©2012, College for Financial Planning, all rights reserved.

Module 3Time Value of Money

Foundations in Financial PlanningSM Professional Education Program

Learning Objectives

3–1: Identify the effect that rate assumptions can have on goal achievement.

3–2: Explain the relationship between time value of money variables.

3–3: Calculate a present or future value for a situation.

3–4: Calculate the interest rate per compounding period for a situation.

3–5: Calculate the number of compounding periods for a situation.

3–6: Calculate the periodic payment for a situation.

3-2

Questions To Get Us Warmed Up

3-3

Time Value of Money

• Value of money changes over time

• The importance of future assumptions

3-4

Time Value of Money Concepts

3-5

Solving for Variables

N = number of compounding periodsI/YR = interest ratePV = present valueFV = future valuePMT = payment

With most time value of money problems, three values are given and solve for the fourth. Some provide four and solve for a fifth.

3-6

$1,000 earns 8% for 3 years = ?

Future Value for a Single Sum

3-7

Year

1 ($1,000)(1+.08) = $1,080

2 ($1,080)(1+.08) = $1,166.40

3 ($1,166.40)(1+.08)

= $1,259.71

$1,000 × 1.2597 = $1,259.70

Present Value of a Single Sum

If $1,000 is needed in 3 years, @ 8% how much must be set aside now?

3-8

Year

1 ($1,000) ÷ (1.08)

= $925.93

2 ($925.93) ÷ (1.08)

= $857.34

3 ($857.34) ÷ (1.08)

= $793.83

$1,000 × 0.7938

= $793.80

TVM Relationships: PV & FV

• Frequency of compounding/discounting periods

• Compound/discount rate• Frequency of payments• Timing of payments (ordinary annuity vs.

annuity due)

3-9

Common Errors Using Calculators

• Not clearing the calculator correctly• Not correctly adjusting for ‘N’ and ‘I/YR’

for problems other than annual compounding or discounting

• Calculating an annuity due instead of an ordinary annuity and vice versa

• Not checking for reasonableness

3-10

Future Value of a Lump Sum

You are provided:• PV = present value• I/YR = interest rate

(rate of return)• N = number of

compounding or discounting periods (e.g., years, quarters)

• Solve for FV

3-11

Present Value of a Future Lump Sum

You are provided:• FV = future value• I/YR = interest rate

(rate of return)• N = number of

periods (e.g., years)• Solve for PV

3-12

Present Value Ordinary Annuity

You are given:• PMT = payment• I/YR = interest rate

(rate of return)• N = number of periods

(e.g., years)• Calculator should be

in ‘END’ mode• Solve for PV

3-13

Present Value Annuity Due

You are given:• PMT = payment• I/YR = interest rate

(rate of return)• N = number of

periods (e.g., years)• Calculator should be

in ‘BEGIN’ mode• Solve for PV

3-14

Future Value Ordinary Annuity

You are given:• PMT = payment• I/YR = interest rate

(rate of return)• N = number of periods

(e.g., years)• Calculator should be in

‘END’ mode• Solve for FV

3-15

Future Value Annuity Due

You are given:• PMT = payment• I/YR = interest rate

(rate of return)• N = number of

periods (e.g., years)• Calculator should be

in ‘BEGIN’ mode• Solve for FV

3-16

1001rate inflation1

returntax -after1IAIR

Inflation-Adjusted Interest Rate

3-17

Present Value Serial Payment Process

3-18

Today

1.Inflate One Payment Rate of Inflation

3. Discount Step 2 ResultDiscount (Investment) Rate

2. PVAD Serial PMT Calculation Inflation-Adjusted Rate (BEG)

Future

Question 1

If a planner wishes to provide clients with a more conservative estimate of the amount of money that will be required to retire comfortably, he or she shoulda. use a higher rate of inflation.b. use a higher rate of after-tax return.c. use a lower rate of inflation.d. use a lower annual dollar requirement.

3-19

Question 2

Harold Holden invested $750,000 in a real estate investment, requiring at least a 10% return from the transaction. He plans to sell the property when it reaches $1,330,000 in value.

Which one of the following shows how long Harold must hold the property before he expects to reach his goal (use the closest estimate)?

a. 5 yearsb. 6 yearsc. 7 yearsd. 8 years

3-20

Question 3

April Assad asked you, her financial planner, approximately how much she would need to invest today if she was able to earn 6.55% annually on her investments and wanted to accumulate $10,000 to be able to return to school in three and a half years. Which one of the following is the closest answer?a. $6,438b. $7,814c. $8,009d. $9,102

3-21

Question 4

Billy Bowen, a 20-year-old college student, has recently inherited a sum of $20,000 from his deceased Aunt Bertha’s estate. He has expressed to you, as his financial advisor, that he needs some help investing the money. Billy has asked you what kind of annual interest rate he would need to receive in order to have $25,000 in three years when he wants to attend graduate school. You have found several investments that all compound on a quarterly basis.

Which of the following is the interest rate that Billy needs?

a. 7.46%b. 7.51%c. 7.72%d. 7.93%

3-22

Question 5

Fiona Fouts currently has $133,500 in her 401(k) account, which pays an average of 6.85% annually. She has asked you to calculate how much she must contribute at the end of each year for the next 17 years that she plans to be working in order to reach her goal of $500,000. The company does not match Fiona’s contributions.a. $2,656b. $2,714c. $2,899d. $2,979

3-23

Question 6

The inflation-adjusted interest rate is the interest rate earned a. by subtracting inflation from the

earned interest rate.b. after taxes have been paid from an

investment’s earnings.c. by adding the rate of inflation to the

real interest rate and dividing by 12.d. after overcoming the effects of

inflation.

3-24

©2012, College for Financial Planning, all rights reserved.

Module 3End of Slides

Foundations in Financial PlanningSM Professional Education Program