Start working on Chapter One Homework

Numbers 10, 12 and 17

Managerial Economics & Business Strategy

Chapter 1The Fundamentals of Managerial

Economics

Present Value of a Series

• What if you are “promised” different amounts every year??

• Present value of a stream of future amounts (FVt) received at the end of each period for “n” periods:

PV

FV

i

FV

i

FV

inn

1

12

21 1 1. . .

Net Present Value• Suppose a manager can purchase a stream of future

receipts (FVt ) by spending “C0” dollars today. The NPV of such a decision is

PV – Costs of the project

NPV

FV

i

FV

i

FV

iCn

n

11

22 01 1 1

. . .

Decision Rule:If NPV < 0: Reject project

NPV > 0: Accept project

What is the maximum we would pay? (number 2)

• What is the maximum amount you would pay for an asset that generates an income of $150,000 at the end of each of five years if the opportunity cost of using the funds is 9 percent?

30.58283560.9740298.10638262.11538442.12605068.137614

09.01

000,150

09.01

000,150

09.01

000,150

09.01

000,150

09.01

000,15054321

PV

Can we do it??• Buzz-Dot-Com is trying to decide whether or not to

purchase a new flying device that will cost them $200,000 and will be “good” for five years. The device will reduce costs by $40,000 the first year, $50,000 the second year, $65,000 the third year, and $80,000 the fourth and fifth years.

• What is the PV of cost savings if the interest rate is 8%.

• Should Buzz-Dot-Com purchase the device?

Can we??

13.752,244

66.5444639.5880210.5159994.4286604.37037

08.1

000,80

08.1

000,80

08.1

000,65

08.1

000,50

08.1

000,405432

PV

!!!

13.752,44

000,20013.752,244

DEVICEININVEST

NPV

NPV

CostPVNPV

Present Value of a Perpetuity• An asset that perpetually generates a stream of cash flows

(CF) at the end of each period is called a perpetuity.

• If cash flow IS THE SAME EACH YEAR such as certain bonds or stocks….

i

CF

i

CF

i

CF

i

CFPVPerpetuity

...111 32

Can we do it? (number 5)

• What is the value of a preferred stock that pays a perpetual dividend of $75 at the end of each year when the interest rate is 4%?

875,1$04.0

75

i

CFPVPerpetuity

How much is a firm worth??

• The value of a firm equals the present value of current and future profits

• So maximization of profits really means… Maximize firm value

• Which means….Maximize present value of current and future profits

...

111

1

33

22

11

0

iiiPV

iPV t

t

• Goal: Compare BENEFITS of the project to the COSTS

• Control Variables Output Price Product Quality Advertising R&D

• Basic Managerial Question: How much of the control variable should be used to maximize net benefits?

Marginal (Incremental) Analysis

Net Benefits

• Net Benefits = Total Benefits - Total Costs

• Profits = Revenue - Costs

Marginal Benefit (MB)

• Change in total benefits arising from a change in the control variable, Q:

• Slope (first derivative) of the total benefit curve.

Q

BMB

Marginal Cost (MC)

• Change in total costs arising from a change in the control variable, Q:

• Slope (first derivative) of the total cost curve

Q

CMC