy ounce)1,000.0800.0950.01,000.01,050.01,100.0
Cumulative revaluations
arising from gold price changes−200.0−50.00.050.0100.0
arising from market price changes37.236.754.2−23.20.0

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