i. Present Worth Alternative is being used.

Question

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Answer 1

Question

Chapter 5, Problem 72P

To determine

i.

Present Worth Alternative is being used.

Expert Solution

Answer to Problem 72P

Using Present Worth Method, Alternative 1 should be selected.

Explanation of Solution

Given:

Interest Rate = 8%.

Concept used:

RATE OF RETURN: It is a return which usually an investor gets on speculation. Investment can be done on shares, bonds etc. If rate of return is calculated for a fiscal year, then it is termed as annual rate of return.

Calculation:

Alternative 1

Present Worth =

$500+$135(P/A,8%,10)−$500(P/F,8%,5)PW = −$500+($135×6.7101)−($500×0.6806)PW = −$500+$905.86−$340.3PW= $65.56

The Present worth of alternative 1 is $65.56

Alternative 2

Present Worth:

−$600+$100(P/A,8%,10)−[($600−$250)(P/F,8%,5)]+$250(P/F,8%,10)−$600+($100×6.7101)−[$350×0.6806]+($250×0.4632)−$600+$671.01−$238.21+$115.8−$51.4

The Present Worth of Alternative 2 is -$51.4

Alternative 3:

PW = −$700+$100(P/A,8%,10)+$180(P/F,8%,10)PW = −$700+$671.01+$83.37PW = $54.38

Alternative 4:

The Present worth of alternative 4 is $0

The Present worth of alternative 1 is numerically higher.

Conclusion:

So, using Present Worth Method, Alternative 1 should be selected.

To determine

ii.

Present Worth Alternative is being used.

Expert Solution

Answer to Problem 72P

Interest Rate is 12%.

Explanation of Solution

Given:

Interest Rate is 12%.

Concept used:

RATE OF RETURN: It is a return which usually an investor gets on speculation. Investment can be done on shares, bonds etc. If rate of return is calculated for a fiscal year, then it is termed as annual rate of return.

Calculation:

Alternative 1

Present Worth =

PW = −$500+$135(P/A,12%,10)−$500(P/F,12%,5)PW = −$500+($135×5.6502)−($500×0.5674)PW = −$500+$762.77−$283.7PW = −$20.93

The Present worth of Alternative 1 is -$20.93

Alternative 2

PW = −$600+$100(P/A,12%,10)−[($600−$250)(P/F,12%5)]+$250(P/F,12%,10)PW = −$600+(100×5.6502)−$198.59+$80.5PW = −$153.07

The Present Worth of Alternative 2 is -$153.07

Alternative 3

PW = −$700+$100(P/A,12%,10)+$180(P/F,12%,10)PW = −$700+$565.02+$57.96PW = −$77.02

The Present Worth of Alternative 3 is -$77.02

Alternative 4

The Present Worth of Alternative 4 is $0.

Conclusion:

The Present Worth of Alternative 4 is numerically higher.

So, using Present Worth Method, Alternative 4 should be selected.

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A firm operates with the production function Q = K2 L. Q is the number of units of output per day when the firm rents K units of capital and employs L workers each day. The manager has been given a production target: to produce 8,000 units per day. She knows that the daily rental price of capital is $400 per unit and the wage rate is $200 day. a. What is the returns to scale of this production function? Show mathematically. b. Currently the firm employs 80 workers per day. What is the firm’s daily total cost if it rents just enough capital to produce at its target? c. Compare the marginal product per dollar spent on K and on L when the firm operates at the input choice in part (b). What does this suggest about the way the firm might change its choice of K and L if it wants to reduce the total cost in meeting its target? Explain your answer very clearly. d. In the long run, how much K and L should the firm choose if it wants to minimize the cost of producing 8,000 units of output a day?…

Answer 2

Question

Chapter 5, Problem 72P

To determine

i.

Present Worth Alternative is being used.

Expert Solution

Answer to Problem 72P

Using Present Worth Method, Alternative 1 should be selected.

Explanation of Solution

Given:

Interest Rate = 8%.

Concept used:

RATE OF RETURN: It is a return which usually an investor gets on speculation. Investment can be done on shares, bonds etc. If rate of return is calculated for a fiscal year, then it is termed as annual rate of return.

Calculation:

Alternative 1

Present Worth =

$500+$135(P/A,8%,10)−$500(P/F,8%,5)PW = −$500+($135×6.7101)−($500×0.6806)PW = −$500+$905.86−$340.3PW= $65.56

The Present worth of alternative 1 is $65.56

Alternative 2

Present Worth:

−$600+$100(P/A,8%,10)−[($600−$250)(P/F,8%,5)]+$250(P/F,8%,10)−$600+($100×6.7101)−[$350×0.6806]+($250×0.4632)−$600+$671.01−$238.21+$115.8−$51.4

The Present Worth of Alternative 2 is -$51.4

Alternative 3:

PW = −$700+$100(P/A,8%,10)+$180(P/F,8%,10)PW = −$700+$671.01+$83.37PW = $54.38

Alternative 4:

The Present worth of alternative 4 is $0

The Present worth of alternative 1 is numerically higher.

Conclusion:

So, using Present Worth Method, Alternative 1 should be selected.

To determine

ii.

Present Worth Alternative is being used.

Expert Solution

Answer to Problem 72P

Interest Rate is 12%.

Explanation of Solution

Given:

Interest Rate is 12%.

Concept used:

RATE OF RETURN: It is a return which usually an investor gets on speculation. Investment can be done on shares, bonds etc. If rate of return is calculated for a fiscal year, then it is termed as annual rate of return.

Calculation:

Alternative 1

Present Worth =

PW = −$500+$135(P/A,12%,10)−$500(P/F,12%,5)PW = −$500+($135×5.6502)−($500×0.5674)PW = −$500+$762.77−$283.7PW = −$20.93

The Present worth of Alternative 1 is -$20.93

Alternative 2

PW = −$600+$100(P/A,12%,10)−[($600−$250)(P/F,12%5)]+$250(P/F,12%,10)PW = −$600+(100×5.6502)−$198.59+$80.5PW = −$153.07

The Present Worth of Alternative 2 is -$153.07

Alternative 3

PW = −$700+$100(P/A,12%,10)+$180(P/F,12%,10)PW = −$700+$565.02+$57.96PW = −$77.02

The Present Worth of Alternative 3 is -$77.02

Alternative 4

The Present Worth of Alternative 4 is $0.

Conclusion:

The Present Worth of Alternative 4 is numerically higher.

So, using Present Worth Method, Alternative 4 should be selected.

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Answer 3

Question

Chapter 5, Problem 72P

To determine

i.

Present Worth Alternative is being used.

Expert Solution

Answer to Problem 72P

Using Present Worth Method, Alternative 1 should be selected.

Explanation of Solution

Given:

Interest Rate = 8%.

Concept used:

RATE OF RETURN: It is a return which usually an investor gets on speculation. Investment can be done on shares, bonds etc. If rate of return is calculated for a fiscal year, then it is termed as annual rate of return.

Calculation:

Alternative 1

Present Worth =

$500+$135(P/A,8%,10)−$500(P/F,8%,5)PW = −$500+($135×6.7101)−($500×0.6806)PW = −$500+$905.86−$340.3PW= $65.56

The Present worth of alternative 1 is $65.56

Alternative 2

Present Worth:

−$600+$100(P/A,8%,10)−[($600−$250)(P/F,8%,5)]+$250(P/F,8%,10)−$600+($100×6.7101)−[$350×0.6806]+($250×0.4632)−$600+$671.01−$238.21+$115.8−$51.4

The Present Worth of Alternative 2 is -$51.4

Alternative 3:

PW = −$700+$100(P/A,8%,10)+$180(P/F,8%,10)PW = −$700+$671.01+$83.37PW = $54.38

Alternative 4:

The Present worth of alternative 4 is $0

The Present worth of alternative 1 is numerically higher.

Conclusion:

So, using Present Worth Method, Alternative 1 should be selected.

To determine

ii.

Present Worth Alternative is being used.

Expert Solution

Answer to Problem 72P

Interest Rate is 12%.

Explanation of Solution

Given:

Interest Rate is 12%.

Concept used:

RATE OF RETURN: It is a return which usually an investor gets on speculation. Investment can be done on shares, bonds etc. If rate of return is calculated for a fiscal year, then it is termed as annual rate of return.

Calculation:

Alternative 1

Present Worth =

PW = −$500+$135(P/A,12%,10)−$500(P/F,12%,5)PW = −$500+($135×5.6502)−($500×0.5674)PW = −$500+$762.77−$283.7PW = −$20.93

The Present worth of Alternative 1 is -$20.93

Alternative 2

PW = −$600+$100(P/A,12%,10)−[($600−$250)(P/F,12%5)]+$250(P/F,12%,10)PW = −$600+(100×5.6502)−$198.59+$80.5PW = −$153.07

The Present Worth of Alternative 2 is -$153.07

Alternative 3

PW = −$700+$100(P/A,12%,10)+$180(P/F,12%,10)PW = −$700+$565.02+$57.96PW = −$77.02

The Present Worth of Alternative 3 is -$77.02

Alternative 4

The Present Worth of Alternative 4 is $0.

Conclusion:

The Present Worth of Alternative 4 is numerically higher.

So, using Present Worth Method, Alternative 4 should be selected.

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Answer 4

Question

Chapter 5, Problem 72P

To determine

i.

Present Worth Alternative is being used.

Expert Solution

Answer to Problem 72P

Using Present Worth Method, Alternative 1 should be selected.

Explanation of Solution

Given:

Interest Rate = 8%.

Concept used:

RATE OF RETURN: It is a return which usually an investor gets on speculation. Investment can be done on shares, bonds etc. If rate of return is calculated for a fiscal year, then it is termed as annual rate of return.

Calculation:

Alternative 1

Present Worth =

$500+$135(P/A,8%,10)−$500(P/F,8%,5)PW = −$500+($135×6.7101)−($500×0.6806)PW = −$500+$905.86−$340.3PW= $65.56

The Present worth of alternative 1 is $65.56

Alternative 2

Present Worth:

−$600+$100(P/A,8%,10)−[($600−$250)(P/F,8%,5)]+$250(P/F,8%,10)−$600+($100×6.7101)−[$350×0.6806]+($250×0.4632)−$600+$671.01−$238.21+$115.8−$51.4

The Present Worth of Alternative 2 is -$51.4

Alternative 3:

PW = −$700+$100(P/A,8%,10)+$180(P/F,8%,10)PW = −$700+$671.01+$83.37PW = $54.38

Alternative 4:

The Present worth of alternative 4 is $0

The Present worth of alternative 1 is numerically higher.

Conclusion:

So, using Present Worth Method, Alternative 1 should be selected.

To determine

ii.

Present Worth Alternative is being used.

Expert Solution

Answer to Problem 72P

Interest Rate is 12%.

Explanation of Solution

Given:

Interest Rate is 12%.

Concept used:

RATE OF RETURN: It is a return which usually an investor gets on speculation. Investment can be done on shares, bonds etc. If rate of return is calculated for a fiscal year, then it is termed as annual rate of return.

Calculation:

Alternative 1

Present Worth =

PW = −$500+$135(P/A,12%,10)−$500(P/F,12%,5)PW = −$500+($135×5.6502)−($500×0.5674)PW = −$500+$762.77−$283.7PW = −$20.93

The Present worth of Alternative 1 is -$20.93

Alternative 2

PW = −$600+$100(P/A,12%,10)−[($600−$250)(P/F,12%5)]+$250(P/F,12%,10)PW = −$600+(100×5.6502)−$198.59+$80.5PW = −$153.07

The Present Worth of Alternative 2 is -$153.07

Alternative 3

PW = −$700+$100(P/A,12%,10)+$180(P/F,12%,10)PW = −$700+$565.02+$57.96PW = −$77.02

The Present Worth of Alternative 3 is -$77.02

Alternative 4

The Present Worth of Alternative 4 is $0.

Conclusion:

The Present Worth of Alternative 4 is numerically higher.

So, using Present Worth Method, Alternative 4 should be selected.

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Answer 5

Chapter 5, Problem 72P

To determine

i.

Present Worth Alternative is being used.

Expert Solution

Answer to Problem 72P

Using Present Worth Method, Alternative 1 should be selected.

Explanation of Solution

Given:

Interest Rate = 8%.

Concept used:

RATE OF RETURN: It is a return which usually an investor gets on speculation. Investment can be done on shares, bonds etc. If rate of return is calculated for a fiscal year, then it is termed as annual rate of return.

Calculation:

Alternative 1

Present Worth =

$500+$135(P/A,8%,10)−$500(P/F,8%,5)PW = −$500+($135×6.7101)−($500×0.6806)PW = −$500+$905.86−$340.3PW= $65.56

The Present worth of alternative 1 is $65.56

Alternative 2

Present Worth:

−$600+$100(P/A,8%,10)−[($600−$250)(P/F,8%,5)]+$250(P/F,8%,10)−$600+($100×6.7101)−[$350×0.6806]+($250×0.4632)−$600+$671.01−$238.21+$115.8−$51.4

The Present Worth of Alternative 2 is -$51.4

Alternative 3:

PW = −$700+$100(P/A,8%,10)+$180(P/F,8%,10)PW = −$700+$671.01+$83.37PW = $54.38

Alternative 4:

The Present worth of alternative 4 is $0

The Present worth of alternative 1 is numerically higher.

Conclusion:

So, using Present Worth Method, Alternative 1 should be selected.

To determine

ii.

Present Worth Alternative is being used.

Expert Solution

Answer to Problem 72P

Interest Rate is 12%.

Explanation of Solution

Given:

Interest Rate is 12%.

Concept used:

RATE OF RETURN: It is a return which usually an investor gets on speculation. Investment can be done on shares, bonds etc. If rate of return is calculated for a fiscal year, then it is termed as annual rate of return.

Calculation:

Alternative 1

Present Worth =

PW = −$500+$135(P/A,12%,10)−$500(P/F,12%,5)PW = −$500+($135×5.6502)−($500×0.5674)PW = −$500+$762.77−$283.7PW = −$20.93

The Present worth of Alternative 1 is -$20.93

Alternative 2

PW = −$600+$100(P/A,12%,10)−[($600−$250)(P/F,12%5)]+$250(P/F,12%,10)PW = −$600+(100×5.6502)−$198.59+$80.5PW = −$153.07

The Present Worth of Alternative 2 is -$153.07

Alternative 3

PW = −$700+$100(P/A,12%,10)+$180(P/F,12%,10)PW = −$700+$565.02+$57.96PW = −$77.02

The Present Worth of Alternative 3 is -$77.02

Alternative 4

The Present Worth of Alternative 4 is $0.

Conclusion:

The Present Worth of Alternative 4 is numerically higher.

So, using Present Worth Method, Alternative 4 should be selected.

Answer 6

Chapter 5, Problem 72P

To determine

i.

Present Worth Alternative is being used.

Expert Solution

Answer to Problem 72P

Using Present Worth Method, Alternative 1 should be selected.

Explanation of Solution

Given:

Interest Rate = 8%.

Concept used:

RATE OF RETURN: It is a return which usually an investor gets on speculation. Investment can be done on shares, bonds etc. If rate of return is calculated for a fiscal year, then it is termed as annual rate of return.

Calculation:

Alternative 1

Present Worth =

$500+$135(P/A,8%,10)−$500(P/F,8%,5)PW = −$500+($135×6.7101)−($500×0.6806)PW = −$500+$905.86−$340.3PW= $65.56

The Present worth of alternative 1 is $65.56

Alternative 2

Present Worth:

−$600+$100(P/A,8%,10)−[($600−$250)(P/F,8%,5)]+$250(P/F,8%,10)−$600+($100×6.7101)−[$350×0.6806]+($250×0.4632)−$600+$671.01−$238.21+$115.8−$51.4

The Present Worth of Alternative 2 is -$51.4

Alternative 3:

PW = −$700+$100(P/A,8%,10)+$180(P/F,8%,10)PW = −$700+$671.01+$83.37PW = $54.38

Alternative 4:

The Present worth of alternative 4 is $0

The Present worth of alternative 1 is numerically higher.

Conclusion:

So, using Present Worth Method, Alternative 1 should be selected.

Answer 7

Chapter 5, Problem 72P

To determine

i.

Present Worth Alternative is being used.

Answer 8

Expert Solution

Answer to Problem 72P

Using Present Worth Method, Alternative 1 should be selected.

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given:

Interest Rate = 8%.

Concept used:

RATE OF RETURN: It is a return which usually an investor gets on speculation. Investment can be done on shares, bonds etc. If rate of return is calculated for a fiscal year, then it is termed as annual rate of return.

Calculation:

Alternative 1

Present Worth =

$500+$135(P/A,8%,10)−$500(P/F,8%,5)PW = −$500+($135×6.7101)−($500×0.6806)PW = −$500+$905.86−$340.3PW= $65.56

The Present worth of alternative 1 is $65.56

Alternative 2

Present Worth:

−$600+$100(P/A,8%,10)−[($600−$250)(P/F,8%,5)]+$250(P/F,8%,10)−$600+($100×6.7101)−[$350×0.6806]+($250×0.4632)−$600+$671.01−$238.21+$115.8−$51.4

The Present Worth of Alternative 2 is -$51.4

Alternative 3:

PW = −$700+$100(P/A,8%,10)+$180(P/F,8%,10)PW = −$700+$671.01+$83.37PW = $54.38

Alternative 4:

The Present worth of alternative 4 is $0

The Present worth of alternative 1 is numerically higher.

Conclusion:

So, using Present Worth Method, Alternative 1 should be selected.

Answer 13

To determine

ii.

Present Worth Alternative is being used.

Expert Solution

Answer to Problem 72P

Interest Rate is 12%.

Explanation of Solution

Given:

Interest Rate is 12%.

Concept used:

RATE OF RETURN: It is a return which usually an investor gets on speculation. Investment can be done on shares, bonds etc. If rate of return is calculated for a fiscal year, then it is termed as annual rate of return.

Calculation:

Alternative 1

Present Worth =

PW = −$500+$135(P/A,12%,10)−$500(P/F,12%,5)PW = −$500+($135×5.6502)−($500×0.5674)PW = −$500+$762.77−$283.7PW = −$20.93

The Present worth of Alternative 1 is -$20.93

Alternative 2

PW = −$600+$100(P/A,12%,10)−[($600−$250)(P/F,12%5)]+$250(P/F,12%,10)PW = −$600+(100×5.6502)−$198.59+$80.5PW = −$153.07

The Present Worth of Alternative 2 is -$153.07

Alternative 3

PW = −$700+$100(P/A,12%,10)+$180(P/F,12%,10)PW = −$700+$565.02+$57.96PW = −$77.02

The Present Worth of Alternative 3 is -$77.02

Alternative 4

The Present Worth of Alternative 4 is $0.

Conclusion:

The Present Worth of Alternative 4 is numerically higher.

So, using Present Worth Method, Alternative 4 should be selected.

Answer 14

To determine

ii.

Present Worth Alternative is being used.

Answer 15

Expert Solution

Answer to Problem 72P

Interest Rate is 12%.

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given:

Interest Rate is 12%.

Concept used:

RATE OF RETURN: It is a return which usually an investor gets on speculation. Investment can be done on shares, bonds etc. If rate of return is calculated for a fiscal year, then it is termed as annual rate of return.

Calculation:

Alternative 1

Present Worth =

PW = −$500+$135(P/A,12%,10)−$500(P/F,12%,5)PW = −$500+($135×5.6502)−($500×0.5674)PW = −$500+$762.77−$283.7PW = −$20.93