Rental yields - andrewk4, bbm & anyone

Remember andrewk4's Chinese investment property equation? Veritably veritably I have expatiated a qualitative and quantitative analysis on this one piece of wisdom.

I now admit my debt/equity formula derived from the Chinese investment property cash flow is wrong. d/e is not practical as it implies an exponential model. As e approaches 0, d/e approaches infinity, which throws out the other side of the equation.

Before I bore you with more maths, here are some qualitative and quantitative revelations from my new, unofficially correct linear formula:

Rental yields > interest rates are even worth investing 0% equity or 100% debt in.

Rental yields < cash fund rates are not even worth investing 100% equity or 0% debt in.

For rental yields greater than cash fund rates and less than interest rates, my formula calculates the equity or % deposit needed for that investment to beat 100% equity in a cash fund.

For owner occupier houses, the formula is slightly different and more generous to the debt allowable because the rental yields are turning from negative to positve. That is, a cost of living is being turned into some house equity.

Bear with me for the simple derivation of my new formula:

Let RE = Rental Yields, IR = Interest Rates, CR = Cash fund Rates, e = equity and d = debt.

The left side (we don't need the right side) of the Chinese investment property equation gives us the cash flow of an investment property ->

RY - IR
In one year, this is ->
RY(e+d) - IR(d)

Now e+d = 100% = 1
This is I think where I went wrong last time, not eliminating the constant.

Therefore ->
RY - IR(d) [1]
is now the investment property cash flow

The cash flow in a cash fund is ->
(e)CR [2]

We want to find where the investment property cash flow matches the cash fund cash flow so let [1] = [2] ->

RY - IR(d) = (e)CR

Back to e+d = 1, from this->
d = 1-e
substitute d into the equation above to eliminate d and ultimately solve the equation ->

RY - IR(1-e) = (e)CR ->
RY - IR + IR(e) = (e)CR ->
RY - IR = (e)CR - IR(e) ->
RY - IR = e(CR - IR) ->

e = (RY - IR) / (CR - IR)

YES YES YES!!!

Remember e is also the % deposit which makes it more useful than d, thus I solved for e.

Notice the bottom of the division line is CR - IR which is always negative. What bank would reward their savers with the same rate they punish their debtors? The answer is ING, but why they do this is an anomaly. CR - IR is practically always negative. Therefore as long as the top i.e. RY - IR stays positive, e will always be negative. A negative e is a good thing, because that means the rental yield is good enough for 100% debt. For that to happen RY needs to be > IR.

Furthermore if the top i.e. RY - IR goes slightly negative, e will be positive meaning a certain deposit is needed. For example if e = 0.3, a 30% deposit is needed for that particular investment house and the other bank rates you decide to use.

Lastly if the top = bottom, then e = 1, and that investment house is woefully overvalued. That is if RY - IR = CR - IR or RY = CR. You are better of investing in a cash fund than that house.

Constructive criticism please! I'm only a 23 year old happy to find a use for high school & uni maths.