Chapter 3

Question 1

Compounding

Answer 1

Compounding is the ability of an asset to generate earnings, which are then reinvested in order to generate their own earnings. In other words, compounding refers to generating earnings from previous earnings.

Suppose you invest $10,000 into Cory’s Tequila Company (ticker: CTC). The first year, the shares rises 20%. Your investment is now worth $12,000. Based on good performance, you hold the stock. In Year 2, the shares appreciate another 20%. Therefore, your $12,000 grows to $14,400. Rather than your shares appreciating an additional $2,000 (20%) like they did in the first year, they appreciate an additional $2,400, because the $2,000 you gained in the first year grew by 20% too.

Question 2

Compound Interest

Answer 2

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously-accumulated interest.

Question 3

Discounting

Answer 3

A bond can have a par value of $1,000 and be priced at a 20% discount, which is $800. In other words, the investor can purchase the bond today for a discount and receive the full face value of the bond at maturity. The difference is the investor’s return. A larger discount results in a greater return, which is a function of risk.

Question 4

Discounting Rate

Answer 4

A simple explanation of the discount rate used in DCF analysis is as follows. Let’s say you expect $1,000 in one year. To determine the present value of this $1,000 (what it is worth to you today), you would need to discount it by a particular interest rate. Assuming a discount rate of 10%, the $1,000 in a year’s time would be equivalent to $909.09 to you today (1,000 / [1.00 + 0.10]). If you expect to receive the $1,000 in two years, its present value would be $826.45.

1. To find the discount, multiply the rate by the original price.
2. To find the sale price, subtract the discount from original price.

Question 5

Future Value

Answer 5

The future value (FV) is the value of a current asset at a specified date in the future based on an assumed rate of growth over time.

Question 6

Future Value Interest Factor

Answer 6

(1+r)^n

r=  rate per period
n= number or periods

E.g) I want a 5% on my $100 for a year. so (1+.05+^1 =1.05. 1.05*$100= $105.

Question 7

Growth Rate

Answer 7

Growth rates refer to the percentage change of a specific variable within a specific time period, given a certain context. or investors, growth rates typically represent the compounded annualized rate of growth of a company’s revenues, earnings, dividends and even macro concepts such as GDP and the economy as a whole.

Question 8

Lump-Sum Payment

Answer 8

A lump-sum payment is usually taken in lieu of recurring payments distributed over a period of time. The value of a lump-sum payment is generally less than the sum of all payments that you would otherwise receive, since the party paying the lump-sum payment is being asked to provide more funds up front than it otherwise would have been required to.

Question 9

Present Value

Answer 9

Present value (PV) is the current worth of a future sum of money or stream of cash flows given a specified rate of return.

Question 10

Present Value Interest Factor (PVIF)

Answer 10

The formula for calculating the present value interest factor is as follows:

PVIF = a / (1 + r) ^ n

The “a” represents the future sum to be received, “r” represents the discount interest rate, and “n” represents the number of years or other time period.

Each factor in the table is derived from the formula:

PVIF = 1/(1+r)^t

Where r is the interest rate and t is the time period.

In the example, multiplying $1,000 by the formula of 1/(1+6%)^5 gives the same answer of $705.

Question 11

Rule of 72

Answer 11

The ‘Rule of 72’ is a simplified way to determine how long an investment will take to double, given a fixed annual rate of interest. By dividing 72 by the annual rate of return, investors can get a rough estimate of how many years it will take for the initial investment to duplicate itself.

For example, the rule of 72 states that $1 invested at 10% would take 7.2 years ((72/10) = 7.2) to turn into $2. In reality, a 10% investment will take 7.3 years to double ((1.10^7.3 = 2).

Question 12

Time Value of Money (TVIM)

Answer 12

The time value of money (TVM) is the idea that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received.

Question 13

Time Value of Money (TVM)

Answer 13

The time value of money (TVM) is the idea that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received.

Question 14

What are the four basic parts (variables) of the time value of money equation?

Answer 14

The four variables are present value (PV), time stated as the number of periods ( n ), interest rate ( r ), and future value (FV).

Question 15

What does the term compounding mean?

Answer 15

Compounding means that interest earned in a prior period earns interest in the current period

Question 16

Define a growth rate and a discount rate. What is the difference between them?

Answer 16

A growth rate is the annual percentage increase and the discount rate is the annual reduction rate. The difference between a growth rate and a discount rate is the direction of the problem. A growth rate implies going forward in time; a discount rate implies going backward in time.

Question 17

What happens to future value as you increase the interest (growth) rate?

Answer 17

The future value gets larger as you increase the interest rate.

Question 18

What happens to present value as you increase the discount rate?

Answer 18

The present value gets smaller as you increase the discount rate.

Question 19

What happens to future value as you increase the time to the future date?

Answer 19

The future value increases as you increase the time to the future.

Question 20

What happens to the present value as the time to the future value increases?

Answer 20

The present value decreases as you increase the time between the future value date and the present value date.

Question 21

What is the rule of 72?

Answer 21

The Rule of 72 is a simple estimation method for how long it takes something to double in value or size or at a certain growth or interest rate.

Question 22

Is the present value always less than the future value?

Answer 22

Yes, as long as interest rates are positive—and interest rates are always positive—the present value of a sum of money will always be less than its future value. One can get confused with this concept if one thinks about the depreciation of an asset over time. Present value and future value in the TVM equation refer identical cash flows at two different points in time.

Question 23

When a lottery price is offered as $10,000,000 but will pay out a series of $250,000 payments over forty years, is it really a $10,000,000 lottery prize?

Answer 23

The present value of the lottery is not worth $10,000,000. The total payments over time are $10,000,000, but this is not the value of the lottery because these payments are at different points in time and cash flows can only be added if they are at the same point in time.