start working on chapter one homework numbers 10, 12 and 17
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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