Transcript Managerial Economics & Business Strategy
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Numbers 10, 12 and 17
Managerial Economics & Business Strategy
Chapter 1 The 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 (
FV t
) received at the end of each period for “
n
” periods:
PV
1
FV
1
i
1 1
FV
2
i
2 1
FV n
i
n
Net Present Value
• Suppose a manager can purchase a stream of future receipts (
FV t
) by spending “
C 0
” dollars today. The
NPV
of such a decision is PV – Costs of the project
NPV
1
FV
1
i
1 1
FV
2
i
2 1
FV n
i
n
C
0 If
Decision Rule:
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?
PV
1 150 , 000 0 .
09 1 150 , 000 0 .
09 1 150 , 000 0 .
09 1 150 , 000 0 .
09 1 150 , 000 0 .
09 5 137614 .
68 126050 .
42 115384 .
62 106382 .
98 97402 .
60 582835 .
30
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??
PV
40 , 000 1 .
08 50 , 000 1 .
08 2 65 , 000 1 .
08 3 80 , 000 1 .
08 4 80 , 000 1 .
08 5 37037 .
04 42866 .
94 51599 .
10 58802 .
39 54446 .
66 244 , 752 .
13
NPV NPV NPV
PV
Cost
244 , 752 .
13 200 , 000 44 , 752 .
13
INVEST IN DEVICE
!
!
!
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….
PV Perpetuity
CF
1
i
1
CF
i
1
CF
i
3 ...
CF i
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%?
PV Perpetuity
CF i
75 0 .
04 $ 1 , 875
How much is a firm worth??
• The value of a firm equals the present value of current and future profits
PV PV
0
t
i
1
i t
1 2
i
2 3
i
3 ...
• So maximization of profits really means… Maximize firm value • Which means….Maximize present value of current and future profits
Marginal (Incremental) Analysis
• 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?
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:
MB
B Q
• Slope (first derivative) of the total benefit curve.
Marginal Cost (MC)
• Change in total costs arising from a change in the control variable, Q:
MC
C
Q
• Slope (first derivative) of the total cost curve