Time Value of Money and Integrated Case

Integrated Case
5-42

First National Bank

Time Value of Money Analysis
You have applied for a job with a local bank. As part of its evaluation process, you must take an examination on time value of money analysis covering the following questions.
A.

Draw time lines for (1) a $100 lump sum cash flow at the end of Year
2, (2) an ordinary annuity of $100 per year for 3 years, and (3) an uneven cash flow stream of -$50, $100, $75, and $50 at the end of
Years 0 through 3.

ANSWER: [Show S5-1 through S5-4 here.] A time line is a graphical representation that 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
1
I/YR%
|
|

2 Year
|
100 Cash flow

Lump sum

0
1
I/YR%
|
|
100

2
|
100

3
|
100

Annuity

0
1
I/YR%
|
|
-50
100

2
|
75

3
|
50

Uneven cash flow stream

A lump sum is a single flow; for example, a $100 inflow in Year
2, as shown in the top time line.

Chapter 5: Time Value of Money

Integrated Case

1

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 that do not constitute an annuity, as in the lower time line. -50 represents a cash outflow rather than a receipt or inflow.
B.

(1) What’s the future value of $100 after 3 years if it earns 10%, annual compounding? ANSWER: [Show S5-5 through S5-7 here.] Show dollars corresponding to question mark, calculated as follows:
0
10%
|
100

1
|

2
|

3
|
FV = ?

After 1 year:
FV1 = PV + I1 = PV + PV(I) = PV(1 + I) = $100(1.10) = $110.00.
Similarly:
FV2 = FV1 + I2 = FV1 + FV1(I)
= FV1(1 + I) = $110(1.10) = $121.00
= PV(1 + I)(1 + I) = PV(1 + I)2.
FV3 = FV2 + I3 = FV2 + FV2(I)
= FV2(1 + I) = $121(1.10) = $133.10
= PV(1 + I)2(1 + I) = PV(1 + I)3.
In