Single and dual rate in leasehold investment valuation - UK - Lets say a company wants to buy a property investment and wants a return of 5% on it. If it produces an income of £100 per year, one would pay  £2000 for such an investment. (In this case we will not take into consideration buyers costs  and other complications for the purpose this explanation)

If it is a freehold, then I will still have ownership in the property 10 years later so I will still have £2000. This will be in the value of the property or if I sell it for cash. However in the case of single and dual rates the return is called the remunerative rate. So explained in another way if I invest £2000 and I get a 5% rmunerative rate on my investment, I will still have that money or its equivalent in property value.

Now in the case of a leasehold interest, lets say an investor buys a lease, but the lease lasts for 10 years.Then the analysis is different. Lets say I still want a remunerative rate of 5.00%, but I must take that, in 10 years time, whatever has been paid for the investment will be gone, or in other words not only will the lease will have gone but I will have no interests the property. In this case the real estate/property valuers developed the idea of a sinking fund. Instead of reselling (or keeping) my investment at the end of 10 years, as I can with a freehold, the investor decides to put aside an annual sum out of the income from the lease, to reconstitute the investment. The only source of income to the sinking is the income the investor receives from the property during the lease. If as in the previous example the income is  £100, then each year out that  £100 the investor has to put aside a certain amount so that they can get back their original investment at the end of the term. So therefore in the case of a 10 year lease, this would be one tenth of the price I would pay to buy this leasehold investment.

In the case of the 10 year lease the price I would have to pay and still receive a 5.00% remunerative rate is is roughly £666. So therefore in the investors case they will have to set aside £67 out of the £100 a year income as a sinking fund to reconsitute the fund to the original price that the investor paid. The balance of £33 a year is the 5% on the investment outlay  of £666, so the investor has achieved the remunerative rate he wants.

There is another consideration to be taken into account. Most investors have to pay tax on income. We can use the rate of 40% to illustrate the effects. At the present time HMRC do not regard sinking fund contributions as a cost. Therefore the sinking fund contributions will have pass through a tax funnel. Therefore the investor will have to reserve a larger part of the £100 a year income for those contributions. So in the investors case I will only be able pay £461 if the investor wants to achive the 5% return. The reason is because now the investor will have to make contributions of £77.00. Of that amount £31.00 goes to the HMRC and £46 goes to the sinking fund. That leaves £23 for the investor which is a 5% return on the outlay of £461.00. 

In the case of dual rates, the example above would have slightly understated the value I should pay, because in dual rates the money put into the sinking fund attracts a certain amount of interest which is the second rate to make the rate dual. The rate is usually smaller and this rate will be different from the remunerative rate and is known as the accumulative rate because it is progressively added to the accumulating sinking fund. It is considered the risk free rate. This is why the calculation is called a dual rate years purchase or YP calculation, because the there are two different rates at work which are doing different things. The remunerative rate is providing the return on the invested money  and the accumulative rate which is enhancing the return on the sinking fund.