**Summary**

- A UK state pension is paid for life.
- The pension can be deferred in exchange for a higher pension later or for a lump sum.
- Any decision needs to take into account your time preference for money, your tax profile, and your life expectancy.
- I carried out some modelling for myself and have shared that for educational purposes only.
- My spreadsheet model cannot be relied upon by anyone else and you must do your own calculations for yourself.

Posted 18 July 2015. Risk of death sub-section added 22 July 2015.

I have been looking at this question and have decided to share my thoughts.

For almost all financial questions, building a numerical model helps to think about the problem since few of us have an intuitive insight into the calculations. I always find it helpful for important financial decisions. Accordingly it is worth looking at the methodology, even if the specific question is not immediately relevant to you.

You don't need a large amount of savings or other income to be able to defer your state pension. At its simplest, if your savings exceed one year of state pension, you could spend that year running down your savings and then have a higher state pension for the rest of your life.

Every page of my website contains a disclaimer in the footer. That disclaimer is particularly apposite for a page like this one, which readers may take as constituting advice. The sole purpose of this page is to educate readers about the issues; they then need to consider their own circumstances, prepare their own calculations and reach their own decisions.

For obvious reasons, I will not respond to any comments about readers' individual circumstances.

Lower down I have made available the spreadsheet I prepared when considering the issue for myself. I am acutely aware of how frequently my spreadsheets contain errors, and accept no responsibility for any use of the spreadsheet. If you wish to do calculations, I recommend preparing your own spreadsheet from scratch; mine may help you to understand some of the calculation issues and no other reliance should be placed upon it.

A UK resident male born roughly when I was is entitled to take his state pension on his 65^{th} birthday. I was vaguely aware that you could defer taking your state pension in exchange for a larger pension starting later, but had not looked at the rules. However my eye was caught by an article in the paper issue of "Investors Chronicle" in June.

While I no longer have that issue, the Investors Chronicle website contains the article by Moira O'Neill dated 18 June 2015 "Defer state pension for an extra £40,300." It begins:

"Until April 2016, pensioners who delay taking their state pension get a generous 10.4 per cent boost to state pension for every year deferred. So you only have to live for 9 years to benefit from the decision."

When I read the article I found it intriguing, but felt dissatisfied because the calculations in the article took no account of the time value of money. In other words, they assume that if you gain £1.01 in 15 years time by giving up £1 today, you are 1p better off.

In reality most of us would consider ourselves worse off, because we regard £1 today as being more valuable than £1 in the future. Just how much more valuable is determined by our individual time preference, expressed as a discount rate.

While writing this page, I came across the article "Deferring a state pension – is it worthwhile?" by John Dagpunar which was published in the magazine "Significance: statistics making sense." As you would expect from a statistician, it seems to model very well the statistical risks of dying.

However as a financial article I find it wholly unsatisfactory, as it ignores the time value of money.

The Department for Work and Pensions sets out the basic rules and also publishes a 60 page booklet "Deferring your state pension." Very briefly if you defer one year of state pension, then you can choose:

- either to have the state pension for the remainder of your life as being 10.4% higher than it otherwise would have been. (This percentage is due to reduce for deferrals after April 2016.) OR
- you can receive the deferred pension as a lump sum with interest at 2% over Bank of England rate, with your pension in future years being the same as it would have been, without the 10.4% increase.

I was particularly interested in (1) and decided to do some calculations.

There are two key variables:

- How long will I live? While actuarial tables give population averages, I may be healthier and live longer, or I might die tomorrow of natural or accidental causes.
- My personal discount rate.

Less important is the number of years that you choose to defer, since the principles are the same whether you are deferring one year or three.

I wanted to construct a calculation that I could flex for both of those factors. I am sharing the spreadsheet I constructed for my own use. The following comments about the spreadsheet may help you when building your own spreadsheet if you want to do similar calculations:

It is vital to separate input variables (cells A3 - A8 coloured yellow) from calculations so that you don't mess up any formulae when looking at alternative assumptions about the variables. It also avoids "hard-wiring" numerical assumptions into the calculations, assumptions that you might want to change later.

My time preference of money is taken into account by discounting all future cash flows to their net present value by using a discount rate which is specified in cell A6 where it can easily be varied.

Excel has a built-in NPV formula. However that was not suitable for doing the calculations because I wanted to be able to flex the number of years I might live, and the numbers of years I wanted to defer. Instead I used algebra.

Cell C13 computes the NPV of a state pension with no deferral which lasts for the number of years set in cell A7 and grows each year by the growth rate specified in cell A5. There is an algebraic formula for the sum of a geometric progression, which is what I used.

I wanted to be able to compare it with the built-in Excel NPV function where the first cash flow takes place at the end of period 1, whereas the basic algebraic formula assumes that you include the initial value. Hence the formula subtracts A3 at the end.

All of the references are made absolute. Hence the $ signs as in $A$3. That means that if you copy the formula in the cell and paste it elsehere, it still points to cell A3, instead of being updated to the new location. This makes it easier to copy the formula for use elsewhere on the spreadsheet.

=+$A$3*(1-((1+$A$5)/(1+$A$6))^($A$7+1))/(1-((1+$A$5)/(1+$A$6)))-$A$3

I wanted to test that my algebra gave the same answers as Excel's built in net present value formula and that is done on the tab called "Checks."

This is computed in two stages in cells C17 and C18. I compute the NPV of a higher pension as if there were no deferred years, and then deduct the NPV of the deferred years at that higher pension rate. I wanted to check this formula as well, which is done on the tab called "Checks."

You have to form your own view. I recommend modelling for alternative life expectancies, as I have done. As a general point, people do tend to underestimate their life expectancy.

The Office for National Statistics publishes a number of tables of information on life expectancies in the United Kingdom.

Because life expectancy is so important in these calculations, both data tables treat it as a variable.

To make the calculations more realistic, I have assumed the the government will uplift all pensions each year, and used 2.5% p.a. However that can be flexed by changing cell A5.

The calculations ignore tax. If your tax rate will be the same throughout your life, the base pension amount (here assumed to be £7,000 p.a. but capable of being flexed by changing cell A3) should just be reduced to the post tax amount to get a post tax net present value. However if your tax rate is expected to vary during your life, you need to do more complex calculations.

Excel has a built in facility for doing "what if" calculations, which saves having to do repeated changes of the input variables yourself. You can decide upon either one key variable or two key variables, and construct a "data table".

The spreadsheet has two data tables, each of which has two key variables.

- Data table 1 looks at varying life expectancy and varying the number of years of pension deferred.
- Data table 2 looks at varying life expectancy and varying the personal discount rate. I find this table the more interesting of the two.

For me the most important point is the impact of the personal discount rate.

If you ignore the time value of money, by making putting zero in cell A6, and live a long time, you can make enormous gains by deferring several years of pension. The most extreme cell of Table 1, where you live for 40 years after retiring (until age 105) after deferring 10 years of pension, shows you £338,974 better off.

However if you change the personal discount rate in cell A6 to 7%, deferring 10 years of pension and living to age 105 only makes you £22,483 better off.

I decided not to defer any part of my pension. I estimate my personal discount rate conservatively at 7% p.a. That number comes from my expectation of the likely nominal return from investment in equities. Every £1 of pension I defer means at the margin taking £1 out of my portfolio to spend in substitution, so I think it is appropriate to use my expected return on equities as the discount rate.

With a 7% discount rate the savings from deferring the pension are either negative for shorter life expectancies, or relatively small even for longer life expectancies. I see no point in taking the risk.

While the spreadsheet computes the NPV for any particular level of future life, number of years deferred and personal discount rate, it leaves it to the user to decide the implications of the risk of death. In my view there are two basic ways of taking that into account.

- Increase the personal discount rate. Since a higher discount rate increases the weight you put on money near in time compared with further in the future, it is a way of recognising the risk that you might not live long enough to receive those future pension payments. Quite apart from your investment alternatives (the only reason I gave above for using 7%) this is another reason for using a higher discount rate rather than a lower one.
- The alternative, not used on my spreadsheet, would be to reduce future pension payments by weighting them for the probability of receiving them. Underlying the life expectancy tables are probabilities so that for a person aged 65 one can say that, on average, he has an A% probability of dying before age 66, B% of dying before 67 etc. The values A, B, C etc. would start small and gradually rise. That allows you to weight each year's pension for the likelihood of receiving it, since the probability of receiving the first year's pension would be (100-A)%, the second year's pension (100-B)% etc. If you do this, you do not need to increase the personal discount rate for the risk of dying, since the risk of dying is then directly reflected in the cash flows. I did not do this calculation because I don't have the year by year percentages to hand, and didn't see the need spending time finding them since the basic calculations made deferral unexciting just with a 7% discount rate.

I did not do any calculations on this. With Bank of England rate of 0.5% p.a., deferring to earn 2.5% p.a. is wholly unattractive with a personal discount rate of 7% p.a.

That is even before you consider the risk of premature sudden death causing the deferred amount to be lost.

If you are about to take your state pension, or indeed if you are already taking it, you should at least consider whether to defer any of it. The above discussion may help your thinking process.

However you need to take into account your own likely future tax profile, your own time preference for money, your own thoughts about your life expectancy and your own attitude to the risk of premature death. Furthermore you should do your own independent calculations, since my spreadsheet was devised only for my own use and cannot be relied upon to be accurate.

Follow @Mohammed_Amin