Question

Suppose in a certain property market the typical lease term is 5 years, the cap rate (cash yield) is 8%, long term property value and rental growth rate is 2.0% per year, leases provide rent step-ups of 2.0% per year (per the expected growth rate), and the tenant borrowing rate (intralease discount rate) is 6%. What is the appropriate inter-lease discount rate?

Answer 1

Sol:

Lease term = 5 years

Cap rate = 8%

Growth rate (G) =2% per year

Rent step up = 2%

Tenant borrowing rate = 6%

To compute appropriate inter-lease discount rate:

First let's find present value (PV) of lease per dollar of the initial net rent:

(PV) of lease per dollar = $1 / (1 + 6%) * (1 - (1.02/1.06)^5 / 1 - (1.02 / 1.06)

(PV) of lease per dollar = (1 / 1.06) * (1 - 0.8250 / (1 - 0.9623)

(PV) of lease per dollar = 0.9434 * (0.175 / 0.037736)

(PV) of lease per dollar = 0.9434 * 4.638481 = $4.37

Now its an perpetuity which grows constantly so we have to use geometric series (GS):

GS = 4.37 / (1 - (1.02 / 1 + r)^5

Market prevailing cap rate = $1 / 8%

Putting together both the equations we will have

$1 / 8% = 4.37 / (1 - (1.02 / 1 + r)^5

r = 1.02 / (1 - 8%*4.37)^(1/5) - 1

r = (1.02 /0.917563) - 1

r = 1.11164 - 1 = 0.11164 or 11.16%

Therefore appropriate inter-lease discount rate will be 11.16%