Tag: internal rate of return (IRR)

The UK’s poor record on productivity since the 2008 financial crisis is well documented, not least in this blog series. Output per worker has flatlined over the 17 years since the crisis. As was noted in the blog, The UK’s poor productivity record, low UK productivity is caused by a number of factors, including the lack of investment in training, the poor motivation of many workers and the feeling of being overworked, short-termism among politicians and management, and generally poor management practices.

One of the most significant issues identified by analysts and commentators is the lack of investment in physical capital, both by private companies and by the government in infrastructure. Gross fixed capital formation (a measure of investment) has been much lower in the UK compared to international competitors.

From Figure 1 it can be observed that, since the mid-1990s, the UK has consistently had lower investment as a percentage of GDP compared to other significant developed market economies. The cumulative effect of this gap has contributed to lower productivity and lower economic growth.

Interestingly, since the financial crisis, UK firms have had high profitability and associated high cash holdings. This suggests that firms have had a lot of financial resources to reinvest. However, data from the OECD suggests that reinvestment rates in the UK, typically 40–50% of profit, are much lower than in many other OECD countries. In the USA the rate is 50%, in Germany 60–70% and in Japan 70%+. There is much greater emphasis in the UK on returning funds to shareholders through dividends and share buybacks. However, the reinvestment of much of this cash within firms could have gone some way to addressing the UK’s investment gap – but, it hasn’t been done.

Analysis by the OECD suggest that, while the cost of financing investment has declined since the financial crisis, the gap between this and the hurdle rate used to appraise investments has widened. Between 2010 and 2021 the difference nearly doubled to 4%. This increase in the hurdle rate can be related to increases in the expected rate of return by UK companies and their investors.

In this blog we will analyse (re)investment decisions by firms, discussing how increases in the expected rate of return in the UK raise the hurdle rate used to appraise investments. This reduces the incentive to engage in long-term investment. We also discuss policy prescriptions to improve reinvestment rates in the UK.

Investment and the expected rate of return

Investment involves the commitment of funds today to reap rewards in the future. This includes spending on tangible and intangible resources to improve the productive capacity of firms. Firms must decide whether the commitment of funds is worthwhile. To do so, economic theory suggests that they need to consider the compensation required by their provider of finance – namely, investors.

What rewards do investors require to keep their funds invested with the firm?

When conducting investment appraisal, firms compare the estimated rate of return from an investment with the minimum return investors are prepared to receive (termed the ‘expected return’). Normally this is expressed as a percentage of the initial outlay. Firms have to offer returns to investors which are equal to or greater than the minimum expected return – the return that is sufficient to keep funds invested in the firm. Therefore, returns above this minimum expected level are termed ‘excess returns’.

When firms conduct appraisals of potential investments, be it in tangible or intangible capital, they need to take into account the fact that net benefits, expressed as cash flows, will accrue over the life of the investment, not all at once. To do this, they use discounted cash flow (DCF) analysis. This converts future values of the net benefits to their present value. This is expressed as follows:

Where:
NPV = Net present value (discounted net cash flows);
K = Capital outlay (incurred at the present time);
C = Net cash flows (occur through the life of the investment project);
r = Minimum expected rate of return.

In this scenario, the investment involves an initial cash outlay (K), followed in subsequent periods by net cash inflows each period over the life of the investment, which in this case is 25 years. All the cash flows are discounted back to the present so that they can be compared at the same point in time.

The discount rate (r) used in appraisals to determine the present value of net cash flows is determined by the minimum expected return demanded by investors. If at that hurdle rate there are positive net cash flows (+NPV), the investment is worthwhile and should be pursued. Conversely, if at that hurdle rate there are negative net cash flows (–NPV), the investment is not worthwhile and should not be pursued.

According to economic theory, if a firm cannot find any investment projects that produce a positive NPV, and therefore satisfy the minimum expected return, it should return funds to shareholders through dividends or share buybacks so that they can invest the finance more productively.

Firm-level data from the OECD suggest that UK firms have had higher profits and this has been associated with increased cash holdings. But, due to the higher hurdle rate, less investment is perceived to be viable and thus firms distribute more of their profits through dividends and share buybacks. These payouts represent lost potential investment and cumulatively produce a significant dent in the potential output of the UK economy.

Why are expected rates of return higher in the UK?

This higher minimum rate of expected return can be explained by factors influencing its determinants; opportunity cost and risk/uncertainty.

Higher opportunity cost.  Opportunity cost relates to the rate of return offered by alternatives. Investors and, by implication firms, will have to consider the rate of return offered by alternative investment opportunities. Typically, investors have focused on interest rates as a measure of opportunity cost. Higher interest rates raise the opportunity cost of an investment and increase the minimum expected rate of return (and vice versa with lower interest rates).

However, it is not interest rates that have increased the opportunity cost, and hence the minimum expected rate of return associated with investment, in the UK since the financial crisis. For most of the period since 2008, interest rates have been extremely low, sitting at below 1%, only rising significantly during the post-pandemic inflationary surge in 2022. This indicates that this source of opportunity cost for the commitment of business investment has been extremely low.

However, there may be alternative sources of opportunity cost which are pushing up the expected rate of return. UK investors are not restricted to investing in the UK and can move their funds between international markets determined by the rate of return offered. The following table illustrates the returns (in terms of percentage stock market index gain) from investing in a sample of UK, US, French and German stock markets between August 2010 and August 2025.

When expressed in sterling, returns offered by UK-listed companies are lower across the whole period and in most of the five-yearly sub-periods. Indeed, the annual equivalent rate of return (AER) for the FTSE 100 index across the whole period is less than half that of the S&P 500. The index offered a paltry annual return of 2.57% between 2015 and 2020, while the US index offered a return of 16.48%. Both the French and German indices offered higher rates of return, in the latter part of the period particularly. This represents a higher opportunity cost for UK investors and may have increased their expectations about the return they require for UK investments.

Greater perceived risk/uncertainty.  Expected rates of return are also determined by perceptions of risk and uncertainty – the compensation investors need to bear the perceived risk associated with an investment. Investors are risk averse. They demand higher expected return as compensation for higher perceived risk. Higher levels of risk aversion increase the expected rate of return and related investment hurdle rates.

There has been much discussion of increased uncertainty and risk aversion among global investors and firms (see the blogs Rising global uncertainty and its effects, World Uncertainty Index, The Chancellor’s fiscal dilemma and Investment set to fall as business is baffled by Trump). The COVID-19 pandemic, inflation shocks, the war in Ukraine, events across the Middle East and the trade policies adopted by the USA in 2025 have combined to produce a very uncertain business environment.

While these have been relatively recent factors influencing world-wide business uncertainty, perceptions of risk and uncertainty concerning the UK economy seem to be longer established. To measure policy-related economic uncertainty in the UK, Baker, Bloom and Davis at www.PolicyUncertainty.com construct an index based on the content analysis of newspaper articles mentioning terms reflecting policy uncertainty.

Figure 2 illustrates the monthly index from 1998 to July 2025. The series is normalised to standard deviation 1 prior to 2011 and then summed across papers, by month. Then, the series is normalised to mean 100 prior to 2011.

Some of the notable spikes in uncertainty in the UK since 2008 have been labelled. Beginning with the global financial crisis, investors and firms became much more uncertain. This was exacerbated by a series of economic shocks that hit the economy, one of which, the narrow vote to leave the European Union in 2016, was specific to the UK. This led to political turmoil and protracted negotiations over the terms of the trade deal after the UK left. This uncertainty has been exacerbated recently by the series of global shocks highlighted above and also the budget uncertainty of Liz Truss’s short-lived premiership and now the growing pressure to reduce government borrowing.

While spikes in uncertainty occurred before the financial crises, the average level of uncertainty, as measured by the index, has been much higher since the crisis. From 1998 to 2008, the average value was 89. Since 2008, the average value has been 163. Since the Brexit vote, the average value has been 185. This indicates a much higher perception of risk and uncertainty over the past 15 year and this translates into higher minimum expected return as compensation. Consequently, this makes many long-term investment projects less viable because of higher hurdle rates. This produces less productive investment in capital, contributing significantly to lower productivity.

Policy proposals

There has been much debate in the UK about promoting greater long-term investment. Reforms have been proposed to improve public participation in long-term investment through the stock market. To boost investment, this would require the investing public to be prepared to accept lower expected returns for a given level of risk or accept higher risk for a given level of returns.

Evidence suggests that the appetite for this may be very low. UK savers tend to favour less risky and more liquid cash deposits. It may be difficult to encourage them to accept higher levels of risk. In any case, even if they did, many may invest outside the UK where the risk-return trade-off is more favourable.

Over the past 10 years, policy uncertainty has played a significant role in deterring investment. So, if there is greater continuity, this may then promote higher levels of investment.

The Labour government has proposed policies which aim to share or reduce the risk/uncertainty around long-term investment for UK businesses. For instance, a National Wealth Fund (NWF) has been established to finance strategic investment in areas such as clean energy, gigafactories and carbon capture. Unfortunately, the Fund is financed by borrowing through financial markets and the amount expected to be committed over the life of the current Parliament is only £29 billion, assuming that private capital matches public commitments in the ratio expected. It is questionable whether the Fund’s commitment will be sufficient to attract private capital.

Alternatively, Invest 2035 is a proposal to create a stable, long-term policy environment for business investment. It aims to establish an Industrial Strategy Council for policy continuity and to tackle issues like improving infrastructure, reducing energy costs and addressing skills gaps. Unfortunately, even if there is some attempt at domestic policy stability, the benefits may be more than offset by perceptions around global uncertainty, which may mean that UK investors’ minimum expected rates of return remain high and long-term investment low for the foreseeable future.

Articles

Data

Questions

  1. Use the marginal efficiency of capital framework to illustrate the ‘lost’ investment spending in the UK due to the investment hurdle rate being higher than the cost of capital.
  2. Explain the arbitrage process which produces the differences in valuations of UK securities and foreign ones due to differences in the expected rate of return.
  3. Sketch an indifference curve for a risk-averse investor, treating expected return and risk as two characteristics of a financial instrument.
  4. How does higher uncertainty affect the slope of an indifference curve for such an investor? How does this affect their investment hurdle rate?
  5. Analyse the extent to which the proposed polices can reduce the investment hurdle rate for UK companies and encourage greater levels of investment.

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.

Articles

Information and data

Questions

  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?