Chapter 2
Time Value of Money
MINI CASE
Assume that you are nearing graduation and that you have applied for a job with a local bank. As part of the bank's evaluation process, you have been asked to take an examination which covers several financial analysis techniques. The first section of the test addresses discounted cash flow analysis. See how you would do by answering the following questions. a.

Draw time lines for (a) a $100 lump sum cash flow at the end of year 2, (b) an ordinary annuity of $100 per year for 3 years, and (c) an uneven cash flow stream of -$50, $100, $75, and $50 at the end of years 0 through 3.

Answer: (Begin by discussing basic discounted cash flow concepts, terminology, and solution methods.) A time line is a graphical representation which is used to show the timing of cash flows. The tick marks represent end of periods (often years), so time 0 is today; time 1 is the end of the first year, or 1 year from today; and so on.
0
|

i%

1

2

|

|

year

lump sum
100
0

cash flow

i%

1

2

3

|

|

|

100

|

100

100

1

2

3

|

|

|

75

50

annuity
0
|

i%

uneven cash flow stream
-50
100

A lump sum is a single flow; for example, a $100 inflow in year 2, as shown in the top time line. An annuity is a series of equal cash flows occurring over equal intervals, as illustrated in the middle time line. An uneven cash flow stream is an irregular series of cash flows which do not constitute an annuity, as in the lower time line. -50 represents a cash outflow rather than a receipt or inflow.

Mini Case: 2 - 1

b.

1. What is the future value of an initial $100 after 3 years if it is invested in an account paying 10 percent annual interest?

Answer: Show dollars corresponding to question mark, calculated as follows:
0
|

10%

1

2

3

|