Traditional method of investment valuation for beginners
What is investment valuation?
This method involves reflecting risk, return and expectations of growth through the use of a yield. This yield is fed into the years purchase (YP) formula and the present value of £1 (PV £1) formula to produce the figures that the rent is multiplied by.
Years purchase and present value are explained mathematically below but first we need to understand the concept of the time value of money.
Why do we do this?
Time value of money is an economic principle that is always in the news as politicians argue about the cost of living.
Think about inflation: a loaf of bread costs more this year than last year. The amount of the increase is the inflation percentage, averaged over many products to produce the retail price index and the headline inflation figures.
It is the same principle in valuation: your money will buy less in the future than it does today.
There is also a risk that you might not get any future promised income. There is an opportunity cost, you can’t invest it elsewhere and make more money.
The investor may be optimistic about capital or rental growth and be prepared to accept a lower yield in exchange, this investor thought process is also reflected. So, this yield percentage has a lot of thinking behind it.
How is the time value of money reflected?
If you were to multiply an income of £10,000 per year for 4 years on a straight line basis the answer would be £40,000. But we now know this is not accurate enough because there is no allowance for the risk, return (reflecting time value of money) and expectations of growth.
The answer will be less… but how much less?
Valuers use a formula called years purchase (which is also used throughout the financial world) to work this figure out. This is the number of years it will take the income of £10,000 to add up to the capital value reflecting the time value of money.
This formula has another name: the present value of £1 per annum and this means, the current value of the right to receive £10,000 income for 4 years.
Same thing, different words.
The formula is:
YP = 1-PV/ i
Mathematical proof
Let’s assume that the valuer thinks 8% is the appropriate yield.
Present value PV = 1/(1+i)^n
Same thing, different words.
The formula is:
PV = 1/(1+0.08)^4
PV = 0.73503
Years purchase
Same thing, different words.
The formula is:
YP = (1- 0.73503)/0.08
YP = 3.3121
This means that the right to receive £1 per annum for 4 years at 8% is worth £3.3121. This is less than £4 because of the time value of money and risk.
Put another way, it will take 3.3121 years for the income to equal the capital value.
The valuation should be laid out in columns with the YP calculation factors in the first column and the calculation outcome in the second column.
Valuation | ||
£ | £ | |
Rent | 10,000 | |
YP 4 years @ 8% | 3.3121 | |
Capital value | 33,120 |
That is how we value the period up until the next rent review – the term.
Future money
What if there is a reversion?
In many valuations, the rent will go up at a rent review (or at the end of the lease). There is often about 3 years between rent reviews. In this period rents will go up but the landlord can’t increase the rent until the review.
Let’s assume the property is 1 year into a 3-year review and rents have increased to, say, £12,000.
So, the valuer needs to value an income of £10,000 for 2 years till review – this is the term.
The valuer then needs to value the market rent of £12,000 after 2 years – this is the reversion.
It is a fundamental principle with the traditional method that we do not project rental growth and today’s full market rent is the highest figure we can use.
We will also assume that this figure is received into perpetuity – forever.
The chances of future growth (or decline) and the risks are reflected in the choice of yield. The valuer will make adjustments to comparable yields to reflect these risks.
Imagine a good tenant covenant in a prime area, the risk of tenant default will be less and the valuer will be expecting rental levels to rise. Imagine the comparable yields have poorer locations and uncertain income – currently at say 6%.
The valuer will adjust the yield on the subject property to say 5% to reflect the better prospects. This is somewhat counter-intuitive. The fundamental principle is that the better the prospects the LOWER the yield. This is because an investor will accept a lower yield (return on his investment) when he feels optimistic about the future.
The yield used as a starting point is found by analysing comparable transactions. Valuers will divide the rent by the capital value to give a gross initial all risks yield, this is the starting point for adjustments in our simple example.
Rent/capital value = gross initial yield
The key point with the traditional method is that these adjustments will be subjective and selected using valuer judgement. The growth and risks are implicit in the yield with traditional method. This is often cited as a major drawback of the method.
Applying the formula to the reversion
The same economic principles apply to the relationship between rent and capital value. We will still need a YP to capitalise and we will also need to discount using present value £1 (PV).
Time value of money is a bigger issue with the reversion because:
- it is further away;
- it has more risks;
- there is less value to the money because of inflation; and
- there is an inability to invest elsewhere.
This introduces an extra step in the valuation using the PV formula.
Capitalising
The YP reflects the time value of money in converting a flow of income into a lump sum. This is the same formula as before but much simpler because the income is forever.
This is 100/i.
We need to reflect the risk and the fact that the expected growth has already happened so an investor will be looking for a slightly higher yield. We will use 8.5%.
100/8.5 = 11.7647
This figure will be used to value the right to receive £12,000 p.a. forever.
Discounting
The PV formula is used to reflect the time value of money because it is future money.
The PV formula is 1/(1+i)^n.
Mathematical proof
PV = 1/(1+i)^n
PV = 1/(1 + 0.085)^2
PV = 1/1.085 ^2 (^2 = 1.085 x 1.085)
PV = 1/1.1772
PV = 0.8497
The YP is multiplied by the PV to give a deferred YP. It is easiest to explain in steps in the valuation. The PV x YP calculation is shown in italics.
Term | |||
£ | £ | ||
Rent | 10,000 | ||
YP 2 years @ 8% | 1.7832 | ||
Capital value term rent | 17,832.00 | ||
Reversion | |||
Rent | 12,000 | ||
YP perp @ 8.5% | 11.7647 | ||
Deferred 2 years | X | ||
PV £1 @ 8.5% 2 years | 0.8497 | ||
YP in perp @ 8.5% def 2 years | 9.9964 | ||
Capital value reversion | 119,956.80 | ||
Total |
137,788.80 |
The good news
Valuers do not need to work out this formula every time. You can use valuation tables, such as Parry’s or an online calculator such as the isurv calculator, which will do these calculations for you in a single click.
Valuers need to understand which fomula to use and why, but the maths is very simple once you get the hang of using the appropriate tables as tools to help.
Kate Taylor FRICS is an experienced APC assessor