# HOW TO CALCULATE NET PRESENT VALUE (NPV)

NPV is an acronym for Net Present Value. NPV is defined as a method of assessing the value of money received in the future. This blog will help you understand it.

“The value of money changes over time.”FACT CHECK: We all know about inflation. Currently in the UK inflation is roughly 2% per year. This means that a grocery trolley at a supermarket may cost £100 now, but come this time next year that same trolley will cost

£102. Things generally get more expensive over time. Another way of looking at it is that next year’s £102 is only worth £100 today. Once you grasp the concept that money received in the future has a lower value today, you’re done!

## Net Present Value Analysis

The concept applies to both income and expenditure, assets and liabilities. Arithmetically, you may choose to think of income as positive numbers and expenses as negative numbers, or the other way round. It doesn’t matter. Both positive and negative numbers shrink when you adjust backwards in time, and grow when you adjust forward in time.

### HOW TO CALCULATE NPV VALUE

This is a relatively complicated mathematical formula, which is why we let our computer models do this for us. If you want to do it yourself, you will need a business / scientific / engineering calculator (not a standard office calculator) or a spreadsheet. Now don’t be frightened by this NPV formula, because you don’t need to remember it, and if you do
manage to remember it, it won’t greatly increase your understanding of NPV, but we give it here just for your amusement if nothing else…

Going backwards in time:
PV = FV / ( (1 + APR) ^ (t) )

In this formula:
PV is the Present Value
FV
is the Future Value, at some time in the future
APR is the Annual Percentage Rate, where a value of 0.05 means 5% and it is the number of years from today of the Future Value.

Going forwards in time:
FV = PV * ( ( 1 + APR) ^ (t) )

So where does the “Net” come into Net Present Value then?
The Present Value (PV) is a single value at a point in time. In our supermarket example above, the Present Value of next year’s receipt of £102 is £100. The Net Present Value (NPV) is the sum of a series of Present Values, for example, rental income over five years. In that example, the NPV would be the sum of the Present Values for years 1, 2, 3, 4 and 5.

### Rental income NPV

Imagine you are building a house to rent and you want to work out whether the rental income that you are going to receive during the first 30 years is worth more than the cost of building the house. Assuming the rent will be paid on a monthly basis, that is 30 years x 12 months = 360 individual payments.

Let’s say you start renting out your new house on 1 January 2020. Initially, the rent is £500 per month (paid at the end of the month) and every subsequent year you inflate the rent by 3% (i.e. CPI+1%). Therefore, in the second year the rent will be £515 per month and in the third year it will be £530.45 and so on.

To simplify things we will work with 30 calculations; each calculation representing one year of income. So we are assuming, for this example, that all 12 monthly payments in the year are received in one lump at the end of the year, i.e. 31 December 2020.

We are further assuming that you are borrowing money to build this house at 6% APR and so that is the rate at which we will discount your future annual incomes.

#### The table below illustrates the figures in each year:

The first year’s rental income in 2020 is £6,000 (12 x £500), which is worth £5,660 after discounting. In the second year, the annual income is now £6,180 (because of the 3% rent inflation) but discounted back at 6% APR it is only worth £5,500 today. And so on over the next 30 years.

When we add up all these present values over 30 years, the NPV of the rental income is £115,478.

### So what does this mean?

Well, assuming that you can borrow £115,478 at 6% APR over 30 years (and ignoring the impact of expenses), you will pay off your loan completely over that time and break even.

But at the end of this period, the house is still yours and you continue to receive rental income if you decide not to sell it.

The Discount Rate is a percentage rate that is used to reduce future income. It is made up of two key factors: the interest rate (APR) and the level of risk. In the social housing sector, housing development is considered low risk (as associations receive grant and are regulated), so the discount rate is typically the same as the borrowing rate, hence why we have used APR in the example above. The difference between a traditional NPV Discount Rate and an APR is very small and very technical.

Generally the higher the perceived risk in a scheme, the higher the APR used in the NPV calculations. If this housing project was in an earthquake zone, you may want to considerably raise the rate of discount. If there is a mild risk of flooding or subsidence, you may wish to just add a percentage point or two to the discount rate. As you increase the discount rate, the NPV will be lowered.

Alternatively, you could take out insurance against these risks and deduct the cost of that insurance from the NPV.

When tenants move out, they sometimes leave without paying the last month’s (or more!) rent. Additionally, the property may remain empty for a while before new tenants move in. Either way, this leaves you with a gap in the anticipated rental income stream.

Even though this is a risk factor, the general approach to this problem is not to increase the discount APR, but to reduce the rent amount instead.

For social housing, the norm is to reduce the rent by 2 to 3%, depending on tenure. This does not mean reducing the actual rent charged to the tenant by 3 to 4%, just assuming that over 30 years we will lose between 2 and 3% of rent due to periods of no occupancy, and/or unrecoverable rent arrears. A 3% allowance translates into a £3,464 drop in NPV using the earlier example of £500 per month rent inflating at 3% per year for 30 years and discounted at 6% APR.

Voids and bad debts are often modelled at a higher rate for private market rented schemes. It is common to exclude it for shared ownership schemes (as there won’t be a void period between purchasers); however, it is prudent to allow a percentage for bad debt/arrears.

### Pulling this all together

NPV analysis is a methodology to calculate the financial return on investment for a project. Net present value is the total future income of your project discounted to today’s values and then compared to the initial investment (i.e. the total cost of the scheme less any initial sales/grant).

A project is financially worthwhile if the NPV analysis shows that NPV of the income is greater than the investment value. If the NPV is negative then the scheme will lose the amount of money represented by the shortfall.

When comparing the NPV of two assets, like a house, the asset with the higher NPV is more valuable in financial terms. Housing Associations can optimise their portfolio by divesting existing properties with negative NPVs and investing in building properties with positive NPVs. This will improve the sustainability of the portfolio over the longer term.

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