Time Value of Money

1

Cash Flows
• Cash flows include:
– Future cash revenue
– Any future savings in ongoing cash operating costs – Any future residual value of the asset

2

Time Value of Money
• Invested money earns income over time
• Cash received sooner preferred over being received later

3

Time Value of Money Factors
– Principal amount (p)
• Single lump sum
• Annuity
– Number of periods (n)
– Interest rate (i)
• Simple interest
• Compound interest

4

Simple Interest Calculation
Simple interest means interest is calculated only on the principal amount.
Simple Interest

Year
1
2
3
4
5

Interest Calculation
$10,000 x 6% =
$10,000 x 6% =
$10,000 x 6% =
$10,000 x 6% =
$10,000 x 6% =
Total Interest

Simple Interest
$600
$600
$600
$600
$600
$3,000

5

Compound Interest Calculation
Compound interest means interest is calculated on the principal and on all interest earned to date
Compound Interest
Year

Compound Interest Calculation

1
2
3
4
5

$10,000 x 6% =
($10,000 + 600) x 6% =
($10,000 + 600 + 636) x 6% =
($10,000 + 600 + 636 + 674) x 6% =
($10,000 + 600 + 636 + 674 + 715) x 6% =
Total Interest

Simple interest =
Compound interest =

Compound Interest

$ 600
$ 636
$ 674
$ 715
$ 758
$ 3,383

$3,000
$3,383
$383 extra interest from compounding
6

Present Value & Future Value

Principal + Compound interest = $13,383 from last slide
Using table $10,000 x 1.338 = $13,380
7

Future Value of an Annuity
What if I invest $2,000 each year for 5 years instead of $10,000 all at once? Future value = Amount of each cash installment (Annuity FV factor for i = 6%, n = 5)
= $2,000 (5.637)
= $11,274
8

Compare Retirement Savings Plan—
Req #1 – assume you are 22
Exercise: 2 strategies from which to choose:
(1) save $3,000 a year starting now for 30 years or
(2) wait until you are 40 to start saving and then save
$7,500 per year for the next 12 years.
Assume that you will earn an average of 10% per year.
1. How much out-of-pocket cash will you invest under the two options?

Option 1: $3,000 x 30 years = $90,000
Option 2: $7,500 x 12 years = $90,000
9

Compare Retirement Savings Plans—
Req #2
2. How much savings will you have accumulated at age 52 under each option?
Plan 1
Future value = Payment x (Annuity FV factor, i = 10%, n = 30)

= $3,000 x 164.494
= $493,482
Plan 2
Future value = Payment x (Annuity FV factor, i = 10%, n = 12)

= $7,500 x 21.384
= $160,380
10

Compare Retirement Savings Plans — what is your plan worth at 62?
Plan 1
Future value of $1 = present value x table factor
= $493,482 x 2.594
= $1,280,092
Plan 2
Future value of $1 = present value x table factor
= $160,380 x 2.594
= $416,026
11

Fund Future Cash Flows
Katherine wants to take the next five years off work to travel around the world. She estimates her annual cash needs at $30,000 (if she needs more, she will work odd jobs). Katherine believes she can invest her savings at 8% until she depletes her funds.

Req. 1 – What to invest now?
Present value of annuity = Payment x table factor
= $30,000 x 3.993
= $119,790
Req. 2 – What to invest if only earn 6%?
Present value of annuity = Payment x table factor
= $30,000 x 4.212
= $126,360
12

Choosing a Lottery Payout Option
(assume 8%)
Option 1: $12,000,000 five years from now

Option 2: $2,250,000 at end of each year for 5 yrs

Option 3: $10,000,000 three years from now

13

Choosing a Lottery Payout Option
(assume 8%)
Option 1: $12,000,000 five years from now
Present value of $1
= $12,000,000 x .681
= $8,172,000
Option 2: $2,250,000 at end of each year for 5 yrs
Present value annuity = $2,250,000 x 3.993
= $8,984,250
Option 3: $10,000,000 three years from now
Present value of $1
= $10,000,000 x .794
= $7,940,000
14

Four Popular Methods of Capital
Budgeting Analysis
Method
Payback period
Accounting Rate of Return (ARR)
Net Present Value (NPV)
Internal Rate of Return (IRR)

Advantage/Disadvantage
Quick and easy to calculate, used for shorter life span investments More difficult to calculate, used for longer