Reading 39 - Real Estate Valuation- The term ad reversion approach + layer method

Example 18 and Example 19 of the BB.

Under both the term and reversion and, layer method, when we either discount the reversion income or when we discount the incremental income in the layer method to time 0, why are we using the cap rate and not the discount rate?

I correctly valued the reversion method and the layer method to the time the change in the income happened, but when it came to bringing everything back to 0, it was all wrong because the curriculum uses the cap rate.

The cap rate for the reversion part has a growth rate of 0 (i.e. constant rental upon revision of rental to market rates)

Cap rate = r - g
Cap rate = r - 0
Cap rate = r

So when you discount the PV of reversion to time 0 you will use the discount rate (which in this case is the cap rate as well)

so why are discounting the cash flows as 1+cap rate or just with the cap rate? Because if you say that g=o , then we should discount it as a perpetuity, but I believe the curriculum does 1+cap rate.

For the reversion rent starting from Year N (i.e. perpetuity), we calculate the PV of the reversion rent at Year (N-1) as:

\frac{Reversion ~rent}{Cap ~rate} = \frac{Reversion ~rent}{r - g} = \frac{Reversion ~rent}{r - 0} = \frac{Reversion ~rent}{r}

The PV is for a perpetuity with no growth.

Then the PV of the reversion rent at Year 0 will be:

\frac{1}{(1+ Discount ~rate)^{(N-1)}} \times \frac{Reversion ~rent}{Cap ~rate}

For this case, the cap rate = r - g = r - 0 = r = discount rate. So the cap rate is also equal to the discount rate (in the case of g = 0)

Hence:

\frac{1}{(1+ Cap ~rate)^{(N-1)}} \times \frac{Reversion ~rent}{Cap ~rate}