Question

10. Consider an investor with a four-year investment horizon, evaluating an income producing property. The property may currently be purchased for $5,000,000. Last year's NOI of $450,000 is projected to grow at 4% annually into the foreseeable future. At the end of the investor's holding period, cap rates are expected to be 8.00% on properties of this nature. Decompose the expected return into its component pieces. Specifically, what percentage of the promised return is attributable to:

1. Periodic Cashflows (NOI):

2. Interest-on-Interest (I-on-I):

3. Capital Gains / (Losses):

Please show all steps and thought processes with a FINANCIAL CALCULATOR so that I can understand!

Answer 1

1] Cash flows at end of each year :

CF at end of 1st year = 450000 *1.04 = 468000

Enter these values in financial calculator

PMT = 468000 , N = 4 , PV = 0 , I/Y = 4

Compute FV in financial calculator

FV = 1987345.15

This value can also be arrived by calculating cashflow at end of each year and then adding them all together.

For example cashflow at end of year 2 = CF at end of year 1 * 1.04

This is the total cash inflow from NOI over 4 years without reinvestment of any cashflows received at end of years 1,2 and 3.

Return on investment from NOI = Total cash inflow from NOI / Property purchase value

= 1987345.15 / 5000000

= 0.3974 = 39.74%

2) Cashflows at end of each year

Year 1	Year 2	Year 3	Year 4
468000	486720	506188.8	526436.35

Assuming that these cashflows at end of years 1, 2 and 3 are reinvested at annual risk free rate of 4% (since reinvestment rate is not mentioned) and all these investments expire at end of year 4.

For example : For Year 1 cashflow 468000 reinvestment

Interest on interest ( compound interest )

= Investment * (1 + interest rate)^(no of years till maturity) - Investment

= 468000 * (1.04)^3 - 468000

= 526436.35 - 468000

= 58436.35

Similarly for year 2 cashflow

Interest on interest

= 486720 * (1.04)^2 - 486720

= 39716.35

Similarly for year 3 cashflow

Interest on interest

=506188.8 * 1.04 - 506188.8

=20247.55

Total sum of all compounded interests at end of year 4

= 58436.35 + 39716.35 + 20247.55

= 118400.25

Return on investment from interest on interest

= Total sum of all compounded interests at end of year 4 / Property purchase value

= 118400.25 / 5000000

=0.02368

=2.368 %

3) GIven : Capitalization rate at end of year 4 = 8%

Cap rate = NOI at end of year 4 / Property value at end of year 4

0.08 = 526436.35 / Property value at end of year 4

Property value at end of year 4 = 526436.35 / 0.08

=6580454.375

Capital gains = Property value at end of year 4 - Property purchase value

=6580454.375 - 5000000

=1580454.375

Return on investment from capital gains

= Capital gains / Property purchase value

= 1580454.375 / 5000000

=0.3161

=31.61 %