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