Chapter 4: Time Value Of Money

Question 1

What is a stream of cash flows?

Answer 1

A series of cash flows lasting several periods.

Question 2

How can we represent a stream of cash flows

Answer 2

We can represent a stream of cash flows on a timeline, a linear representation of the timing of the expected cash flows.

Question 3

Why are timelines important in finance?

Answer 3

Timelines are an important first step in organizing and then solving a financial problem.

Question 4

What does Date 0 on a timeline represent? What do Dates 1 and 2 signify?

Answer 4

Date 0 represents the present. Date 1 signifies one year later (end of the first year) and Date 2 signifies two years later (end of the second year).

Question 5

How can you differentiate between inflows and outflows on a timeline?

Answer 5

Inflows are positive cash flows, while outflows are negative cash flows.

Question 6

Provide an example of inflows and outflows on a timeline.

Answer 6

Lending $10,000 today (outflow: -$10,000) and receiving $6,000 at the end of each of the next two years (inflows: +$6,000 each).

Question 7

Why should you draw a timeline for every financial problem?

Answer 7

Drawing a timeline helps avoid overlooking important events and prevents flawed financial decisions.

Question 8

How can timelines represent rental or tuition payments?

Answer 8

Timelines can show cash flows at specific intervals, such as monthly for rent or semesterly for tuition, by labeling each period accordingly.

Question 9

What are the three rules of time travel in financial decision-making?

Answer 9

Only cash flow values at the same point in time can be compared or combined.

To move a cash flow forward in time, you must compound it.

To move a cash flow backward in time, you must discount it.

Question 10

What does Rule 1 of time travel state?

Answer 10

Only cash flow values at the same point in time can be compared or combined. This is because a dollar today is not equivalent to a dollar in the future due to the time value of money.

Question 11

How do you move a cash flow forward in time according to Rule 2?

Answer 11

To move a cash flow forward in time, you must compound it by multiplying by the interest rate factor

(1+𝑟)

Question 12

What is the formula to compute the future value of a cash flow in n periods?

Answer 12

Question 13

How do you move a cash flow backward in time according to Rule 3?

Answer 13

To move a cash flow backward in time, you must discount it by dividing by the interest rate factor

(1+𝑟)

Question 14

What is the formula to compute the present value of a cash flow in n periods?

Answer 14

Question 15

What is the Rule of 72?

Answer 15

The Rule of 72 is a simple way to estimate how long it will take for an investment to double in value.

Divide 72 by the annual interest rate to find the approximate number of years.

Question 16

How is simple interest different from compound interest?

Answer 16

Simple interest is earned only on the original principal, while compound interest is earned on both the principal and the accumulated interest.

Question 17

What is the effect of compounding on the future value of an investment over a long period?

Answer 17

Compounding can lead to exponential growth, significantly increasing the future value of an investment over tim

Question 18

How does the composition of interest change over time with compounding?

Answer 18

Over time, the cumulative interest on interest (compound interest) becomes larger than the simple interest (interest on the original principal).

Question 19

Calculate the future value of $1000 in an account paying 10% interest per year for 7, 20, and 75 years.

Answer 19

Question 20

How can you apply the rules of time travel to compute the value of three $1000 savings deposits at the end of three years with a fixed 10% interest rate?

Answer 20

Question 21

How do you compute the present value of a stream of cash flows?

Answer 21