b320 bf06 time will tell 6th presentation 15nov2010

8/8/2019 B320 BF06 Time Will Tell 6th Presentation 15Nov2010

1/35

BF06: Time will Tell

Time Value of Money

6th Presentation


2/35

Specific Learning Objectives

Explain Time value of money (TVM) concept.

Differentiate between the concepts of discounting

and compounding.

Compute present / future value of multiple cash

flows and annuities.

Apply TVM concept to financial decision-making and

investment decisions.


3/35

Problem Analysis

Alabama Tigers

Sponsorship

Rights

Sell exclusive

rights to sponsorfor a period of

3 years

4 Options : Nikey Ltd

Reeback Ltd

Xtreme Ltd Embro Ltd

How to evaluate these

options with different

methods of payment &

decide which is best?


4/35

If you could choose

Get $1

Today

Or Get $1

in a years time

Option A Option B

Obviously, you would opt for Option A.

One dollar in hand today is worth more than adollar promised some time in the future because of

the returns that could be earned while waiting.


5/35

Recap on Simple InterestSimple interest is calculated only on the beginning

principal.

YearInterest earned per

period

Interest earned per

period

Value of investment at

end of period

Year 1 P x R x T = I1 $100 x 0.03 x 1= $3 P + I1 = $103

Year 2 P x R x T = I2 $100 x 0.03 x 1= $3 P + I1 + I2 = $106

Year 3 P x R x T = I3 $100 x 0.03 x 1= $3 P + I1 + I2 + I3= $109

Year 4 P x R x T = I4 $100 x 0.03 x 1 = $3 P + I1 + I2 + I3 + I4 = $112

Year 5 P x R x T = I5 $100 x 0.03 x 1= $3 P + I1 + I2 + I3 + I4 + I5 = $115

For instance, if you invest $100 at a simple interest rate of

3% per annum, the values of the investment at the end of

each period are as follows (assuming no further inflow or

outflow of the initial amount invested):


6/35

Recap on Compound InterestCompound interest is calculated on the beginning principal

AND the interest accumulated as well.

Year Interest earned per period Interest earned per periodValue of investment at

end of period

Year 1 P x R x T = I1 $100 x 0.03 x 1 = $3 P + I1 = $103

Year 2 (P + I1) x R x T = I2 $103 x 0.03 x 1 = $3.09 P + I1 + I2 =$106.09

Year 3 (P + I1 + I2) x R x T = I3 $106.09 x 0.03 x 1 = $3.18 P + I1 + I2 + I3 =$109.27

Year 4 (P +I1+I2+I3) x R x T = I4 $109.27 x 0.03 x 1= $3.28P + I1 + I2 + I3 + I4

=$112.55

Year 5 (P + I1+I2+I3+I4) x R x T = I5 $112.55 x 0.03 x 1 = $3.38 P + I1 + I2 + I3 + I4+ I5=$115.93

Using the earlier example with the difference of a

compound interest of 3% instead of a simple interest, our

investment of $100 will look like this instead.


7/35

Compound Interest

Using EXCEL function:Step 1 : Click fx on menu bar

Step 2 : Or Click on FV

Step 2 : Type FV on Search for a function

Step 3 : Click OK


8/35

Compound Interest

Using EXCEL function:

Step 4: Enter Rate, No. of periods and PV

Step 5 : Click OK


9/35

If you could choose again

Get $1

Today

Or Get $1.50

in a years time

Option A Option B

How will you decide? Will the $0.50 be enough to

compensate you for the 1 year wait?


10/35

Future ValueOne way to look at this problem is to see whether you are

able to invest the $1 today and get back more than $1.50after a year.

Assuming we could invest the money at 3%, after 1 year we

will be getting:

$1 x (1+r) = $1 x (1.03)

= $1.03

r = interest rate/rate of return/discount rate

Since $1.50 is much more than $1.03, we should choose

option B.


11/35

Future Value



12/35

Present Value

We could also look at how much the $1.50 we will be

getting in a years time is worth to us today.

Assuming we could invest the money at 3%, the 1.50 is worth:

1.50 = 1.46 today

(1+0.03)

Since $1.46 is much more than the $1, we should chooseoption B.


13/35

Present Value



14/35

PV Present Value. What future cash flows are worth today.

FVt Future Value. What cash flows are worth in the future.

r - interest rate, rate of return, discount rate per period

t - number of periods

Basic Present Value Equation

(1+r)tPV =

FVt

FVt = PV (1+r)t

These are the equations we have been using:

PV FV

Compounding

Discounting


15/35

Types of Cash Flows

Unequal Cash Flows

Annuities

Perpetuities

An annuity is a stream of constantcash flows that occur at regular

intervals for a fixed period of time.

Examples include:Student Loan Payments

Insurance Premiums

Annuities


16/35

Types of Cash Flows

Unequal Cash Flows

Perpetuities

To Calculate Present Value/Future Value,

we can consider each individual Cash Flowand discount/compound it to the

present/future value before adding it all

together.

Year 1 Year 2 Year 3 Year 4 Year 5Now

$500 $500 $500 $500$500

Annuities

Annuity Due: Payments or receipts occurat the beginning of each period.

Ordinary Annuity: Payments or receiptsoccur at the end of each period.


17/35

Ordinary Annuity (at end of each period)


Note:The defaultvalue of Type

= 0.Where the

payment is

made at the

endof each

period.


18/35

Annuity Due (at the beginning of each period)


Enter 1 for Type


19/35

Types of Cash Flows

Unequal Cash Flows

Annuities

Perpetuities

For unequal Cash Flows,


$500 $300 $200 $400 $100

To Calculate Present Value/Future Value,

we can consider each individual Cash Flow

and discount it to the present value/future

value before adding it all together.


20/35

Unequal cash flows



21/35

Unequal cash flows



22/35

Types of Cash Flows

Unequal Cash Flows

Annuities

Perpetuities

A perpetuity is an annuity that

lasts forever.


$500 $500 $500 $500 $500

PV of Perpetuity =Cr

C cash flow

r - interest rate, rate of return, discount rate


23/35

Summary - Types of Cash Flows


24/35

Application to Problem

Statement


25/35

We will determine the present value and future value of each of

the options.Nikey Ltd

One time present payment (upfront payment of $20,000,000)

Reeback Ltd

Ordinary Annuity (pay $4,100,000 at the end ofevery six months)Xtreme Ltd

One time future payment (pay at the end of three years)

Embro Ltd

Unequal cash flows (different payments as shown in Table 1)

To decide which option is more attractive, we have to makeassumptions about the rate of return.

To assume interest to be compounded semi-annually

Solving the Problem


26/35

FV Calculation


27/35

FV Calculation


28/35

FV Calculation


29/35

PV Calculation


30/35

PV Calculation


31/35

PV Calculation


32/35

Comparing the Options using

different discount rates

Different assumptions of discount rate made will result in different conclusions.But using either FV or PV will give the same conclusion for the same discountrate.

Future Value

Present Value


33/35

Other factors affecting the cash flow such as the need to payoff loans that are due soon.

Other needs, especially since the company is a young one,

options that provide a cash flow upfront early may be moreattractive.

Consider the uncertainty of the cash flow i.e. the risks

involved for each option especially for the sales forecastprobability.

Consider the current distribution channels, stability andfinancial reputation of the four companies.

Other Considerations


34/35

Concept Diagram

Time ValueOf Money

Interest

Cash flows

Simple or

Compound?

Present

Value

Future

Value

Annuities

Unequal cash

flows

Perpetuity


35/35

ReferencesRecommended Textbooks

Ross, S.A., Westerfield, R.W., & Jordan, B.D. (2008). Corporate Finance Fundamentals (8th ed.) [Chapter 5,

pp.122-140 & Chapter 6, pp. 146-170]. New York: McGraw-Hill Irwin

Reference Textbooks

Brealey, R.A.,Myers, S.C., & Marcus A.J. (2007). Fundamentals of Corporate Finance, Time Value of Money

(5th ed.) New York: McGraw-Hill Irwin. [Chapter 4]

Block, S.B., Hirt, G.A. (2008). Foundations of Financial Management, Time Value of Money(12th ed.) New

York: McGraw-Hill Irwin. [Chapter 9]

Brigham, E.F. & Houston, J.F. (2007). Fundamentals of Financial Management, Time Value of Money

(Concise 4th ed.). Thomson South-Western. [Chapter 6]

Websites

The Time Value of Money. (n.d.) Retrieved October 10, 2010, from TeachMeFinance.com website:

http://teachmefinance.com/timevalueofmoney.html

Understanding the Time Value of Money. (n.d.) Retrieved October 10, 2010, from Investopedia.comwebsite: http://www.investopedia.com/articles/03/082703.asp

NetMBA Business Knowledge Center. (n.d.) Retrieved October 10, 2010 from netmba.com website:

http://www.netmba.com/finance
http://teachmefinance.com/timevalueofmoney.htmlhttp://www.investopedia.com/articles/03/082703.asphttp://www.netmba.com/financehttp://www.netmba.com/financehttp://www.investopedia.com/articles/03/082703.asphttp://teachmefinance.com/timevalueofmoney.html

b320 bf06 time will tell 6th presentation 15nov2010

Documents