Solution
:
The abstracted going-in capitalization rates from the four properties are listed below:
Comparable 1:
0.110
Comparable 2:
0.120
Comparable 3:
0.112
Comparable 4: 0.115
Simple Ave.
0.114
The simple average of the four comparable cap rates is 0.114.
Thus, the indicated
value of the subject property is $390, 351, ($44,500 / 0.114), which rounds to
$390,000.
7.
You are estimating the value of a small office building.
Suppose the estimated NOI
for the first year of operations is $100,000.
a. If you expect that NOI will remain constant at $100,000 over the next 50 years and
that the office building will have no value at the end of 50 years, what is the present
value of the building assuming a 12.2% discount rate?
If you pay this amount, what
is the indicated initial cap rate?
Solution
:
The present value, using a financial calculator, is $817,078.
N = 50
I = 12.2
PV = ?
PMT = 100,000
FV = 0
The initial (going-in) cap rate is $100,000/$817,078 = 12.24%
b. If you expect that NOI will remain constant at $100,000 forever, what is the value
of the building assuming a 12.2% discount rate?
If you pay this amount, what is the
indicated initial cap rate?
Solution
:
The value of the building with NOI remaining constant at $100,000 is
calculated using the formula for a perpetuity, which is $100,000/0.122, or $819,672.
If you pay $819,672 for the property, the initial (going-in) cap rate is 12.2%
($100,000 / $819,672).
c. If you expect the initial $100,000 NOI will grow forever at a 3% annual rate, what
is the value of the building assuming a 12.2% discount rate?
If you pay this amount,
what is the indicated initial cap rate?
Solution
: The capitalization rate consists of a required IRR on equity and a growth
rate.
Applying the general constant-growth formula and assuming that the growth
rate is 3%, the indicated capitalization rate is equal to 9.2% (12.2% - 3.0%.).
6