Tag: discount rate

To finance budget deficits, governments have to borrow. They can borrow short-term by issuing Treasury bills, typically for 1, 3 or 6 months. These do not earn interest and hence are sold at a discount below the face value. The rate of discount depends on supply and demand and will reflect short-term market rates of interest. Alternatively, governments can borrow long-term by issuing bonds. In the UK, these government securities are known as ‘gilts’ or ‘gilt-edged securities’. In the USA they are known as ‘treasury bonds’, ‘T-bonds’ or simply ‘treasuries’. In the EU, countries separately issue bonds but the European Commission also issues bonds.

In the UK, gilts are issued by the Debt Management Office on behalf of the Treasury. Although there are index-linked gilts, the largest proportion of gilts are conventional gilts. These pay a fixed sum of money per annum per £100 of face value. This is known as the ‘coupon payment’ and the rate is set at the time of issue. The ‘coupon rate’ is the payment per annum as a percentage of the bond’s face value:

Payments are made six-monthly. Each issue also has a maturity date, at which point the bonds will be redeemed at face value. For example, a 4½% Treasury Gilt 2028 bond has a coupon rate of 4½% and thus pays £4.50 per annum (£2.25 every six months) for each £100 of face value. The issue will be redeemed in June 2028 at face value. The issue was made in June 2023 and thus represented a 5-year bond. Gilts are issued for varying lengths of time from 2 to 55 years. At present, there are 61 different conventional issues of bonds, with maturity dates varying from January 2024 to October 2073.

Bond prices

Bonds can be sold on the secondary market (i.e. the stock market) before maturity. The market price, however, is unlikely to be the coupon price (i.e. the face value). The lower the coupon rate relative to current interest rates, the less valuable the bond will be. For example, if interest rates rise, and hence new bonds pay a higher coupon rate, the market price of existing bonds paying a lower coupon rate must fall. Thus bond prices vary inversely with interest rates.

The market price also depends on how close the bonds are to maturity. The closer the maturity date, the closer the market price of the bond will be to the face value.

Bond yields: current yield

A bond’s yield is the percentage return that a person buying the bond receives. If a newly issued bond is bought at the coupon price, its yield is the coupon rate.

However, if an existing bond is bought on the secondary market (the stock market), the yield must reflect the coupon payments relative to the purchase price, not the coupon price. We can distinguish between the ‘current yield’ and the ‘yield to maturity’.

The current yield is the coupon payment as a percentage of the current market price of the bond:

Assume a bond were originally issued at 2% (its coupon rate) and thus pays £2 per annum. In the meantime, however, assume that interest rates have risen and new bonds now have a coupon rate of 4%, paying £4 per annum for each £100 invested. To persuade people to buy old bonds with a coupon rate of 2%, their market prices must fall below their face value (their coupon price). If their price halved, then they would pay £2 for every £50 of their market price and hence their current yield would be 4% (£2/£50 × 100).

Bond yields: yield to maturity (YTM)

But the current yield does not give the true yield – it is only an approximation. The true yield must take into account not just the market price but also the maturity value and the length of time to maturity (and the frequency of payments too, which we will ignore here). The closer a bond is to its maturity date, the higher/lower will be the true yield if the price is below/above the coupon price: in other words, the closer will the market price be to the coupon price for any given market rate of interest.

A more accurate measure of a bond’s yield is thus the ‘yield to maturity’ (YTM). This is the interest rate which makes the present value of all a bond’s future cash flows equal to its current price. These cash flows include all coupon payments and the payment of the face value on maturity. But future cash flows must be discounted to take into account the fact that money received in the future is worth less than money received now, since money received now could then earn interest.

The yield to maturity is the internal rate of return (IRR) of the bond. This is the discount rate which makes the present value (PV) of all the bond’s future cash flows (including the maturity payment of the coupon price) equal to its current market price. For simplicity, we assume that coupon payments are made annually. The formula is the one where the bond’s current market price is given by:

Where: t is the year; n is the number of years to maturity; YTM is the yield to maturity.

Thus if a bond paid £5 each year and had a maturity value of £100 and if current interest rates were higher than 5%, giving a yield to maturity of 8%, then the bond price would be:

In other words, with a coupon rate of 5% and a higher YTM of 8%, the bond with a face value of £100 and five years to maturity would be worth only £88.02 today.

If you know the market price of a given bond, you can work out its YTM by substituting in the above formula. The following table gives examples.

The higher the YTM, the lower the market price of a bond. Since the YTM reflects in part current rates of interest, so the higher the rate of interest, the lower the market price of any given bond. Thus bond yields vary directly with interest rates and bond prices vary inversely. You can see this clearly from the table. You can also see that market bond prices converge on the face value as the maturity date approaches.

Recent activity in bond markets

Investing in government bonds is regarded as very safe. Coupon payments are guaranteed, as is repayment of the face value on the maturity date. For this reason, many pension funds hold a lot of government bonds issued by financially trustworthy governments. But in recent months, bond prices in the secondary market have fallen substantially as interest rates have risen. For those holding existing bonds, this means that their value has fallen. For governments wishing to borrow by issuing new bonds, the cost has risen as they have to offer a higher coupon rate to attract buyers. This make it more expensive to finance government debt.

The chart shows the yield on 10-year government bonds. It is calculated using the ‘par value’ approach. This gives the coupon rate that would have to be paid for the market price of a bond to equal its face value. Clearly, as interest rates rise, a bond would have to pay a higher coupon rate for this to happen. (This, of course, is only hypothetical to give an estimate of market rates, as coupon rates are fixed at the time of a bond’s issue.)

Par values reflect both yield to maturity and also expectations of future interest rates. The higher people expect future interest rates to be, the higher must par values be to reflect this.

In the years following the financial crisis of 2007–8 and the subsequent recession, and again during the COVID pandemic, central banks cut interest rates and supported this by quantitative easing. This involved central banks buying existing bonds on the secondary market and paying for them with newly created (electronic) money. This drove up bond prices and drove down yields (as the chart shows). This helped support the policy of low interest rates. This was a boon to governments, which were able to borrow cheaply.

This has all changed. With quantitative tightening replacing quantitative easing, central banks have been engaging in asset sales, thereby driving down bond prices and driving up yields. Again, this can be seen in the chart. This has helped to support a policy of higher interest rates.

Problems of higher bond yields/lower bond prices

Although lower bond prices and higher yields have supported a tighter monetary policy, which has been used to fight inflation, this has created problems.

First, it has increased the cost of financing government debt. In 2007/8, UK public-sector net debt was £567bn (35.6% of GDP). The Office for Budget Responsibility forecasts that it will be £2702bn (103.1% of GDP in the current financial year – 2023/24). Not only, therefore, are coupon rates higher for new government borrowing, but the level of borrowing is now a much higher proportion of GDP. In 2020/21, central government debt interest payments were 1.2% of GDP; by 2022/23, they were 4.4% (excluding interest on gilts held in the Bank of England, under the Asset Purchase Facility (quantitative easing)).

In the USA, there have been similar increases in government debt and debt interest payments. Debt has increased from $9tn in 2007 to $33.6tn today. Again, with higher interest rates, debt interest as a percentage of GDP has risen: from 1.5% of GDP in 2021 to a forecast 2.5% in 2023 and 3% in 2024. What is more, 31 per cent of US government bonds will mature next year and will need refinancing – at higher coupon rates.

There is a similar picture in other developed countries. Clearly, higher interest payments leave less government revenue for other purposes, such as health and education.

Second, many pension funds, banks and other investment companies hold large quantities of bonds. As their price falls, so this reduces the value of these companies’ assets and makes it harder to finance new purchases, or payments or loans to customers. However, the fact that new bonds pay higher interest rates means that when existing bond holdings mature, the money can be reinvested at higher rates.

Third, bonds are often used by companies as collateral against which to borrow and invest in new capital. As bond prices fall, this can hamper companies’ ability to invest, which will lead to lower economic growth.

Fourth, higher bond yields divert demand away from equities (shares). With equity markets falling back or at best ceasing to rise, this erodes the value of savings in equities and may make it harder for firms to finance investment through new issues.

At the core of all these problems is inflation and budget deficits. Central banks have responded by raising interest rates. This drives up bond yields and drives down bond prices. But bond prices and yields depend not just on current interest rates, but also on expectations about future interest rates. Expectations currently are that budget deficits will be slow to fall as governments seek to support their economies post-COVID. Also expectations are that inflation, even though it is falling, is not falling as fast as originally expected – a problem that could be exacerbated if global tensions increase as a result of the ongoing war in Ukraine, the Israel/Gaza war and possible increased tensions with China concerning disputes in the China Sea and over Taiwan. Greater risks drive up bond yields as investors demand a higher interest premium.


Information and data


  1. Why do bond prices and bond yields vary inversely?
  2. How are bond yields and prices affected by expectations?
  3. Why are ‘current yield’ and ‘yield to maturity’ different?
  4. What is likely to happen to bond prices and yields in the coming months? Explain your reasoning.
  5. What constraints do bond markets place on fiscal policy?
  6. Would it be desirable for central banks to pause their policy of quantitative tightening?

Did the benefits of the London Olympics outweigh the costs? The government’s UK Trade and Industry (part of the Department of Business, Innovation & Skills) has just published a report, London 2012, Delivering the economic legacy, which itemises the economic benefits of the games one year on. It claims that benefits to date are some £9.9 billion.

This compares with costs, estimated to be somewhere between £8.9 billion and £9.3 billion, although this figure does not include certain other costs, such as maintenance of the stadium. Nevertheless, according to the figures, even after just a year, it would seem that the Games had ‘made a profit’ – just.

The £9.9 billion of benefits consist of £5.9 billion of additional sales, £2.5 billion of additional inward investment and £1.5 billion of Olympic-related high value opportunities won overseas. Most of these can be seen as monetary external benefits: in other words, monetary benefits arising from spin-offs from the Games. The ‘internal’ monetary benefits would be largely the revenues from the ticket sales.

In a separate report for the Department of Culture, Media & Sport, Report 5: Post-Games Evaluation, it has been estimated that the total net benefits (net gross value added (GVA)) from 2004 to 2020 will be between £28 billion and £41 billion.

But benefits are not confined just to internal and external monetary benefits: there are also other externalities that are non-monetary. The Culture, Media & Sport report identified a number of these non-monetary externalities. The Summary Report itemises them. They include:

• The health and social benefits of more people participating in sport
• Inspiring a generation of children and young people
• A catalyst for improved elite sporting performance in the UK
• Setting new standards for sustainability
• Improved attitudes to disability and new opportunities for disabled people to participate in society
• Greater social cohesion as communities across the UK engaged with the Games
• Increased enthusiasm for volunteering
• Accelerated physical transformation of East London
• Beneficial socio-economic change in East London
• Important lessons learned for the co-ordination and delivery of other large-scale public and public/private projects

But with any cost–benefit analysis there are important caveats in interpreting the figures. First there may be monetary and non-monetary external costs. For example, will all the effects on social attitudes be positive? Might greater competitiveness in sport generate less tolerance towards non sporty people? Might people expect disabled people to do more than they are able (see)? Second, the costs generally precede the benefits. This then raises the question of what is the appropriate discount rate to reduce future benefits to a present value.

Perhaps the most serious question is that of the quantification of benefits. It is important that only benefits that can be attributed to the Games are counted and not benefits that would have occurred anyway, even if connected to the Games. For example, it is claimed in the UK Trade & Industry report that much of the Olympic park and stadium for the Winter Olympics in Russia was “designed and built by British businesses”. But was this the direct result of the London Olympics, or would this have happened anyway?

Another example is that any inward investment by any company that attended the London Olympics is counted in the £2.5 billion of additional inward investment (part of the £9.9 billion). As the London Evening Standard article below states:

In London, it credited the Games with helping seal the deal for the £1.2 billion investment in the Royal Albert Docks by Chinese developer ABP, the £1 billion investment in Croydon by Australian shopping centre developer Westfield with UK firm Hammerson and the £700 million investment in Battersea Nine Elms by Dalian Wander Group.

It is highly likely that some or all of these would have gone ahead anyway.

Then there are the £5.9 billion of additional sales. These are by companies which engaged with the Olympics. But again, many of these sales could have taken place anyway, or may have displaced other sales.

Many cost–benefit analyses (or simply ‘benefit analyses’) concern projects where there are strong vested interests in demonstrating that a project should or should not go ahead or, in this case, have gone ahead. The more powerful the vested interests, the less likely it is that the analysis can be seen as objective.

Webcasts and Podcasts

Have Olympics and Paralympics really boosted trade? Channel 4 News, Jackie Long (19/7/13)
Economy boosted by Olympics Sky Sports News, Amy Lewis (19/7/13)
Olympic investment boost to last decade – Cable BBC News (19/7/13)
Did the UK gain from the Olympics? BBC Today Programme (19/7/13)


Government announces almost £10bn economic boost from London 2012 Specification Online (19/7/13)
Olympic Legacy Boosted Economy By £10bn, Government Insists The Huffington Post (19/7/13)
Olympics are delivering economic gold but volunteering legacy is at risk The Telegraph, Tim Ross (19/7/13)
Vince Cable: Case for HS2 still being made The Telegraph, Christopher Hope and Tim Ross (19/7/13)
Olympic legacy ‘gave London a £4bn windfall’ London Evening Standard, Nicholas Cecil and Matthew Beard (19/7/13)
London 2012 Olympics ‘have boosted UK economy by £9.9bn’ BBC News (19/7/13)
The great Olympic stimulus BBC News, Stephanie Flanders (19/7/13)
London Olympics still costing the taxpayer one year on Sky Sports (19/7/13)
Mayor missed long-term London Olympic jobs targets, says report BBC News, Tim Donovan (19/7/13)
Olympics legacy: Have the London 2012 Games helped Team GB develop a winning habit? Independent, Robin Scott-Elliot (19/7/13)
London 2012 added up to more than pounds and pence The Guardian, Zoe Williams (19/7/13)

Government Reports

London 2012 – Delivering the economic legacy UK Trade & Investment (19/7/13)
London 2012: Delivering the economic legacy UK Trade & Investment (19/7/13)
Report 5: Post-Games Evaluation: Summary Report Department for Culture, Media & Sport (July 2013)
Report 5: Post-Games Evaluation: Economy Evidence Base Department for Culture, Media & Sport (July 2013)


  1. Distinguish between gross and net benefits; monetary and non-monetary externalities; direct costs (or benefits) and external costs (or benefits).
  2. How should the discount rate be chosen for a cost–benefit analysis?
  3. Give some examples of monetary and non-monetary external costs of the Games.
  4. What are the arguments for and against including non-monetary externalities in a cost–benefit analysis?
  5. Why might the £9.9 billion figure for the monetary benefits of the Games up to the present time be questioned?