04 eind4303 time value of money

1

Dr. Sadiq AbdelallAssistant Professor Industrial Engineering DepartmentIslamic University of Gaza

Money‐time Relationships and Equivalence

CHAPTER 4

Dr. Sadiq AbdelallAssistant Professor Industrial Engineering DepartmentIslamic University of Gaza Page 2

Objective

The objective of Chapter 4 is to explain time value of money calculationsand to illustrate economic equivalence.

2


Money

Medium of Exchange

Means of payment for goods or services;

What sellers accept and buyers pay;

Store of Value

A way to transport buying power from one time period to another;

Unit of Account

A precise measurement of value or worth;

Allows for tabulating debits and credits;


Capital

Capital refers to wealth in the form of money or property that can beused to produce more wealth.

Engineering economy studies involve the commitment of capital forextended periods of time.

A dollar today is worth more than a dollar one or more years from now(for several reasons)

3


Cash flow comparisons

Gives information about magnitude and timing of costs and benefits.

Needed for all kinds of decision making

We compare cash flows to decide which cash flow is better for us.

Example: Buying a car alternatives:

$18,000 now, or

$600 per month for 3 years (= $21,600 total)

Which is better?

It depends!

Issue: how much is money now worth compared to money in the future?

In other words: it depends on the interest rate at the moment.

This leads to idea of Time value of money!


Time value of money

Would you rather have:

$100 today, or

$100 a year from now?

Basic assumption:

Given a fixed amount of money, and

A choice of having it now or in the future,

Most people would prefer to have it sooner rather than later because:

Security

Interests

Currency strength

Uncertainty

4


What this means for us

In this chapter, we will learn methods to:

Compare different cash flows over time

Using the interest rate or discount rate:

How much more a dollar today is worth, compared to a dollar in one year

For example, if the interest rate is 5%:

Then $1 today is worth as much as $1.05 next year


Why Consider Return to Capital?

Return to capital in the form of interest and profit is an essentialingredient of engineering economy studies.

Interest and profit pay the providers of capital for forgoing its use duringthe time the capital is being used.

Interest and profit are payments for the risk the investor takes in lettinganother use his or her capital.

Any project or venture must provide a sufficient return to be financiallyattractive to the suppliers of money or property.

5


Interest

Interest

The fee that a borrower pays to a lender for the use of his or her money.

Interest rate

The percentage of money being borrowed that is paid to the lender on some timebasis.


Simple Interest

When the total interest earned or charged is linearly proportional to theinitial amount of the loan (principal), the interest rate, and the numberof interest periods, the interest and interest rate are said to be simple.

When applied, total interest “I” may be found by

I = ( P ) ( N ) ( i ), where

P = principal amount lent or borrowed

N = number of interest periods ( e.g., years )

i = interest rate per interest period

6


Simple Interest

If $1,000 were loaned for three years at a simple interest rate of 10%per year, the interest earned would be

I = ( P ) ( N ) ( i )

I = 1,000 x 3 x 0.1 = $ 300

So, the total amount repaid at the end of three years would be theoriginal amount ($ 1,000) plus the interest ($ 300)

$ 1,000 + $ 300 = $ 1,300


Compound Interest

Whenever the interest charge for any interest period is based on theremaining principal amount plus any accumulated interest charges up tothe beginning of that period.

Period Amount OwedBeginning of period

Interest amount for period @ 10%

Amount Owed at the end of period

1 $ 1,000 $ 100 $ 1,100

2 $ 1,100 $ 110 $ 1,210

3 $ 1,210 $ 121 $ 1,331

7


Simple and Compound Interest


Concept of Equivalence

Economic equivalence allows us to compare alternatives on a commonbasis.

Established when we are indifferent between a future payment, or aseries of future payments, and a present sum of money .

Each alternative can be reduced to an equivalent basis depending on:

interest rate;

amounts of money involved;

timing of the affected monetary receipts and/or expenditures;

Using these elements we can “move” cash flows so that we cancompare them at particular points in time

8


Concept of Equivalence

Suppose you have a $17,000 balance on your credit card. So you decideto repay the 17,000 debt in four months. An unpaid credit card balanceat the beginning of a month will be charged interest at the rate of 1% byyour credit card company. For this situation, we have three plans torepay the $17,000 principle plus interest owed.


(1)Month

(2)Amount owed at the Begining of month

(3) = 1% x (2)Interest Accrued for month

(4) = (2) + (3)Total owed at the end of month

(6)Total end‐of‐month payment

Plan 1: Pay interest due at end of each month and principle at end of fourth month

1 17,000 170 17,170 170

2 17,000 170 17,170 170

3 17,000 170 17,170 170

4 17,000 170 17,170 17,170

Total 680

Plan 2: Pay off the debt in four equal end‐of‐month installements

1 17,000 170 17,170 4,357.10

2 12,812.90 128.13 12,941.03 4,357.10

3 8,583.93 85.84 8,669.77 4,357.10

4 4,312.67 43.13 4,355.80 4,357.10

Total 427.10

Plan 3: Pay principal and interest in one payment at end of four month

1 17,00 170 17,170 0

2 17,170 171.70 17,341.70 0

3 17,341.70 173.42 17,515.12 0

4 17,515.12 175.15 17,690.27 17,690.27

Total 690.27

9


Cash Flow Diagrams / Table Notation

Notation used in formulas for compound interest calculations.

i = Effective interest rate per interest period

N = Number of compounding (interest) periods

P = Present Worth: present sum of money equivalent value of one or more cashflows at a reference point in time; the present

F = Future Worth: future sum of money: equivalent value of one or more cashflows at a reference point in time; the future

A = Annual Worth: end‐of‐period cash flows in a uniform series continuing for acertain number of periods, starting at the end of the first period and continuingthrough the last


Cash Flow Diagram

A cash flow diagram is an indispensable tool for clarifying and visualizinga series of cash flows.

10


Cash Flow Diagram

Example 4.1


Cash Flow Table

Example 4.2

11


Finding F when Given P

Finding future value when given present value

F = P ( 1+i )N

(1+i)N single payment compound amount factor

functionally expressed as F = ( F / P, i%, N )

predetermined values of this are presented in column 2 of Appendix C of text.


Finding F when Given P

Example 4.3

Exercise 4.11

12


Finding P when Given F

Finding present value when given future value

P = F (1+i)‐N

(1+i)‐N single payment present worth factor

functionally expressed as P = F ( P / F, i%, N )

predetermined values of this are presented in column 3 of Appendix C of text;


Finding P when Given F

Example 4.4

Exercise 4.14

04 eind4303 time value of money

Documents

idea of time value of

form of money

suppliers of money

time period

providers of capital

use duringthe time

store of value

discount rate