Question

The law firm of Saul Goodman and Associates must choose between two different leases for their new space. The first lease, Lease A, is a 5-year gross lease with a base rent of $36.25/sf. If rents will increase by $1.00/sf each year and the cash flows from the lease are discounted at 6%, what is the corresponding effective rent when evaluated from the tenant's perspective?

The second lease, Lease B, is a 5-year net lease with a base rent of $25/sf with expenses expected to be $10/sf in the first year. If rents will increase by $1.00/sf each year and expenses by 5% a year, what is the corresponding effective rent from the tenant's perspective if cash flows are discounted at 6% annually?

Answer 1

First Lease:

Initial Rent = $36.25/sf

Gradient = $1/sf

Time=5 years

Rate = 6%

The payments can be split into 2 set of cashflow

i) Annuity of $36.25

ii)Gradient of $1

Hence PV of Annuity = A*(1-(1+r)^-n)/r

=36.25*(1-(1+6%)^-5)/6%

=36.25*(1-1.06^-5)/0.06

=36.25*(1-0.7473)/0.06

=36.25*0.2527/0.06

=$152.70

PV of gradient = G*((1+i)^n-I*n-1)/((1+i)^n*i^2)

=1*((1+6%)^5-6%*5-1)/((1+6%)^5*6%^2)

=1*(1.06^5-0.3-1)/(1.06^5*0.0036)

=1*(1.3382-1.3)/(1.3382*0.0036)

=1*(0.0382)/0.0048

=$7.93

Hence Total PV = 152.70+7.93 = $160.63

Hence Effective Annual Rent can be given by PV= A*(1-(1+r)^-n)/r

or, 160.63 =A*(1-(1+6%)^-5)/6%

or, 160.63 =A*(1-1.06^-5)/0.06

or, 160.63 =A*(1-0.7473)/0.06

or, 160.63 =A*0.2527/0.06

or, A = 160.63*0.06/0.2527

=$38.14

Second Lease

Initial Rent = $25/sf

Gradient = $1/sf

Initial Expense =$10/sf

Growth rate of expense, g = 5%

Time=5 years

Rate = 6%

The rent payments can be split into 2 set of cashflow

i) Annuity of $25

ii)Gradient of $1

Hence PV of Annuity = A*(1-(1+r)^-n)/r

=25*(1-(1+6%)^-5)/6%

=25*(1-1.06^-5)/0.06

=25*(1-0.7473)/0.06

=25*0.2527/0.06

=$105.29

PV of gradient = G*((1+i)^n-I*n-1)/((1+i)^n*i^2)

=1*((1+6%)^5-6%*5-1)/((1+6%)^5*6%^2)

=1*(1.06^5-0.3-1)/(1.06^5*0.0036)

=1*(1.3382-1.3)/(1.3382*0.0036)

=1*(0.0382)/0.0048

=$7.93

Hence Total PV of rent = 105.29+7.93 = $113.22

PV of expense =A*(1-(1+g)^n/(1+r)^n)/(r-g)

=10*(1-(1+5%)^5/(1+6%)^5)/(6%-5%)

=10*(1-(1.05/1.06)^5)/1%

=10*(1-0.9906^5)/0.01

=10*(1-0.9537)/0.01

=10*0.0463/0.01

=$46.29

Total PV of cost = 113.22+46.29 = $159.51

Hence Effective Annual Rent can be given by PV= A*(1-(1+r)^-n)/r

or, 159.51 =A*(1-(1+6%)^-5)/6%

or, 159.51 =A*(1-1.06^-5)/0.06

or, 159.51 =A*(1-0.7473)/0.06

or, 159.51 =A*0.2527/0.06

or, A = 159.51*0.06/0.2527

=$37.87