Real Estate Investments David M. Harrison, Ph.D. Texas Tech University TVM - Compounding $ TodayFuture $ Discounting Time Value of Money.

Real Estate Investments

TVM -

Compounding

$ Today Future $

Discounting

Time Value of Money


Future Value (FV)

Definition -

»

FV = ?

0 1 2 N

PV=x

FVn = PV(1 + i)n


Future Value Calculations

Suppose you have $10 million and decide to invest it in a security offering an interest rate of 9.2% per annum for six years. At the end of the six years, what is the value of your investment?

What if the (interest) payments were made semi-annually?

Why does semi-annual compounding lead to higher returns?


Future Value of an Annuity (FVA)

Definition -

»

FVA = ?

0 1 2 N

i

iFVA

n

n

1)1(

AA A


Ordinary Annuity vs. Annuity Due

Ordinary Annuity

A AA

0 1 2 Ni%

A A

0 1 2 Ni%

Annuity Due

A


Future Value of an Annuity Examples

Suppose you were to invest $5,000 per year each year for 10 years, at an annual interest rate of 8.5%. After 10 years, how much money would you have?

What if this were an annuity due?

What if you made payments of $2,500 every six-months instead?


Present Value (PV)

Definition -

»

FV = x

0 1 2 N

PV= ?

PV = P0 = FV / (1 + i)n


Present Value Calculations

How much would you pay today for an investment that returns $5 million, seven years from today, with no interim cashflows, assuming the yield on the highest yielding alternative project is 10% per annum?

What if the opportunity cost was 10% compounded semi-annually?

Why does semi-annual compounding lead to lower present values?


Present Value of an Annuity (PVA)

Definition -

» PVA = ?

0 1 2 N

ii

PVAn)1(

11

AA A


Present Value of an Annuity Examples

How much would you spend for an 8 year, $1,000, annual annuity, assuming the discount rate is 9%?

What if this were an annuity due?

What if you were to receive payments of $500 every six-months instead?


TVM Properties Future Values

An increase in the discount rate

An increase in the length of time until the CF is received, given a set interest rate,

Present Values An increase in the discount rate

An increase in the length of time until the CF is received, given a set interest rate,

Note: For this class, assume nominal interest rates can’t be negative!


Definition -

Perpetuities

PVperpetuity = ?

0 1 2

i

PMT

RateInterest

PaymentPVPerpetuity

$$ $


Perpetuity Examples

What is the value of a $100 annual perpetuity if the interest rate is 7%?

What if the interest rate rises to 9%?

Principles of Perpetuities:» »


Uneven Cash Flow Streams Description -

Ex. Given a discount rate of 8%, how much would you be willing to pay today for an investment which provided the following cash flows:

Year Cashflow Present Value

1 1002 2003 250

4 200

5 400


Uneven Cash Flow Streams

Ex. Given a discount rate of 8%, what is the future value of the following cash flows stream:

Year Cashflow Future Value

1 1002 2003 250

4 200

5 400


Nominal vs. Effective Rates

Nominal Rate - Effective Rate -

What’s the difference?

1Rate Nominal

1

m

mEAR


Nom. vs. Eff. Rate Examples

Ex. #1: A bond pays 7% interest semi-annually, what is the effective yield on the bond?

A credit card charges 1.65% per month (APR=19.8%), what rate of interest are they effectively charging?

What nominal rate would produce an effective rate of 9.25% if the security pays interest quarterly?


Amortization Amortized Loan -

Ex. Suppose you borrow $10,000 to start up a small business. The loan offers a contract interest rate of 8.5%, and must be repaid in equal, annual installments over the next 4 years. How much is your annual payment?

What percentage of your payments go toward the repayment of principal in each year?


Amortization Schedules

Year Beg. Bal. PMT INT PRIN End. Bal.

1 $10,000

2

3

4

Year #1, Principal % =Year #2, Principal % =Year #3, Principal % =Year #4, Principal % =


Continuous Compounding

Definition/Description -

inninn eFV

e

FVPV

inn ePVFV


What is the present value of $200 to be received 2 years from today, if the discount rate is 9% compounded continuously?

How much more would the cash flow be worth if the discount rate were 9% compounded annually?

What is the future value, in 10 years, of a $5,000 investment today, if the interest rate is 8.75% compounded continuously?

How much lower would the future value be if the interest rate were 8.75% compounded annually?

Does Compounding Matter?

Real Estate Investments David M. Harrison, Ph.D. Texas Tech University TVM - Compounding $ TodayFuture $ Discounting Time Value of Money.

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