Time Value Of Money Cap Investments 2 Essay

Submitted By stan5277
Words: 2251
Pages: 10

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)