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Pertemuan 12

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

Time Value of Money

Business investments Business investments extend over long periods extend over long periods of time, so we must of time, so we must recognize the time value recognize the time value of money.of money.

Investments that promise Investments that promise returns earlier in time are returns earlier in time are preferable to those that preferable to those that promise returns later in promise returns later in time.time.

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

Time Value of Money

A dollar today is worth A dollar today is worth more than a dollar a more than a dollar a

year from now since a year from now since a dollar received today dollar received today

can be invested, can be invested, yielding more than a yielding more than a

dollar a year from now.dollar a year from now.

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

If $100 is invested today at 8% interest, how much will you have in two years?

At the end of one year: At the end of one year: $100 + 0.08 $100 + 0.08 $100 = (1.08) $100 = (1.08) $100 = $100 =

$108$108At the end of two years: (1.08)$108 = $116.64$116.64

or

(1.08)2 × $100 = $116.64

Interest and the Time Value of Money

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

Interest and the Time Value of Money

If If PP dollars are invested today at dollars are invested today at the annual interest rate the annual interest rate rr, then in , then in nn years you would have years you would have FFnn dollars dollars

computed as follows:computed as follows:

FFnn = P(1 + r) = P(1 + r)nn

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

The The present valuepresent value of any sum to of any sum to be received in the future can be be received in the future can be computed by turning the interest computed by turning the interest formula around and solving for P:formula around and solving for P:

(1 + r)(1 + r)nnP = FP = Fnn11

Interest and the Time Value of Money

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

Time Value of Money

RatePeriods 10% 12% 14%

1 0.909 0.893 0.877 2 0.826 0.797 0.769 3 0.751 0.712 0.675 4 0.683 0.636 0.592 5 0.621 0.567 0.519

RatePeriods 10% 12% 14%

1 0.909 0.893 0.877 2 0.826 0.797 0.769 3 0.751 0.712 0.675 4 0.683 0.636 0.592 5 0.621 0.567 0.519

Excerpt from Excerpt from Present Value of $1Present Value of $1 Table in Table in the Appendix to Chapter 14the Appendix to Chapter 14

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

A bond will pay $100 in two years. What is A bond will pay $100 in two years. What is the present value of the $100 if an investor the present value of the $100 if an investor can earn a return of 12% on investments?can earn a return of 12% on investments?

Interest and the Time Value of Money

(1 + .12)(1 + .12)22P = 100P = 10011

P = $100 (0.797)P = $100 (0.797)P = $79.70P = $79.70P = $100 (0.797)P = $100 (0.797)P = $79.70P = $79.70

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

What does this mean?What does this mean?If $79.70 is put in the bank today, If $79.70 is put in the bank today, it will be worth $100 in two years.it will be worth $100 in two years.

In that sense, $79.70 today is In that sense, $79.70 today is equivalent to $100 in two years.equivalent to $100 in two years.

What does this mean?What does this mean?If $79.70 is put in the bank today, If $79.70 is put in the bank today, it will be worth $100 in two years.it will be worth $100 in two years.

In that sense, $79.70 today is In that sense, $79.70 today is equivalent to $100 in two years.equivalent to $100 in two years.

Interest and the Time Value of Money

Present Value = $79.70Present Value = $79.70

A bond will pay $100 in two years. What is A bond will pay $100 in two years. What is the present value of the $100 if an investor the present value of the $100 if an investor can earn a return of 12% on investments?can earn a return of 12% on investments?

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

Let’s verify that if we put $79.70 in the bank Let’s verify that if we put $79.70 in the bank today at 12% interest that it would grow to today at 12% interest that it would grow to

$100 at the end of two years.$100 at the end of two years.

Year 1 Year 2Beginning balance 79.70$ 89.26$ Interest @ 12% 9.56$ 10.71$ Ending balance 89.26$ 99.97$

Year 1 Year 2Beginning balance 79.70$ 89.26$ Interest @ 12% 9.56$ 10.71$ Ending balance 89.26$ 99.97$

Interest and the Time Value of Money

We can also determine the present We can also determine the present value using value using present value tablespresent value tables..

We can also determine the present We can also determine the present value using value using present value tablespresent value tables..

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

Time Value of Money

RatePeriods 10% 12% 14%

1 0.909 0.893 0.877 2 0.826 0.797 0.769 3 0.751 0.712 0.675 4 0.683 0.636 0.592 5 0.621 0.567 0.519

RatePeriods 10% 12% 14%

1 0.909 0.893 0.877 2 0.826 0.797 0.769 3 0.751 0.712 0.675 4 0.683 0.636 0.592 5 0.621 0.567 0.519

Excerpt from Excerpt from Present Value of $1Present Value of $1 Table in Table in the Appendix to Chapter 14the Appendix to Chapter 14

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

RatePeriods 10% 12% 14%

1 0.909 0.893 0.877 2 0.826 0.797 0.769 3 0.751 0.712 0.675 4 0.683 0.636 0.592 5 0.621 0.567 0.519

RatePeriods 10% 12% 14%

1 0.909 0.893 0.877 2 0.826 0.797 0.769 3 0.751 0.712 0.675 4 0.683 0.636 0.592 5 0.621 0.567 0.519

Time Value of Money

$100 $100 ×× 0.797 = $79.70 present value 0.797 = $79.70 present value

Present value factor of $1 for 2 periods at 12%.Present value factor of $1 for 2 periods at 12%.Present value factor of $1 for 2 periods at 12%.Present value factor of $1 for 2 periods at 12%.Atau dapat dihitung dengan mempergunakan kalkulator. Caranya: Tekan angka 1 dan tekan bagi 1,12, terus tekan sama dengan, yang akan menghasilkan 0.893 untuk tahun pertama. Lalu tekan sama dengan lagi untuk menghasikan 0.797, dan seterusnya.

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

Time Value of Money

11 22 33 44 55 66

$100$100 $100$100 $100$100 $100$100 $100$100 $100$100

An investment that involves a series of identical cash flows at the end of

each year is called an annuityannuity.

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

Quick Check

How much would you have to put in the bank today to have $100 at the end of five years if the interest rate is 10%?

a. $62.10

b. $56.70

c. $90.90

d. $51.90

How much would you have to put in the bank today to have $100 at the end of five years if the interest rate is 10%?

a. $62.10

b. $56.70

c. $90.90

d. $51.90

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

How much would you have to put in the bank today to have $100 at the end of five years if the interest rate is 10%?

a. $62.10

b. $56.70

c. $90.90

d. $51.90

How much would you have to put in the bank today to have $100 at the end of five years if the interest rate is 10%?

a. $62.10

b. $56.70

c. $90.90

d. $51.90

Quick Check

$100 $100 0.621 = 0.621 = $62.10$62.10$100 $100 0.621 = 0.621 = $62.10$62.10

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

Time Value of Money

Lacey Inc. purchased a tract of land on which a $60,000 payment will be due

each year for the next five years. What is the present value of this stream of cash

payments when the discount rate is 12%?

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

Time Value of Money

We could solve the problem like this . . .

Look in Appendix C of this Chapter for thePresent Value of an Annuity of $1 Table

Periods 10% 12% 14%1 0.909 0.893 0.877 2 1.736 1.690 1.647 3 2.487 2.402 2.322 4 3.170 3.037 2.914 5 3.791 3.605 3.433

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

Time Value of Money

We could solve the problem like this . . .

Periods 10% 12% 14%1 0.909 0.893 0.877 2 1.736 1.690 1.647 3 2.487 2.402 2.322 4 3.170 3.037 2.914 5 3.791 3.605 3.433

$60,000 × 3.605 = $216,300$60,000 × 3.605 = $216,300

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

Quick Check

If the interest rate is 14%, how much would you have to put in the bank today so as to be able to withdraw $100 at the end of each of the next five years?

a. $34.33

b. $500.00

c. $343.30

d. $360.50

If the interest rate is 14%, how much would you have to put in the bank today so as to be able to withdraw $100 at the end of each of the next five years?

a. $34.33

b. $500.00

c. $343.30

d. $360.50

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

If the interest rate is 14%, how much would you have to put in the bank today so as to be able to withdraw $100 at the end of each of the next five years?

a. $34.33

b. $500.00

c. $343.30

d. $360.50

If the interest rate is 14%, how much would you have to put in the bank today so as to be able to withdraw $100 at the end of each of the next five years?

a. $34.33

b. $500.00

c. $343.30

d. $360.50

Quick Check

$100 $100 3.433 = $343.30 3.433 = $343.30$100 $100 3.433 = $343.30 3.433 = $343.30

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

Quick Check

If the interest rate is 14%, what is the present value of $100 to be received at the end of the 3rd, 4th, and 5th years?

a. $866.90

b. $178.60

c. $ 86.90

d. $300.00

If the interest rate is 14%, what is the present value of $100 to be received at the end of the 3rd, 4th, and 5th years?

a. $866.90

b. $178.60

c. $ 86.90

d. $300.00

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

If the interest rate is 14%, what is the present value of $100 to be received at the end of the 3rd, 4th, and 5th years?

a. $866.90

b. $178.60

c. $ 86.90

d. $300.00

If the interest rate is 14%, what is the present value of $100 to be received at the end of the 3rd, 4th, and 5th years?

a. $866.90

b. $178.60

c. $ 86.90

d. $300.00

Quick Check

$100(3.433-1.647)= $1001.786 = $178.60or

$100(0.675+0.592+0.519)= $1001.786 = $178.60

$100(3.433-1.647)= $1001.786 = $178.60or

$100(0.675+0.592+0.519)= $1001.786 = $178.60

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

Typical Cash Outflows

Repairs andRepairs andmaintenancemaintenance

IncrementalIncrementaloperatingoperating

costscosts

InitialInitialinvestmentinvestment

WorkingWorkingcapitalcapital

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

Typical Cash Inflows

ReductionReductionof costsof costs

SalvageSalvagevaluevalue

IncrementalIncrementalrevenuesrevenues

Release ofRelease ofworkingworkingcapitalcapital

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

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