buy or save?  

Market Value

We calculate the present value of the net cashflows (rent - expenses) expected from the property, discounting at a combination of the expected inflation rate and opportunity cost (short term cash deposit). Adjustments are made for tax on savings and rental income. Risk associated with holding the property is mostly factored into expenses (via insurance) and anticipated vacancy rate, but a (small) factor for expropriation can also be incorporated into the discount rate. Risk of expropriation of deposits can also be incorporated into the discount rate.

Note on intuition for using opportunity cost in discount rate: you need to borrow your money away from a presumably already invested pool of cash, thereby foregoing the associated interest (until the cashflows come in).

Remarks:

1. The market, in aggregate, does not purchase property with cash. It uses leverage. Is it better therefore to use a discount rate appropriate to this. I guess you'd work out how leveraged the property market is in aggregate (and your expectations of this going forward), and do a weighted average of the borrowing vs saving rates.
   • The increased discount rate mostly reflects bank profits rather than higher risk.
   • In this model, negative gearing laws would result in a further adjustment to the discount rate (downwards). Probably not especially easy to work this factor out.
2. The market, in aggregate, doesn't hold properties indefinitely. There is some amount of turnover, with associated transaction costs (and taxes). This could be incorporated into the discount rate as well (upward adjustment). Note on taxes: a large part of the housing stock is owner / occupier, which is subjected to different tax laws.
3. Using NPV assumes indifference as to when the cashflows are recieved. Assuming fairly stable demographic trends, in aggregate this probably isn't such a bad assumption so it's probably not a bad way to determine the market value of the property. The same argument can be made by a public company doing an NPV calculation to determine whether or not to undertake a project (diverse collection of shareholders). However, for individuals buying property, this assumption is far from correct.
   1. Someone using a high proportion of cash in the purchase obviously does not want to use that cash now.
   2. Interest rates and rents will both broadly move with the inflation rate, but not exactly and their relative movement will change with time. Therefore, the relative (real) value of a fixed interest and real estate investment will depend on when they are divested. Indeed, many people invest in real esatate because they believe it to be a good inflation hedge (and that cash/interest is not). They don't wan't to know the value of their investments relative to cash today, they want to know this at the point of time in the future when they want to use the money.
      1. Note: People's propensity to avoid cash will change with time. This is modelled by specifying real interest / real rent expectations.

Value to an Individual

In practice, people are going to want to use the value tied up in their investments over an extended period of time (their retirement). However, they will generally need to divest their property investment at a single point in time, and I think it is useful model regardless.

The valuation can be automatically repeated for many timeframes of interest, and the results shown in a chart. This is useful to indicate the effect of time on when the property is sold.

During the investment timeframe, it is fairly straightforward to model all of the (nominal) cashflows to arrive at the final net position. The terminal value of the property (in timeframe's dollars) can be determined by the market NPV approach specified above. Any capital gain can be taxed and anticipated transaction costs estimated as a percentage of the terminal value.

Finally, the result of the above calculation can be expressed in today's dollars by adjusting for inflation. I think expressing in today's dollars is the most intuitive way of expressing the relative values.

Drivers

Most developed countries attempt to engineer price inflation of between 2 and 3 percent per year, though the actual rate could fall outside this range for an extened period of time for a number of reasons:

1. Multiple Mandates - Price stability is usually of primary concern, but central banks may have other objectives including maximizing employment and ensuring stability of the financial system. These objectives may be prioritized over price stability.
2. Market Forces - Market forces may overwhelm the tools that central banks and the government have available ot them to influence the rate of inflation.
3. Policy Change - For example, in the US, some prominent people are calling for an inflation rate target of 4% or higher.

Predictability

Policies are generally designed to result in average long term inflation that is relatively predictible and controllable, however there are arguments to suggest both deflation and very high inflation are distinct possiblitis in the forseeable future.

We suggest considering a wide range of potential inflation scenarios.

Historical Data

TODO: Chart of Australian and US CPI over the last 50 years.

What To Measure?

TODO: Discussion of how CPI is calculated and possible deficiencies.

Parameters

At any given time, there are many different interest rates in the market place, applicable to different situations. Reference Interest Rate is a simplification of reality and is intended to reflect the general level of market interest rates anticipated in the future. Specifically

You also specify two constant offsets that specify the deposit and lending interest rates relative to the (time varying) reference interest rate. This too is a simplification - in reality, the spread between deposit and lending rates is not constant and depends on many factors. This effect is beyond the scope of our model, and also probably not very predictable.

Drivers

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Over the long term, average rent paid as a proportion of income will rise at the same pace as the general price level. It is not possible for average rent price changes to over- or under- perform inflation indefinitely because otherwise rents will go to infinity or zero. That said, extended periods of divergence are possible and observed historically.

For individual properties in a growing city however, it is reasonable to assume that rental increases will outpace inflation in many cases. Inflation adjusted, people may not pay any more rent in the future, however the average dwelling may be an apartment, rather than a house. The cost of renting the house will rise faster. Although indefinite out performance is impossible (leading to infinite prices), for some properties, it's not a bad model for a very long time.

I the model, it is assumed rents rise with the inflation plus a modifier, which may vary with time. This may reflect expectations about the growth of a cities population or land restrictions currently in place that may eventually be lessened. Or it might reflect recent under or over perfromance of inflation and expectations about this mean reverting.