Module 3--Time Value of Money

Question 1

What is concept of the “Time Value of Money”?

Answer 1

Present value (PV) will increase to a future value (FV)
with the inclusion of time (N) and interest rate (%i).

■ Money in the past / money today / money in the future – Money in hand today is worth more than money promised at some future time, because it can be invested with interest and grow over time.

■ Opportunity costs and lost earnings potential – Opportunity costs and lost earnings potential should influence decisions.
* Opportunity costs refers to what is given up when a decision is made (the trade-off).
* The lost earnings potential is the opportunity cost.
* When an option is chosen from alternatives, the opportunity cost is the “cost” incurred by not
enjoying the benefit associated with the best alternative choice.

■ Applications of TVM in business / HR decisions – The application of TVM principles to business/
HR decisions is now commonplace.

■ Calculations easier now – Present-value tables, calculators, spreadsheets and Internet calculators
have made calculations easy.

Question 2

What are the four componenets of TIME VALUE OF MONEY

Answer 2

1. Present Value
2. Future Value
3. Time Time Period
4. The interest rate

Question 3

What is the underlying principle of the TIME VALUE of MONEY

Answer 3

COMPOUNDING INTEREST

Question 4

What is COMPOUNDING INTEREST

Answer 4

COMPOUNDING INTEREST sit he given interest upon interest, year after year.

Question 5

What is “OPPORTUNITY COST”?

Answer 5

Strait present value/future value analysis.

Question 6

What is the formula to compute future value?

Answer 6

Future value = the principle plus the principle times the percentage interest rate.

FV=PV(1+%i) N

Question 7

Why is the Value of Money over Time of Interest?

Answer 7

Why the Value of Money Over Time is of Interest
■ Savings account planning
* Wedding fund
* College savings fund
* Home purchase fund
* Retirement savings fund
■ Alternative purchase and investment decisions
* Home ownership
* Personal computer
* Automobile
– Direct purchase (cash)
– Bank loan
– Lease
– Balloon payment
■ Equities vs. fixed income investing
* Equities (stocks) vs. fixed income (bonds)
– Capital gains
– Dividend streams
– Yield to maturity
– Par value and coupon interest

Question 8

What are the applications of Time Value of Money to Compensation Problem Solving?

Answer 8

Applications to Compensation Problem Solving

■ Growth rate of base salary costs – Formulas can be applied to determine growth rate (e.g., sales,
population, participation, salaries, costs).

■ Executive compensation payments – Assess value of current vs. future compensation and benefits to negotiate an employment offer.
* Sign-on bonuses
* Long-term cash bonuses
* Termination payouts
* Deferred compensation plans

■ Employee incentive plans – Determine current funding requirements to pay for incentive plan payments to be made in the future.

Question 9

What is Compound Interest?

Answer 9

Compound Interest

■ Compounding – The process of finding future values (of a payment or a series of payments) is called compounding.

■ Compound vs. simple interest
* Simple interest – Interest is applied at the end of the period and only on the beginning
balance or principal.
* Compound interest – Interest is applied during the period, which results in a return not only
on the principal amount but also on the interest (thus, interest on interest, or compounding).
The interest is applied at certain intervals or frequencies (i.e., monthly, quarterly) during the
total time interval being studied.

Question 10

What is PEMDAS?

Answer 10

PEMDAS
* Parenthesis ()
* Exponent y^x
* Multiply x
* Divide /
* Add
* Subtract

Question 11

Future Value Definition/Formula

Answer 11

Future Value Definition/Formula

■ The formula provides a means of seeing the future value (FV) of an investment (PV) that receives
compound interest (% i) over a period of time (N).

■ Utilizing this formula to calculate future value, given that you have any three of the four variables
(FV, PV,% i, N), you can solve for the missing fourth variable.

Question 12

How to Calculate of Future Value

Answer 12

FV= PV (1+%i) N

Calculation of Future Value
PV = Present value
% i = Interest rate per period
N = Number of periods
FV = Future value

Question 13

Compute using the “Future Value” (FV) formula in a spreadsheet

PV = 1,000
RATE = 4% per period
Nper = 2 (years)
FV =

Answer 13

We know three of the four variables, so we can solve for the unknown variable FV.
PV = 1,000
RATE1 = 4% per period
Nper2 = 2 (years)
FV = ?

Question 14

Calculation of Future Value

Answer 14

1. Select a blank cell and click the Insert Function (fx) button located just above the
   column header.
2. Select FV for future value.
3. For Rate, enter .01 for 1% per period (quarter).
4. For Nper, enter 8 for 8 periods (quarters).
5. For Pmt, enter 0 as there are no additional payments to be made in this example.
6. For Pv, enter -1,000 as the amount you are investing (you are giving 1,000 to the bank so the
   amount is entered as a deficit).
7. For Type, leave blank because it is not applicable.
8. Click OK, and the results will appear in the selected cell.
   Formula: = FV(0.01,8,0,-1000)
   Answer: 1,082.86

Question 15

How do you calculate Present Value

Answer 15

■ Future value process in reverse
* Present value is the future value process in reverse.
* It’s the inverse of compounding and involves removing or unraveling compound interest.
* How do you determine the amount of money you need to invest today in order to realize a
specific future value?

■ PV = FV / (1 + %i )N
* Present value calculations reflect the economic trade-off between money received
today versus a future date, based on a length of time involved and the available earnings
opportunity.
* The greater the %i, the smaller the PV needs to be.
* The greater the N (i.e., the further in the future a sum is to be received), the less you have to
invest at the current time.

Question 16

How do you calculate Compound Interest

Question 17

What is Compound Salary Growth Rate

Answer 17

Compound Salary Growth Rate

What is it?

A special case of compound interest that helps determine the rate at which a salary has grown.

Question 18

What is the Rule of 72?

Answer 18

Financial Concept. How many years does it take double

Years to double = 72
——————
Growth Rate

What is it?
■ The rule of 72 is a commonly used concept in finance, allowing quick calculations of compound interest.

■ The rule of 72 is an approximation. As the interest rate (or growth rate) increases, the rule becomes less accurate. For practical purposes, it usually provides a reasonable approximation until the interest rate begins to approach or exceed 20%. For lower interest rates, it is generally very accurate.
What are its applications?

■ The rule of 72 provides a good approximation of how long it will take to double something, given a specified constant interest rate.

■ It is a valuable tool for understanding investments in financial planning processes.

Question 19

Using the Rule of 72 to Determine Time to Double

Answer 19

■ Note that by solving for the number of periods (Nper) in a spreadsheet, you can determine that the actual number years for Pierre’s salary to double is 5.89830503, given a compound salary growth rate (CSGR) of 12.47. Thus, 5.77 years is a reasonably good approximation to the actual value of 5.90 (rounded).

■ The rule can be tested by selecting a value for PV (such as 25,000*) and a value for FV that is double the value for PV (such as 50,000), and letting RATE equal .1247. The resulting value will be
Nper = 5.90 (rounded).

Question 20

What is Constant Midpoint Progression

Answer 20

Constant Midpoint Progression
■ Use the RATE formula in a spreadsheet – When constructing salary ranges, we can use RATE formula to calculate a constant midpoint progression, as we did when calculating the interest rate.
■ Use salary grade and survey midpoints – Use the four salary grades provided along with survey average salary.
■ Calculate between lowest and highest midpoints – Calculate a constant midpoint progression
between the lowest and the highest midpoints.

Question 21

What is an Annuity?

Answer 21

■ Definition – an investment that pays on a scheduled basis over a fixed amount of time
* A series of regular periodic payments comprising principal and interest that lead to a predetermined amount in the future
* A stream of equal cash flows delivered over some finite period of time (a perpetuity* that ends)
* A series of future cash flows (i.e., payments, receipts, deposits or withdrawals)

■ Examples
* Mortgage payment – 1,200 monthly payment paid over 30 years
* Lottery – win 1,000,000 jackpot and get paid in 20 annual payments
* Retirement annuity – pension payment of 800 received on the first of every month, beginning at age 65 and continuing for the lifetime of the retiree
* Perpetuity is a cash flow without a fixed end point or time period.

Question 23

Q1 Which of the following should be used to determine the amount of interest earned on money over a specified period of time?
A. Percent difference
B. Percent adjustment
C. Compound interest
D. Compa-ratio

Answer 23

C. Compound interest

Question 24

Q2. How much interest will you earn on 2,500 in three years, if the interest rate is 6%, and the interest is compounded annually? This problem may require a basic calculator.
A. 309.00
B. 477.54
C. 489.05
D. 977.54

Answer 24

477.54

Question 25

Q3. You start with 1,800 in your savings account. You do not make any deposits or withdrawals and
you earn 10% interest, compounded quarterly. How much money will you have in your account
after five years? This problem may require a basic calculator.
A. 1,149.51
B. 2,674.71
C. 2,898.92
D. 2,949.51

Answer 25

D. 2,949.51

Question 26

Q4. You have been asked to comment on a proposed provision in the union contract. Over the next three years, management proposes increases of 2.0%, 2.5%, 3.0% over the three-year life of the
contract. The union negotiator insists that it be 3%, 2.5%, 2.0%. Assuming the hourly rate for a job class is 12.50/hr., what is the rate in three years?

A. It will be 13.46 after three years.
B. Management rate is higher.
C. Union rate is higher.
D. Cannot calculate.

Answer 26

A. It will be 13.46 after three years.

Question 27

Q5. Makayla’s salary has grown at a rate of 7.3% per year for the past six years. If her increases remain the same, how long will her salary take to double?
A. 9.86 years
B. 10.42 years
C. 13.20 years
D. 27.10 years

Answer 27

A. 9.86 years

Question 28

Q6. You have the following salary grades and midpoints. Your organization wants to have a constant midpoint progression.

GRADE Midpoint
10 2,000
11 2,217
12 2,456
13 2,698

What would be the midpoint percentage?
A. 8.0%
B. 9.6%
C. 10.5%
D. 11.7%

Answer 28

C. 10.5%

Question 29

Q7. Which of the following describes an annuity?

A. What is given up when an investment decision is made
B. An investment that pays on a scheduled basis over a fixed amount of time
C. Interest that is applied at the end of the period and only on the beginning balance or principle.

Answer 29

B. An investment that pays on a scheduled basis over a fixed amount of time