Economics 373

MANAGERIAL ECONOMICS
Spring 2015
 
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Answers to Recommended Problems III

.

Chapter 15

9. ke = rf + rp = rf + p1 + p2 = 7 + (9 - 7) + 4 = 13%

.

10.

D = $100 M / 100 M = $1

Earnings per share (EPS) = $200 M / 100 M = $2

P = 8 * $2 = $16

ke = D / P + g = 1 / 16 + 0.075 = 0.1375 or 13.75%

.

11.

a.  kd = r (1 - t) = 11 (1 - 0.40) = 6.6%

b.  ke = rf + β (km - rf) = 7.5 + 2 (11.55 - 7.5) = 15.6%

c. kc = wd kd + we ke = 0.40 * 6.6 + 0.60 * 15.6 = 12.0%

.

Chapter 14

4.

a.

E (πTV) = (8000 * 0.2) + (10000 * 0.3) + (12000 * 0.3) + (14000 * 0.2) = $11,000

E (πR) = (8000 * 0.3) + (12000 * 0.4) + (16000 * 0.3) = $12,000

b.

σ2TV = (8000 - 11000)2 * 0.2 + (10000 - 11000)2 * 0.3 + (12000 - 11000)2 * 0.3 + (14000 - 11000)2 * 0.2 = 4,200,000 => σTV = 4200000^0.5 = $2,049

σ2R = (8000 - 12000)2 * 0.3 + (12000 - 12000)2 * 0.4 + (16000 - 12000)2 * 0.3 = 9,600,000 => σR = 9600000^0.5 = $3,098

c.  Radio is more risky because it has a higher standard deviation.

d.  Radio has the higher expected value but is riskier.  It depends on the attitude towards risk of the decision maker.

.

5.

a. E (π) = (40000 * 0.2) + (-10000 * 0.8) = 0

b.

E (UA) = (10 * 0.2) + (-5 * 0.8) = -2

E (UB) = (20 * 0.2) + (-5 * 0.8) = 0

E (UC) = (30 * 0.2) + (-5 * 0.8) = 2

C would invest in the venture because expected utility is positive.  B would be indifferent because utility is zero.

.

7.

a.

NPVA = 40000 / (1 + 0.08)1 + 60000 / (1 + 0.08)2 + 40000 / (1 + 0.08)3 + 110000 / (1 + 0.08)4 = $201,084

NPVB = 30000 / (1 + 0.08)1 + 80000 / (1 + 0.08)2 + 50000 / (1 + 0.08)3 + 104000 / (1 + 0.08)4 = $212,500

b.

NPVA = 40000 / (1 + 0.10)1 + 60000 / (1 + 0.10)2 + 40000 / (1 + 0.10)3 + 110000 / (1 + 0.10)4 = $191,135

NPVB = 30000 / (1 + 0.14)1 + 80000 / (1 + 0.14)2 + 50000 / (1 + 0.14)3 + 104000 / (1 + 0.14)4 = $183,198

A should be adopted because it has a higher NPV.

.

9.

NPVA = (40000 * 0.90) / (1 + 0.08)1 + (60000 * 0.85) / (1 + 0.08)2 + (40000 * 0.75) / (1 + 0.08)3 + (110000 * 0.70) / (1 + 0.08)4 = $157,470

NPVB = (30000 * 0.96) / (1 + 0.08)1 + (80000 * 0.92) / (1 + 0.08)2 + (50000 * 0.90) / (1 + 0.08)3 + (104000 * 0.85) / (1 + 0.08)4 = $190,466

.

11.

            | High Price
----------
0.5		 $12,000
            |    
        | High Price
-------------------------------||-------------------------------
E(π) = 12000 * 0.5 + 10000 * 0.3 + 8000 * 0.2 = 10600		 Competitor
Decision		 Medium Price
----------
0.3		 $10,000
        |   |    
        |   | Low Price
----------
0.2		 $8,000
        |       
        |   | High Price
----------
0.3		 $12,000
        |   |    
                                           |------------------------- Yes
----------
0.80		 Company
Decision		 Medium Price
-------------------------------||-------------------------------
E(π) = 12000 * 0.3 + 10000 * 0.5 + 6000 * 0.2 = 9800		 Competitor
Decision		 Medium Price
----------
0.5		 $10,000
    |   |   |    
    |   |   | Low Price
----------
0.2		 $6,000
    |   |        
    |   |   | High Price
----------
0.0		 $25,000
    |   |   |    
    |   | LP
----------------------------------------------------------------
E(π) = 25000 * 0.0 + 15000 * 0.4 + 10000 * 0.6 = 12000		 Competitor
Decision		 Medium Price
----------
0.4		 $15,000
| Introduce Product
------------------
 Competition?
|
E(π) = 12000 * 0.80 + 40000 * 0.20 = 17600 		      |    
|   |       | Low Price
----------
0.6		 $10,000
|   |            
|   |   | High Price
----------------------------------------------------------------
 $40,000    
|   |   |        
|                                         |------------------------- No
----------
0.20		 Company
Decision		 Medium Price
-------------------------------||-------------------------------
 $30,000    
|       |        
Company
Decision		       | Low Price
-------------------------------||-------------------------------
 $20,000    
|                
|                
|                
| Don't Introduce
--------||--------		 E(π) = 0            

The product should be introduced because it has a positive expected profit of $17,600.

.

Chapter 12

7.

a.  Skip

b.

MC = = 4

MR1 = MC => 16 - 0.2 Q1 = 4 => 12 = 0.2 Q1 => Q1 = 60

MR2 = MC => 10 - 0.1 Q2 = 4 => 6 = 0.1 Q2 => Q2 = 60

QT  = Q1 + Q2 = 60 + 60 = 120

.

c.

P1 = 16 - 0.1 (60) = 10

TR1 = P1 * Q1 = 10 * 60 = 600    

P2 = 10 - 0.05 (60) = 7

TR2 = P2 * Q2 = 7 * 60 = 420

. 

d. Skip profit per unit

π = TR - TC = (600 + 420) - [120 + 4 (60 + 60)] = 420

.

e. 

Q = Q1 * Q2 = 160 - 10 P1 + 200 - 20 P2 = 160 - 10 P + 200 - 20 P = 360 - 30 P

=> 30 P = 360 - Q => P = 12 - 1/30 Q => TR = P * Q = 12 Q - 1/30 Q2 => MR = 12 - 1/15 Q

MR = MC => 12 - 1/15 Q = 4 => 8 = 1/15 Q => Q = 120

120 = 360 - 30 P => 30 P = 240 => P = 8

TR = P * Q = 8 * 120 = 960

π = TR - TC = 960 - [120 + 4 (120)] = 360