Review of The Time Value of Money

1

Reference: Lawrence J. Gitman

“Principles of Managerial Finance” (12th edition),

Chapter 4

Professor Medhat Hassanein

Review of: The Time Value of Money

Future value of a single amount:

Example: if you place $ 100 in savings account paying 8%interest compounded annually. What would be the sum ofmoney in your account at the end of one year?

Solution

Future value = present value + present value X the annualinterest

= 100 + 100(.08)

= 100 + .08

= $ 108

= 100 [1 + .08]

= principal [1 + interest rate]2

Review of: The Time Value of Money

3

Review of: The Time Value of Money

4

Review of: The Time Value of Money

5

Review of: The Time Value of Money

6

Review of: The Time Value of Money

7

Review of: The Time Value of Money

8

Review of: The Time Value of Money

9

Review of: The Time Value of Money

10

* The difference is due to approximation of decimal points

Review of: The Time Value of Money

11

Review of: The Time Value of Money

Finding the present value of an ordinary annuity…Cont’d

Therefore: 20,000 is a cash flow concept not a profit concept.

The 20,000 each year will include: a return of 10% on yourinvestment and returning part of your initial investment whichis the $ 49,740.

In order to understand this cash flow concept, refer to theappendix of this Review.

12

Review of: The Time Value of Money

Find the future of an annuity due:

Assume that in the example of the ordinary annuity youchanged the pattern of saving i.e. instead of saving at the endof each year you decided to save at the beginning of eachyear. What will be the amount of savings at the end of threeyears?

Solution:

Your savings will increase by (1 + .07) i.e. 3,215 (1 +.07) =$3,440.05

Let us see how?

13

Review of: The Time Value of Money

14

Review of: The Time Value of Money

Find the present value of an annuity due:

Suppose that the owner of the accessories shop will generatethe $ 20,000 cash flow at the beginning of each year insteadof the end of each year, what is the amount of initialinvestment you have to invest in the purchase of this offer?

Solution:

The answer is 49,740 (1 + .10) = $ 54,714

Let us see how?

15

Review of: The Time Value of Money

16

Review of: The Time Value of Money

Appendix: the accessories shop investment exercise:

To see how much of the annual $ 20,000 cash flow contains the 10% returnon your investment and how much each year you return portion of the initialinvestment of the $ 49,740. Refer to the loan amortization exercise.

Solution:

Construct the following table:

17

Years Principal(Initial Investment)

Cash flow(annual)

Return(10%)

Repay of I.I. Balance unpaid

$ $ $ $ $

1 49,740 20,000 4,974 15,026 34,714

2 34,714 20,000 3,471 16,529 18,185

3 18,185 20,000 1,818 18,183

10,263 49,740

60,003