When will interest rates go up? That's the question lots of people seem to be asking these days. The Bank of England has kept its base rate (the interest rate it charges to lend to other banks) at 0.5% for over 6 years. Some people think that having stayed so low for so long that it will have to go up sooner or later.

I've no idea what will happen. For all I know, base rates could stay at 0.5% for a long time to come. After all, there's no signs of inflation in the economy at the moment. They have been near zero in Japan for well over twenty years already so it is possible.

However, what I do know is that the level of interest rates matters a lot if you are an investor. As well as determining how much people and companies pay to borrow money they determine the price of virtually every financial asset.

If you invest in bonds, buy-to-let properties and shares then you need to understand this crucial link between interest rates and the value of your investments. And once you do, you will be well on the path to becoming a better informed and more successful investor.

In this article I am going to explain the theory behind the some of the simple models that professional investors use to value bonds and shares. Hopefully by doing this you will see why interest rates are so important. I'll also show you how to value a share based on the dividends that it is expected to pay.

There is a little bit of simple maths involved here, but don't worry. Stay with me and hopefully everything will become clear.

To me, the whole point of investing is to grow the value of your savings. I want the money I invest today to buy me a lot more things in the future than it does today.

If we are given the choice of having £100 today or £100 in a year's time, most of us should choose £100 today. Why on earth would you wait to be given exactly the same amount of money? We need some kind of incentive to wait.

This incentive comes from being offered a return on your money on top of the £100. If you were to put your money in a savings account or bonds that return would come in the form of interest income earned on your money - your £100. The value of a bond investment can change as well during its life but to keep things as simple as possible I am going to ignore this for now

With property and shares you might get some income in the form of rents and dividends but also the possibility that the value of your £100 investment might go up as well. It can also go down which makes them more risky. More on this shortly.

Let's start with a simple bank account and say that the bank offers you an annual interest rate of 5% on your £100. So in one year's time £5 will be added to your £100 and you will have £105.

So with interest rates at 5% you can say that £105 in a year's time is the same as £100 today. Or you could say that £100 is the present value of £105 in a year's time discounted at an interest rate of 5%

Here's the very simple simple maths that explain this:

Future value = £100 x (1.05) = £105 (1+5% is the same as 1.05)

Present value = £105/1.05 = £100

When we are working out the future value of money we multiply it by an interest rate. If we want to work out the present value of money we use what is known as a discount rate. A discount rate is best seen as an interest rate working in reverse. You use it to reduce the value of money in the future to give it a value today.

The other way to do this is to multiply a future value by something known as a discount factor. Using a 5% interest rate the discount factor to calculate a present value of something one year from now would be:

1/1.05 = 0.9524.

So £105 x 0.9525 = £100.

You can apply this technique to values at any time in the future and calculate their value today. If you invested £100 at 5% for five years, the future value of that £100 in five years' time would be:

£100 x 1.05 x 1.05 x 1.05 x 1.05 x 1.05 (multiplying by five lots of 1.05) or £127.63.

What you can see here is the power of compound interest. The longer you leave your money invested at a given rate of interest the bigger the future sum of money can be.

If you have a financial calculator or a spreadsheet you would get the same answer by multiplying £100 by 1.05 to the power of 5.

£100 x 1.05^{5} = £127.63

Its present value would be:

£127.63/1.05^{5} = £100

These fairly simple mathematical formulas are used to value bonds and shares. The price of a bond or a share is the present value of the future cash flows discounted at a rate of interest.

So if you know:

- The future cash flows of an investment
- An interest rate

You can get an estimate of how much something is worth. This kind of approach works best with bonds because all the cash flows are usually known.

Let's use a government bond as an example. A government decides to issue a ten year bond with an interest rate (coupon) of 5%. This represents the market rate demanded by bond investors at the time of issue. The bond is initially sold to investors with a principal or par value of £100.

- The cash flows for this bond are made up of £5 of interest every year for ten years and the return of £100 at the end of the tenth year.
- The interest rate to discount the cash flows is 5%. That the return that bond investors want to part with their cash.

The value of the bond is calculated in the table below.

Year | Cash flow | Discount factor | Discount factor no | Present value of cash flow |
---|---|---|---|---|

1 | 5 | 1/1.05 | 0.9524 | 4.76 |

2 | 5 | 1/1.05^{2} | 0.907 | 4.54 |

3 | 5 | 1/1.05^{3} | 0.8638 | 4.32 |

4 | 5 | 1/1.05^{4} | 0.8227 | 4.11 |

5 | 5 | 1/1.05^{5} | 0.7835 | 3.92 |

6 | 5 | 1/1.05^{6} | 0.7462 | 3.73 |

7 | 5 | 1/1.05^{7} | 0.7107 | 3.55 |

8 | 5 | 1/1.05^{8} | 0.6768 | 3.38 |

9 | 5 | 1/1.05^{9} | 0.6446 | 3.22 |

10 | 105 | 1/1.05^{10} | 0.6139 | 64.46 |

Total | 100 |

The present values of every single cash flow from the bond are all added together in the right hand column to give a value for the bond. As you can see they equal £100.

£100 is the value of the bond to someone who wants a 5% return from owning it for all of its life - for 10 years.

The price of bonds move in the opposite direction to the movement in interest rates. So if interest rates go up, the price of the bond goes down.

The logic behind this is fairly straightforward. Why would anyone accept a 5% return on the bond when they could buy a similar investment offering 6%? The answer is that they will not.

The price of the bond falls to £92.64 so that it gives a return of 6% to someone buying the bond and holding it until it matures (known as the yield to maturity). As the £5 annual income stream does not change, the buyer gets their 6% by paying the lower price of £92.64 and getting £100 back in year ten and bagging themselves a £7.36 profit.

Year | Cash flow | Discount factor | Discount factor no | Present value of cash flow |
---|---|---|---|---|

1 | 5 | 1/1.06 | 0.9434 | 4.72 |

2 | 5 | 1/1.06^{2} | 0.89 | 4.45 |

3 | 5 | 1/1.06^{3} | 0.8396 | 4.2 |

4 | 5 | 1/1.06^{4} | 0.7921 | 3.96 |

5 | 5 | 1/1.06^{5} | 0.7473 | 3.74 |

6 | 5 | 1/1.06^{6} | 0.705 | 3.52 |

7 | 5 | 1/1.06^{7} | 0.6651 | 3.33 |

8 | 5 | 1/1.06^{8} | 0.6274 | 3.14 |

9 | 5 | 1/1.06^{9} | 0.5919 | 2.96 |

10 | 105 | 1/1.06^{10} | 0.5584 | 58.63 |

Total | 92.64 |

The higher interest rate gives a lower discount factor (1/1.06) and lower present value of all the cash flows of the bond. The 6% discount factor reduces the value of the future cash flow by a bigger amount than one of 5%.

Hopefully you can see why investors start running scared if they think that interest rates are going to go up. **It's because the present value of future cash flows will be worth less than they are today**. This will cause the value of investments to fall in price.

Can you use the same principles used with bonds to value shares?

Yes, but it's more complicated. With bonds you know the value of future cash flows in advance. They are pretty much cast in stone and fixed unless the bond issuer goes bust. With shares you are facing two main problems:

**You do not know what the value of future profits or cash flows will be**. Company profits and cash flows can move up and down a lot. It is virtually impossible to make an accurate prediction of what they will be in ten or twenty years' time. Even predicting next year's can be very difficult. Yet this is what professional investors spend most of their time trying to work out. It also explains why the biggest reason by far for a share price to change is when the herd of professional investors change their minds about the size of future profits. That's why profit warnings (when companies announce that their profits will be a lot less than previously expected) can produce devastating falls in share prices.**What interest rate to use to reduce the future profits to a present value**. Academics and finance professionals have been arguing about this for years. What is clear is that shares are more risky than bonds. Shareholders are last in the queue to get paid their share of the company's profits and can lose all their money. They also have to put up with the ups and downs of the stock market which can see the value of their shares move up and down too. To compensate them for these risks they need to be paid a higher interest rate than they can get from bonds. This extra bit of interest is known in financial jargon as the equity risk premium. How much extra it should be is open to debate (typical ranges are from 2% to 7% more than government bonds).

When professional investors are trying to value a share they first try and forecast its future profits or cash flows. For example, they may focus on post tax profits or free cash flows (the amount of cash left over for shareholders). Sometimes a more practical alternative is to predict future dividends per share - as long as the company is paying a dividend of course.

Dividends tend to be more stable than profits and free cash flows. Companies don't like to reduce dividends and ideally want to see them rise steadily over time. So one way to value a share is to forecast its future dividends and discount them back to their present value just as we did with the bond earlier. The approach we use to do this is known as a **dividend discount model** (or DDM for short). One of the best-suited types of company for DDM is a utility which tends to pay out most of its profits in dividends to shareholders.

Electricity and gas networks make for very predictable businesses. Their profits are also regulated. Every five or so years the regulator tells them how much money they can charge their customers. This means that a company has a fairly good idea of how much money it can make for the next few years and the dividends it can pay out.

So let's try and set about valuing National Grid on the basis of its future dividends.

The company has been very helpful here. It has publicly stated that it intends to increase its dividends by at least the rate of RPI (retail prices index) inflation for the foreseeable future. Alternatively, you could take some of the dividend forecasts from ShareScope or SharePad as your starting point.

A word of warning. Be careful about using past dividend growth rates to predict the future. Companies mature and trading conditions can and do change and so the recent past may not repeat itself in the future. Your dividend forecasts need to be prudent and realistic.

Looking in ShareScope or SharePad I can see that the company paid a dividend of 42.87p per share for 2015. I know that RPI is currently 1%. I've decided to forecast dividend growth of 2% per year until 2021, the date of the next regulatory review. To keep things simple, I am also assuming that National Grid can grow its dividends by inflation forever after 2021 and that the long-term rate of inflation will be 2%.

I've decided I want a total return (dividends received plus share price growth) of 7% per year to put my money into National Grid shares. So I will discount National Grid's future dividends at a discount rate of 7%.

Based on my assumptions and 7% discount rate, I get the value of National Grid's shares to be 866p. The current share price at the time of writing (August 2015) is 820p.

National Grid | Dps | Discount Factor | PV |
---|---|---|---|

2016 | 43.3 | 0.9346 | 40.47 |

2017 | 44.2 | 0.8734 | 38.58 |

2018 | 45 | 0.8163 | 36.77 |

2019 | 45.9 | 0.7629 | 35.05 |

2020 | 46.9 | 0.713 | 33.42 |

2021 | 47.8 | 0.6663 | 31.85 |

After 2021 (Terminal value) | 975.2 | 0.6663 | 649.84 |

865.97 |

You'll notice that most of the 866p value comes from something known as a terminal value.

I can't possibly forecast what National Grid's dividends will be forever, so I need some way of estimating it. This is done by assuming a constant growth rate in dividends after my forecasting period and estimating the price of the shares at that date on the back of it.

This can be done with a very neat formula:

Share Price = (next year's dividend per share) / (interest rate - constant growth rate)

So in 2022, my dividend per share estimate is 47.8p x 1.02 = 48.76p. Assuming a 7% interest rate and 2% growth rate gives a value of National Grid shares at 2021 of 975p.

48.76p / (0.07-0.02) = 975p or a present value of 649.84p.

Given that I have assumed a constant growth in dividends of 2% from today I could have just applied this formula to my forecast dividend for 2016 and come up with the same value of 866p per share.

43.3p / (0.07-0.02) = 866p

(Note: This formula only works if the constant rate of growth is less than the interest rate)

Let's say that interest rates in general go up by 2%. A 7% return might not be enough to tempt me or others to invest in National Grid shares. I might want 9% instead. This sees the value of the shares fall to 618p which would be pretty painful for anyone owning National Grid shares today (Disclosure: I do).

This hopefully shows you why interest rates matter and why rising interest rates could be very bad news for our investments.

National Grid | Dps | DF | PV |
---|---|---|---|

2016 | 43.3 | 0.9174 | 39.72 |

2017 | 44.2 | 0.8417 | 37.17 |

2018 | 45 | 0.7722 | 34.79 |

2019 | 45.9 | 0.7084 | 32.55 |

2020 | 46.9 | 0.6499 | 30.46 |

2021 | 47.8 | 0.5963 | 28.5 |

After 2021 (Terminal value) | 696.6 | 0.5963 | 415.35 |

618.55 |

This way of valuing shares is a good way of working out what rates of growth are factored into the current share price. You can also play around with different scenarios to see what would happen to your investment.

However, the values produced are very sensitive to the choice of interest rate. They are also dependent on predictions of the future which are almost certainly going to be wrong. If your assumptions are unrealistic or ill thought out then your valuation won't be worth the paper it is printed on.

It also should go without saying that the process falls to bits if the future dividends are cut or scrapped completely. This is why you need to understand the company you are investing in and do some research. It's very tempting to just plug some numbers into a spreadsheet to get an answer that you like. Never forget that those numbers - the dividends - are produced from the profits and cash flows of a real business.

If you can get a share to look cheap on prudent assumptions of the future and a high interest rate then you stand a better chance of protecting yourself from mistakes - you are giving yourself an all important margin of safety. Most people don't even bother with this kind of approach. Instead they go for shortcuts such as PE ratios or multiples of EBIT or EBITDA which also have their drawbacks.

I think the approach of using profits and interest rates to value a company is very powerful but it has to be used in a smart way and not based on trying to predict the future. That's what I am going to show you in part two.

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This article is for educational purposes only. It is not a recommendation to buy or sell shares or other investments. Do your own research before buying or selling any investment or seek professional financial advice.