Find out the payback period for the new equipment for each of KD’s projects. Recommend the project to be chosen if rapid payback is important. Also, recommend the project should be chosen.

Question

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Answer 1

Question

Chapter 12, Problem 37E

1.

To determine

Find out the payback period for the new equipment for each of KD’s projects. Recommend the project to be chosen if rapid payback is important. Also, recommend the project should be chosen.

1.

Expert Solution

Explanation of Solution

Payback Period:

The time taken by an investment to recover its original value is known as payback period. It is calculated by dividing the original amount of investment by annual cash flow from the investment.

Calculate payback period for Project A:

Year	Unrecovered investment($) (Beginning of year)	Annual cash Flow($)	Time needed for payback (Years)
1	20,000	6,000	1.0
2	14,000	8,000	1.0
3	6,000¹	10,000	0.60
	0		2.60

Table (1)

Therefore, payback period is 2.60 years.

Calculate payback period for Project B:

Year	Unrecovered investment($) (Beginning of year)	Annual cash Flow($)	Time needed for payback (Years)
1	20,000	6,000	1.0
2	14,000	8,000	1.0
3	6,000¹	10,000	0.60
	0		2.60

Table (2)

Therefore, payback period is 2.60 years.

As both the projects have same payback period, the profitable project must be chosen. The cash flow from project B beyond the payback period is lesser than that of project A. Therefore, project A should be chosen because it is more profitable.

Working Note:

1. Calculation of payback period for third year:

Payback period=Unrecovered investmentAnnual cash flow=$6,000$10,000=0.60

2.

To determine

Find out the project to be chosen on the basis of accounting rate of return (ARR). Also, explain the reason for better performance of ARR in this setting than payback period.

2.

Expert Solution

Explanation of Solution

Accounting Rate of Return:

A method that measures returns from an investment in terms of income instead of cash flow is known as accounting rate of return. It is a non-discounting model of capital investment decision.

Use the following formula to calculate accounting rate of return (ARR) for project A:

ARR=Average incomeInitial investment

Substitute $4,800¹ for average income and $20,000 for initial investment in the above formula.

ARR=$4,800$20,000=24%

Therefore, accounting rate of return is 24%.

Use the following formula to calculate accounting rate of return (ARR) for project A:

ARR=Average incomeInitial investment

Substitute $2,000² for average income and $20,000 for initial investment in the above formula.

ARR=$2,000$20,000=10%

Therefore, accounting rate of return is 10%.

ARR considers the cash inflow from a project beyond its payback period which is not the case in the payback period. Therefore, ARR performs better than the payback period in this case.

Working Note:

1. Calculation of average cash inflow:

Average cash inflow=Total cash inflowNumber of years=($6,000+$8,000+$10,000+$10,000+$10,000)5=$44,0005=$8,800

Calculation of depreciation:

Depreciation=Cost−Salvage valueUseful life=$20,000−05=$4,000

Calculation of average income:

Average income=Average cash inflow−Depreciation=$8,800−$4,000=$4,800

2. Calculation of average cash inflow:

Average cash inflow=Total cash inflowNumber of years=($6,000+$8,000+$10,000+$3,000+$3,000)5=$30,0005=$6,000

Calculation of depreciation:

Depreciation=Cost−Salvage valueUseful life=$20,000−05=$4,000

Calculation of average income:

Average income=Average cash inflow−Depreciation=$6,000−$4,000=$2,000

3.

To determine

Calculate present value of the annuity to recommend that Person WG should accept the lump sum amount or annuity.

3.

Expert Solution

Explanation of Solution

Calculate present value of a future annuity:

Use the following formula to calculate present value of a future annuity;

Present value=Annuity value×Discount factor

Substitute $30,000 for annuity value and 11.46992 for discount factor in the above formula.

Present value=$30,000×11.46992=$344,098

Therefore, the present value of the annuity is $344,098.

The present value of the future annuity is lesser than the lump sum amount. Therefore, Person WG should accept the lump sum amount.

4.

To determine

Find out the NPV of the investment if the RRR is 8%. Also, recommend that Person D should invest or not.

4.

Expert Solution

Explanation of Solution

Net Present Value:

The remaining balance of the present value of a project’s inflows and outflows is known as net present value (NPV). It is a discounting model of capital investment decision. A project with a positive NPV increases the wealth of a firm whereas a project with a negative NPV decreases the wealth of a firm.

Use the following formula to calculate NPV of the investment:

NPV=Present value of cash inflow(P)−Present value of cash outflow(I)

Substitute $41,606³ for P and $30,000 for I in the above formula.

NPV=$41,606−$30,000=$11,606

Therefore, net present value of the investment is $11,606.

Person D should make the investment because NPV of the investment is positive.

Working Note:

3. Calculation of present value of future cash flow:

Present value of future cash flow=Future value×Discount factor=$9,000×4.62288=$41,606

5.

To determine

Find out the IRR for Person PF’s project. Also recommend that Person PF should acquire the equipment or not.

5.

Expert Solution

Explanation of Solution

Internal Rate of Return:

An interest rate at which the present value of an investment’s cash inflows is equal to the present value cost of the investment is known as internal rate of return. The value of NPV is zero in case of an internal rate of return.

Use the following formula to calculate discount factor:

Discount factor=InvestmentAnnual cash flow

Substitute $400,000 for investment and $75,000 for annual cash flow in the above formula.

Discount factor=$40,000$75,000=5.33333

Therefore, discount factor for Model CX is 5.33333.

The IRR is approximately 13% which is more than Person PF’s cost of capital. Therefore, Person PF should acquire the equipment.

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Students have asked these similar questions

Payback, Accounting Rate of Return, Present Value, Net PresentValue, Internal Rate of ReturnAll scenarios are independent of all other scenarios. Assume that all cash flows are after-tax cashflows.a. Kambry Day is considering investing in one of the following two projects. Either projectwill require an investment of $20,000. The expected cash flows for the two projects follow.Assume that each project is depreciable b. Wilma Golding is retiring and has the option to take her retirement as a lump sum of$450,000 or to receive $30,000 per year for 20 years. Wilma’s required rate of return is6%.c. David Booth is interested in investing in some tools and equipment so that he can doindependent drywalling. The cost of the tools and equipment is $30,000. He estimatesthat the return from owning his own equipment will be $9,000 per year. The tools andequipment will last 6 years.d. Patsy Folson is evaluating what appears to be an attractive opportunity. She is currentlythe owner of a small…

2) Assume that you are considering a project. Its initial after-tax cost is $1,500,000 and it is expected to provide after-tax operating cash inflows of $1,800,000 in year 1, $2,900,000 in year2, $2,700,000 in year 3 and $2,300,000 in year 4. a. Roughly calculate the Internal Rate of Return (IRR) of the project. b. Discuss whether you accept the project or not.

sd

Answer 2

Question

Chapter 12, Problem 37E

1.

To determine

Find out the payback period for the new equipment for each of KD’s projects. Recommend the project to be chosen if rapid payback is important. Also, recommend the project should be chosen.

1.

Expert Solution

Explanation of Solution

Payback Period:

The time taken by an investment to recover its original value is known as payback period. It is calculated by dividing the original amount of investment by annual cash flow from the investment.

Calculate payback period for Project A:

Year	Unrecovered investment($) (Beginning of year)	Annual cash Flow($)	Time needed for payback (Years)
1	20,000	6,000	1.0
2	14,000	8,000	1.0
3	6,000¹	10,000	0.60
	0		2.60

Table (1)

Therefore, payback period is 2.60 years.

Calculate payback period for Project B:

Year	Unrecovered investment($) (Beginning of year)	Annual cash Flow($)	Time needed for payback (Years)
1	20,000	6,000	1.0
2	14,000	8,000	1.0
3	6,000¹	10,000	0.60
	0		2.60

Table (2)

Therefore, payback period is 2.60 years.

As both the projects have same payback period, the profitable project must be chosen. The cash flow from project B beyond the payback period is lesser than that of project A. Therefore, project A should be chosen because it is more profitable.

Working Note:

1. Calculation of payback period for third year:

Payback period=Unrecovered investmentAnnual cash flow=$6,000$10,000=0.60

2.

To determine

Find out the project to be chosen on the basis of accounting rate of return (ARR). Also, explain the reason for better performance of ARR in this setting than payback period.

2.

Expert Solution

Explanation of Solution

Accounting Rate of Return:

A method that measures returns from an investment in terms of income instead of cash flow is known as accounting rate of return. It is a non-discounting model of capital investment decision.

Use the following formula to calculate accounting rate of return (ARR) for project A:

ARR=Average incomeInitial investment

Substitute $4,800¹ for average income and $20,000 for initial investment in the above formula.

ARR=$4,800$20,000=24%

Therefore, accounting rate of return is 24%.

Use the following formula to calculate accounting rate of return (ARR) for project A:

ARR=Average incomeInitial investment

Substitute $2,000² for average income and $20,000 for initial investment in the above formula.

ARR=$2,000$20,000=10%

Therefore, accounting rate of return is 10%.

ARR considers the cash inflow from a project beyond its payback period which is not the case in the payback period. Therefore, ARR performs better than the payback period in this case.

Working Note:

1. Calculation of average cash inflow:

Average cash inflow=Total cash inflowNumber of years=($6,000+$8,000+$10,000+$10,000+$10,000)5=$44,0005=$8,800

Calculation of depreciation:

Depreciation=Cost−Salvage valueUseful life=$20,000−05=$4,000

Calculation of average income:

Average income=Average cash inflow−Depreciation=$8,800−$4,000=$4,800

2. Calculation of average cash inflow:

Average cash inflow=Total cash inflowNumber of years=($6,000+$8,000+$10,000+$3,000+$3,000)5=$30,0005=$6,000

Calculation of depreciation:

Depreciation=Cost−Salvage valueUseful life=$20,000−05=$4,000

Calculation of average income:

Average income=Average cash inflow−Depreciation=$6,000−$4,000=$2,000

3.

To determine

Calculate present value of the annuity to recommend that Person WG should accept the lump sum amount or annuity.

3.

Expert Solution

Explanation of Solution

Calculate present value of a future annuity:

Use the following formula to calculate present value of a future annuity;

Present value=Annuity value×Discount factor

Substitute $30,000 for annuity value and 11.46992 for discount factor in the above formula.

Present value=$30,000×11.46992=$344,098

Therefore, the present value of the annuity is $344,098.

The present value of the future annuity is lesser than the lump sum amount. Therefore, Person WG should accept the lump sum amount.

4.

To determine

Find out the NPV of the investment if the RRR is 8%. Also, recommend that Person D should invest or not.

4.

Expert Solution

Explanation of Solution

Net Present Value:

The remaining balance of the present value of a project’s inflows and outflows is known as net present value (NPV). It is a discounting model of capital investment decision. A project with a positive NPV increases the wealth of a firm whereas a project with a negative NPV decreases the wealth of a firm.

Use the following formula to calculate NPV of the investment:

NPV=Present value of cash inflow(P)−Present value of cash outflow(I)

Substitute $41,606³ for P and $30,000 for I in the above formula.

NPV=$41,606−$30,000=$11,606

Therefore, net present value of the investment is $11,606.

Person D should make the investment because NPV of the investment is positive.

Working Note:

3. Calculation of present value of future cash flow:

Present value of future cash flow=Future value×Discount factor=$9,000×4.62288=$41,606

5.

To determine

Find out the IRR for Person PF’s project. Also recommend that Person PF should acquire the equipment or not.

5.

Expert Solution

Explanation of Solution

Internal Rate of Return:

An interest rate at which the present value of an investment’s cash inflows is equal to the present value cost of the investment is known as internal rate of return. The value of NPV is zero in case of an internal rate of return.

Use the following formula to calculate discount factor:

Discount factor=InvestmentAnnual cash flow

Substitute $400,000 for investment and $75,000 for annual cash flow in the above formula.

Discount factor=$40,000$75,000=5.33333

Therefore, discount factor for Model CX is 5.33333.

The IRR is approximately 13% which is more than Person PF’s cost of capital. Therefore, Person PF should acquire the equipment.

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Answer 3

Question

Chapter 12, Problem 37E

1.

To determine

Find out the payback period for the new equipment for each of KD’s projects. Recommend the project to be chosen if rapid payback is important. Also, recommend the project should be chosen.

1.

Expert Solution

Explanation of Solution

Payback Period:

The time taken by an investment to recover its original value is known as payback period. It is calculated by dividing the original amount of investment by annual cash flow from the investment.

Calculate payback period for Project A:

Year	Unrecovered investment($) (Beginning of year)	Annual cash Flow($)	Time needed for payback (Years)
1	20,000	6,000	1.0
2	14,000	8,000	1.0
3	6,000¹	10,000	0.60
	0		2.60

Table (1)

Therefore, payback period is 2.60 years.

Calculate payback period for Project B:

Year	Unrecovered investment($) (Beginning of year)	Annual cash Flow($)	Time needed for payback (Years)
1	20,000	6,000	1.0
2	14,000	8,000	1.0
3	6,000¹	10,000	0.60
	0		2.60

Table (2)

Therefore, payback period is 2.60 years.

As both the projects have same payback period, the profitable project must be chosen. The cash flow from project B beyond the payback period is lesser than that of project A. Therefore, project A should be chosen because it is more profitable.

Working Note:

1. Calculation of payback period for third year:

Payback period=Unrecovered investmentAnnual cash flow=$6,000$10,000=0.60

2.

To determine

Find out the project to be chosen on the basis of accounting rate of return (ARR). Also, explain the reason for better performance of ARR in this setting than payback period.

2.

Expert Solution

Explanation of Solution

Accounting Rate of Return:

A method that measures returns from an investment in terms of income instead of cash flow is known as accounting rate of return. It is a non-discounting model of capital investment decision.

Use the following formula to calculate accounting rate of return (ARR) for project A:

ARR=Average incomeInitial investment

Substitute $4,800¹ for average income and $20,000 for initial investment in the above formula.

ARR=$4,800$20,000=24%

Therefore, accounting rate of return is 24%.

Use the following formula to calculate accounting rate of return (ARR) for project A:

ARR=Average incomeInitial investment

Substitute $2,000² for average income and $20,000 for initial investment in the above formula.

ARR=$2,000$20,000=10%

Therefore, accounting rate of return is 10%.

ARR considers the cash inflow from a project beyond its payback period which is not the case in the payback period. Therefore, ARR performs better than the payback period in this case.

Working Note:

1. Calculation of average cash inflow:

Average cash inflow=Total cash inflowNumber of years=($6,000+$8,000+$10,000+$10,000+$10,000)5=$44,0005=$8,800

Calculation of depreciation:

Depreciation=Cost−Salvage valueUseful life=$20,000−05=$4,000

Calculation of average income:

Average income=Average cash inflow−Depreciation=$8,800−$4,000=$4,800

2. Calculation of average cash inflow:

Average cash inflow=Total cash inflowNumber of years=($6,000+$8,000+$10,000+$3,000+$3,000)5=$30,0005=$6,000

Calculation of depreciation:

Depreciation=Cost−Salvage valueUseful life=$20,000−05=$4,000

Calculation of average income:

Average income=Average cash inflow−Depreciation=$6,000−$4,000=$2,000

3.

To determine

Calculate present value of the annuity to recommend that Person WG should accept the lump sum amount or annuity.

3.

Expert Solution

Explanation of Solution

Calculate present value of a future annuity:

Use the following formula to calculate present value of a future annuity;

Present value=Annuity value×Discount factor

Substitute $30,000 for annuity value and 11.46992 for discount factor in the above formula.

Present value=$30,000×11.46992=$344,098

Therefore, the present value of the annuity is $344,098.

The present value of the future annuity is lesser than the lump sum amount. Therefore, Person WG should accept the lump sum amount.

4.

To determine

Find out the NPV of the investment if the RRR is 8%. Also, recommend that Person D should invest or not.

4.

Expert Solution

Explanation of Solution

Net Present Value:

The remaining balance of the present value of a project’s inflows and outflows is known as net present value (NPV). It is a discounting model of capital investment decision. A project with a positive NPV increases the wealth of a firm whereas a project with a negative NPV decreases the wealth of a firm.

Use the following formula to calculate NPV of the investment:

NPV=Present value of cash inflow(P)−Present value of cash outflow(I)

Substitute $41,606³ for P and $30,000 for I in the above formula.

NPV=$41,606−$30,000=$11,606

Therefore, net present value of the investment is $11,606.

Person D should make the investment because NPV of the investment is positive.

Working Note:

3. Calculation of present value of future cash flow:

Present value of future cash flow=Future value×Discount factor=$9,000×4.62288=$41,606

5.

To determine

Find out the IRR for Person PF’s project. Also recommend that Person PF should acquire the equipment or not.

5.

Expert Solution

Explanation of Solution

Internal Rate of Return:

An interest rate at which the present value of an investment’s cash inflows is equal to the present value cost of the investment is known as internal rate of return. The value of NPV is zero in case of an internal rate of return.

Use the following formula to calculate discount factor:

Discount factor=InvestmentAnnual cash flow

Substitute $400,000 for investment and $75,000 for annual cash flow in the above formula.

Discount factor=$40,000$75,000=5.33333

Therefore, discount factor for Model CX is 5.33333.

The IRR is approximately 13% which is more than Person PF’s cost of capital. Therefore, Person PF should acquire the equipment.

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Answer 4

Question

Chapter 12, Problem 37E

1.

To determine

Find out the payback period for the new equipment for each of KD’s projects. Recommend the project to be chosen if rapid payback is important. Also, recommend the project should be chosen.

1.

Expert Solution

Explanation of Solution

Payback Period:

The time taken by an investment to recover its original value is known as payback period. It is calculated by dividing the original amount of investment by annual cash flow from the investment.

Calculate payback period for Project A:

Year	Unrecovered investment($) (Beginning of year)	Annual cash Flow($)	Time needed for payback (Years)
1	20,000	6,000	1.0
2	14,000	8,000	1.0
3	6,000¹	10,000	0.60
	0		2.60

Table (1)

Therefore, payback period is 2.60 years.

Calculate payback period for Project B:

Year	Unrecovered investment($) (Beginning of year)	Annual cash Flow($)	Time needed for payback (Years)
1	20,000	6,000	1.0
2	14,000	8,000	1.0
3	6,000¹	10,000	0.60
	0		2.60

Table (2)

Therefore, payback period is 2.60 years.

As both the projects have same payback period, the profitable project must be chosen. The cash flow from project B beyond the payback period is lesser than that of project A. Therefore, project A should be chosen because it is more profitable.

Working Note:

1. Calculation of payback period for third year:

Payback period=Unrecovered investmentAnnual cash flow=$6,000$10,000=0.60

2.

To determine

Find out the project to be chosen on the basis of accounting rate of return (ARR). Also, explain the reason for better performance of ARR in this setting than payback period.

2.

Expert Solution

Explanation of Solution

Accounting Rate of Return:

A method that measures returns from an investment in terms of income instead of cash flow is known as accounting rate of return. It is a non-discounting model of capital investment decision.

Use the following formula to calculate accounting rate of return (ARR) for project A:

ARR=Average incomeInitial investment

Substitute $4,800¹ for average income and $20,000 for initial investment in the above formula.

ARR=$4,800$20,000=24%

Therefore, accounting rate of return is 24%.

Use the following formula to calculate accounting rate of return (ARR) for project A:

ARR=Average incomeInitial investment

Substitute $2,000² for average income and $20,000 for initial investment in the above formula.

ARR=$2,000$20,000=10%

Therefore, accounting rate of return is 10%.

ARR considers the cash inflow from a project beyond its payback period which is not the case in the payback period. Therefore, ARR performs better than the payback period in this case.

Working Note:

1. Calculation of average cash inflow:

Average cash inflow=Total cash inflowNumber of years=($6,000+$8,000+$10,000+$10,000+$10,000)5=$44,0005=$8,800

Calculation of depreciation:

Depreciation=Cost−Salvage valueUseful life=$20,000−05=$4,000

Calculation of average income:

Average income=Average cash inflow−Depreciation=$8,800−$4,000=$4,800

2. Calculation of average cash inflow:

Average cash inflow=Total cash inflowNumber of years=($6,000+$8,000+$10,000+$3,000+$3,000)5=$30,0005=$6,000

Calculation of depreciation:

Depreciation=Cost−Salvage valueUseful life=$20,000−05=$4,000

Calculation of average income:

Average income=Average cash inflow−Depreciation=$6,000−$4,000=$2,000

3.

To determine

Calculate present value of the annuity to recommend that Person WG should accept the lump sum amount or annuity.

3.

Expert Solution

Explanation of Solution

Calculate present value of a future annuity:

Use the following formula to calculate present value of a future annuity;

Present value=Annuity value×Discount factor

Substitute $30,000 for annuity value and 11.46992 for discount factor in the above formula.

Present value=$30,000×11.46992=$344,098

Therefore, the present value of the annuity is $344,098.

The present value of the future annuity is lesser than the lump sum amount. Therefore, Person WG should accept the lump sum amount.

4.

To determine

Find out the NPV of the investment if the RRR is 8%. Also, recommend that Person D should invest or not.

4.

Expert Solution

Explanation of Solution

Net Present Value:

The remaining balance of the present value of a project’s inflows and outflows is known as net present value (NPV). It is a discounting model of capital investment decision. A project with a positive NPV increases the wealth of a firm whereas a project with a negative NPV decreases the wealth of a firm.

Use the following formula to calculate NPV of the investment:

NPV=Present value of cash inflow(P)−Present value of cash outflow(I)

Substitute $41,606³ for P and $30,000 for I in the above formula.

NPV=$41,606−$30,000=$11,606

Therefore, net present value of the investment is $11,606.

Person D should make the investment because NPV of the investment is positive.

Working Note:

3. Calculation of present value of future cash flow:

Present value of future cash flow=Future value×Discount factor=$9,000×4.62288=$41,606

5.

To determine

Find out the IRR for Person PF’s project. Also recommend that Person PF should acquire the equipment or not.

5.

Expert Solution

Explanation of Solution

Internal Rate of Return:

An interest rate at which the present value of an investment’s cash inflows is equal to the present value cost of the investment is known as internal rate of return. The value of NPV is zero in case of an internal rate of return.

Use the following formula to calculate discount factor:

Discount factor=InvestmentAnnual cash flow

Substitute $400,000 for investment and $75,000 for annual cash flow in the above formula.

Discount factor=$40,000$75,000=5.33333

Therefore, discount factor for Model CX is 5.33333.

The IRR is approximately 13% which is more than Person PF’s cost of capital. Therefore, Person PF should acquire the equipment.

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Answer 5

Chapter 12, Problem 37E

1.

To determine

Find out the payback period for the new equipment for each of KD’s projects. Recommend the project to be chosen if rapid payback is important. Also, recommend the project should be chosen.

1.

Expert Solution

Explanation of Solution

Payback Period:

The time taken by an investment to recover its original value is known as payback period. It is calculated by dividing the original amount of investment by annual cash flow from the investment.

Calculate payback period for Project A:

Year	Unrecovered investment($) (Beginning of year)	Annual cash Flow($)	Time needed for payback (Years)
1	20,000	6,000	1.0
2	14,000	8,000	1.0
3	6,000¹	10,000	0.60
	0		2.60

Table (1)

Therefore, payback period is 2.60 years.

Calculate payback period for Project B:

Year	Unrecovered investment($) (Beginning of year)	Annual cash Flow($)	Time needed for payback (Years)
1	20,000	6,000	1.0
2	14,000	8,000	1.0
3	6,000¹	10,000	0.60
	0		2.60

Table (2)

Therefore, payback period is 2.60 years.

As both the projects have same payback period, the profitable project must be chosen. The cash flow from project B beyond the payback period is lesser than that of project A. Therefore, project A should be chosen because it is more profitable.

Working Note:

1. Calculation of payback period for third year:

Payback period=Unrecovered investmentAnnual cash flow=$6,000$10,000=0.60

2.

To determine

Find out the project to be chosen on the basis of accounting rate of return (ARR). Also, explain the reason for better performance of ARR in this setting than payback period.

2.

Expert Solution

Explanation of Solution

Accounting Rate of Return:

A method that measures returns from an investment in terms of income instead of cash flow is known as accounting rate of return. It is a non-discounting model of capital investment decision.

Use the following formula to calculate accounting rate of return (ARR) for project A:

ARR=Average incomeInitial investment

Substitute $4,800¹ for average income and $20,000 for initial investment in the above formula.

ARR=$4,800$20,000=24%

Therefore, accounting rate of return is 24%.

Use the following formula to calculate accounting rate of return (ARR) for project A:

ARR=Average incomeInitial investment

Substitute $2,000² for average income and $20,000 for initial investment in the above formula.

ARR=$2,000$20,000=10%

Therefore, accounting rate of return is 10%.

ARR considers the cash inflow from a project beyond its payback period which is not the case in the payback period. Therefore, ARR performs better than the payback period in this case.

Working Note:

1. Calculation of average cash inflow:

Average cash inflow=Total cash inflowNumber of years=($6,000+$8,000+$10,000+$10,000+$10,000)5=$44,0005=$8,800

Calculation of depreciation:

Depreciation=Cost−Salvage valueUseful life=$20,000−05=$4,000

Calculation of average income:

Average income=Average cash inflow−Depreciation=$8,800−$4,000=$4,800

2. Calculation of average cash inflow:

Average cash inflow=Total cash inflowNumber of years=($6,000+$8,000+$10,000+$3,000+$3,000)5=$30,0005=$6,000

Calculation of depreciation:

Depreciation=Cost−Salvage valueUseful life=$20,000−05=$4,000

Calculation of average income:

Average income=Average cash inflow−Depreciation=$6,000−$4,000=$2,000

3.

To determine

Calculate present value of the annuity to recommend that Person WG should accept the lump sum amount or annuity.

3.

Expert Solution

Explanation of Solution

Calculate present value of a future annuity:

Use the following formula to calculate present value of a future annuity;

Present value=Annuity value×Discount factor

Substitute $30,000 for annuity value and 11.46992 for discount factor in the above formula.

Present value=$30,000×11.46992=$344,098

Therefore, the present value of the annuity is $344,098.

The present value of the future annuity is lesser than the lump sum amount. Therefore, Person WG should accept the lump sum amount.

4.

To determine

Find out the NPV of the investment if the RRR is 8%. Also, recommend that Person D should invest or not.

4.

Expert Solution

Explanation of Solution

Net Present Value:

The remaining balance of the present value of a project’s inflows and outflows is known as net present value (NPV). It is a discounting model of capital investment decision. A project with a positive NPV increases the wealth of a firm whereas a project with a negative NPV decreases the wealth of a firm.

Use the following formula to calculate NPV of the investment:

NPV=Present value of cash inflow(P)−Present value of cash outflow(I)

Substitute $41,606³ for P and $30,000 for I in the above formula.

NPV=$41,606−$30,000=$11,606

Therefore, net present value of the investment is $11,606.

Person D should make the investment because NPV of the investment is positive.

Working Note:

3. Calculation of present value of future cash flow:

Present value of future cash flow=Future value×Discount factor=$9,000×4.62288=$41,606

5.

To determine

Find out the IRR for Person PF’s project. Also recommend that Person PF should acquire the equipment or not.

5.

Expert Solution

Explanation of Solution

Internal Rate of Return:

An interest rate at which the present value of an investment’s cash inflows is equal to the present value cost of the investment is known as internal rate of return. The value of NPV is zero in case of an internal rate of return.

Use the following formula to calculate discount factor:

Discount factor=InvestmentAnnual cash flow

Substitute $400,000 for investment and $75,000 for annual cash flow in the above formula.

Discount factor=$40,000$75,000=5.33333

Therefore, discount factor for Model CX is 5.33333.

The IRR is approximately 13% which is more than Person PF’s cost of capital. Therefore, Person PF should acquire the equipment.

Answer 6

Chapter 12, Problem 37E

1.

To determine

Find out the payback period for the new equipment for each of KD’s projects. Recommend the project to be chosen if rapid payback is important. Also, recommend the project should be chosen.

1.

Expert Solution

Explanation of Solution

Payback Period:

The time taken by an investment to recover its original value is known as payback period. It is calculated by dividing the original amount of investment by annual cash flow from the investment.

Calculate payback period for Project A:

Year	Unrecovered investment($) (Beginning of year)	Annual cash Flow($)	Time needed for payback (Years)
1	20,000	6,000	1.0
2	14,000	8,000	1.0
3	6,000¹	10,000	0.60
	0		2.60

Table (1)

Therefore, payback period is 2.60 years.

Calculate payback period for Project B:

Year	Unrecovered investment($) (Beginning of year)	Annual cash Flow($)	Time needed for payback (Years)
1	20,000	6,000	1.0
2	14,000	8,000	1.0
3	6,000¹	10,000	0.60
	0		2.60

Table (2)

Therefore, payback period is 2.60 years.

As both the projects have same payback period, the profitable project must be chosen. The cash flow from project B beyond the payback period is lesser than that of project A. Therefore, project A should be chosen because it is more profitable.

Working Note:

1. Calculation of payback period for third year:

Payback period=Unrecovered investmentAnnual cash flow=$6,000$10,000=0.60

Answer 7

Chapter 12, Problem 37E

1.

To determine

Find out the payback period for the new equipment for each of KD’s projects. Recommend the project to be chosen if rapid payback is important. Also, recommend the project should be chosen.

Answer 8

1.

Expert Solution

Explanation of Solution

Payback Period:

The time taken by an investment to recover its original value is known as payback period. It is calculated by dividing the original amount of investment by annual cash flow from the investment.

Calculate payback period for Project A:

Year	Unrecovered investment($) (Beginning of year)	Annual cash Flow($)	Time needed for payback (Years)
1	20,000	6,000	1.0
2	14,000	8,000	1.0
3	6,000¹	10,000	0.60
	0		2.60

Table (1)

Therefore, payback period is 2.60 years.

Calculate payback period for Project B:

Year	Unrecovered investment($) (Beginning of year)	Annual cash Flow($)	Time needed for payback (Years)
1	20,000	6,000	1.0
2	14,000	8,000	1.0
3	6,000¹	10,000	0.60
	0		2.60

Table (2)

Therefore, payback period is 2.60 years.

As both the projects have same payback period, the profitable project must be chosen. The cash flow from project B beyond the payback period is lesser than that of project A. Therefore, project A should be chosen because it is more profitable.

Working Note:

1. Calculation of payback period for third year:

Payback period=Unrecovered investmentAnnual cash flow=$6,000$10,000=0.60

Answer 9

1.

Expert Solution

Answer 10

1.

Expert Solution

Answer 11

Expert Solution

Answer 12

2.

To determine

Find out the project to be chosen on the basis of accounting rate of return (ARR). Also, explain the reason for better performance of ARR in this setting than payback period.

2.

Expert Solution

Explanation of Solution

Accounting Rate of Return:

A method that measures returns from an investment in terms of income instead of cash flow is known as accounting rate of return. It is a non-discounting model of capital investment decision.

Use the following formula to calculate accounting rate of return (ARR) for project A:

ARR=Average incomeInitial investment

Substitute $4,800¹ for average income and $20,000 for initial investment in the above formula.

ARR=$4,800$20,000=24%

Therefore, accounting rate of return is 24%.

Use the following formula to calculate accounting rate of return (ARR) for project A:

ARR=Average incomeInitial investment

Substitute $2,000² for average income and $20,000 for initial investment in the above formula.

ARR=$2,000$20,000=10%

Therefore, accounting rate of return is 10%.

ARR considers the cash inflow from a project beyond its payback period which is not the case in the payback period. Therefore, ARR performs better than the payback period in this case.

Working Note:

1. Calculation of average cash inflow:

Average cash inflow=Total cash inflowNumber of years=($6,000+$8,000+$10,000+$10,000+$10,000)5=$44,0005=$8,800

Calculation of depreciation:

Depreciation=Cost−Salvage valueUseful life=$20,000−05=$4,000

Calculation of average income:

Average income=Average cash inflow−Depreciation=$8,800−$4,000=$4,800

2. Calculation of average cash inflow:

Average cash inflow=Total cash inflowNumber of years=($6,000+$8,000+$10,000+$3,000+$3,000)5=$30,0005=$6,000

Calculation of depreciation:

Depreciation=Cost−Salvage valueUseful life=$20,000−05=$4,000

Calculation of average income:

Average income=Average cash inflow−Depreciation=$6,000−$4,000=$2,000

Answer 13

2.

To determine

Find out the project to be chosen on the basis of accounting rate of return (ARR). Also, explain the reason for better performance of ARR in this setting than payback period.

Answer 14

2.

Expert Solution

Explanation of Solution

Accounting Rate of Return:

A method that measures returns from an investment in terms of income instead of cash flow is known as accounting rate of return. It is a non-discounting model of capital investment decision.

Use the following formula to calculate accounting rate of return (ARR) for project A:

ARR=Average incomeInitial investment

Substitute $4,800¹ for average income and $20,000 for initial investment in the above formula.

ARR=$4,800$20,000=24%

Therefore, accounting rate of return is 24%.

Use the following formula to calculate accounting rate of return (ARR) for project A:

ARR=Average incomeInitial investment

Substitute $2,000² for average income and $20,000 for initial investment in the above formula.

ARR=$2,000$20,000=10%

Therefore, accounting rate of return is 10%.

ARR considers the cash inflow from a project beyond its payback period which is not the case in the payback period. Therefore, ARR performs better than the payback period in this case.

Working Note:

1. Calculation of average cash inflow:

Average cash inflow=Total cash inflowNumber of years=($6,000+$8,000+$10,000+$10,000+$10,000)5=$44,0005=$8,800

Calculation of depreciation:

Depreciation=Cost−Salvage valueUseful life=$20,000−05=$4,000

Calculation of average income:

Average income=Average cash inflow−Depreciation=$8,800−$4,000=$4,800

2. Calculation of average cash inflow:

Average cash inflow=Total cash inflowNumber of years=($6,000+$8,000+$10,000+$3,000+$3,000)5=$30,0005=$6,000

Calculation of depreciation:

Depreciation=Cost−Salvage valueUseful life=$20,000−05=$4,000

Calculation of average income:

Average income=Average cash inflow−Depreciation=$6,000−$4,000=$2,000

Answer 15

2.

Expert Solution

Answer 16

2.

Expert Solution

Answer 17

Expert Solution

Answer 18

3.

To determine

Calculate present value of the annuity to recommend that Person WG should accept the lump sum amount or annuity.

3.

Expert Solution

Explanation of Solution

Calculate present value of a future annuity:

Use the following formula to calculate present value of a future annuity;

Present value=Annuity value×Discount factor

Substitute $30,000 for annuity value and 11.46992 for discount factor in the above formula.

Present value=$30,000×11.46992=$344,098

Therefore, the present value of the annuity is $344,098.

The present value of the future annuity is lesser than the lump sum amount. Therefore, Person WG should accept the lump sum amount.

Answer 19

3.

To determine

Calculate present value of the annuity to recommend that Person WG should accept the lump sum amount or annuity.

Answer 20

3.

Expert Solution

Explanation of Solution

Calculate present value of a future annuity:

Use the following formula to calculate present value of a future annuity;

Present value=Annuity value×Discount factor

Substitute $30,000 for annuity value and 11.46992 for discount factor in the above formula.

Present value=$30,000×11.46992=$344,098

Therefore, the present value of the annuity is $344,098.

The present value of the future annuity is lesser than the lump sum amount. Therefore, Person WG should accept the lump sum amount.

Answer 21

3.

Expert Solution

Answer 22

3.

Expert Solution

Answer 23

Expert Solution

Answer 24

4.

To determine

Find out the NPV of the investment if the RRR is 8%. Also, recommend that Person D should invest or not.

4.

Expert Solution

Explanation of Solution

Net Present Value:

The remaining balance of the present value of a project’s inflows and outflows is known as net present value (NPV). It is a discounting model of capital investment decision. A project with a positive NPV increases the wealth of a firm whereas a project with a negative NPV decreases the wealth of a firm.

Use the following formula to calculate NPV of the investment:

NPV=Present value of cash inflow(P)−Present value of cash outflow(I)

Substitute $41,606³ for P and $30,000 for I in the above formula.

NPV=$41,606−$30,000=$11,606

Therefore, net present value of the investment is $11,606.

Person D should make the investment because NPV of the investment is positive.

Working Note:

3. Calculation of present value of future cash flow:

Present value of future cash flow=Future value×Discount factor=$9,000×4.62288=$41,606

Answer 25

4.

To determine

Find out the NPV of the investment if the RRR is 8%. Also, recommend that Person D should invest or not.

Answer 26

4.

Expert Solution

Explanation of Solution

Net Present Value:

The remaining balance of the present value of a project’s inflows and outflows is known as net present value (NPV). It is a discounting model of capital investment decision. A project with a positive NPV increases the wealth of a firm whereas a project with a negative NPV decreases the wealth of a firm.

Use the following formula to calculate NPV of the investment:

NPV=Present value of cash inflow(P)−Present value of cash outflow(I)

Substitute $41,606³ for P and $30,000 for I in the above formula.

NPV=$41,606−$30,000=$11,606

Therefore, net present value of the investment is $11,606.

Person D should make the investment because NPV of the investment is positive.

Working Note:

3. Calculation of present value of future cash flow:

Present value of future cash flow=Future value×Discount factor=$9,000×4.62288=$41,606

Answer 27

4.

Expert Solution

Answer 28

4.

Expert Solution

Answer 29

Expert Solution

Answer 30

5.

To determine

Find out the IRR for Person PF’s project. Also recommend that Person PF should acquire the equipment or not.

5.

Expert Solution

Explanation of Solution

Internal Rate of Return:

An interest rate at which the present value of an investment’s cash inflows is equal to the present value cost of the investment is known as internal rate of return. The value of NPV is zero in case of an internal rate of return.

Use the following formula to calculate discount factor:

Discount factor=InvestmentAnnual cash flow

Substitute $400,000 for investment and $75,000 for annual cash flow in the above formula.

Discount factor=$40,000$75,000=5.33333

Therefore, discount factor for Model CX is 5.33333.

The IRR is approximately 13% which is more than Person PF’s cost of capital. Therefore, Person PF should acquire the equipment.

Answer 31

5.

To determine

Find out the IRR for Person PF’s project. Also recommend that Person PF should acquire the equipment or not.

Answer 32

5.

Expert Solution

Explanation of Solution

Internal Rate of Return:

An interest rate at which the present value of an investment’s cash inflows is equal to the present value cost of the investment is known as internal rate of return. The value of NPV is zero in case of an internal rate of return.

Use the following formula to calculate discount factor:

Discount factor=InvestmentAnnual cash flow

Substitute $400,000 for investment and $75,000 for annual cash flow in the above formula.

Discount factor=$40,000$75,000=5.33333

Therefore, discount factor for Model CX is 5.33333.

The IRR is approximately 13% which is more than Person PF’s cost of capital. Therefore, Person PF should acquire the equipment.

Answer 33

5.

Expert Solution

Answer 34

5.

Expert Solution

Answer 35

Expert Solution

Answer 36

Ch. 12 - Prob. 1DQ Ch. 12 - Explain why the timing and quantity of cash flows...Ch. 12 - The time value of money is ignored by the payback...Ch. 12 - What is the payback period? Compute the payback...Ch. 12 - Name and discuss three possible reasons that the...Ch. 12 - Prob. 6DQ Ch. 12 - The NPV is the same as the profit of a project...Ch. 12 - Explain the relationship between NPV and a firms...Ch. 12 - Prob. 9DQ Ch. 12 - What is the role that the required rate of return...

Find out the payback period for the new equipment for each of KD’s projects. Recommend the project to be chosen if rapid payback is important. Also, recommend the project should be chosen.

Find out the payback period for the new equipment for each of KD’s projects. Recommend the project to be chosen if rapid payback is important. Also, recommend the project should be chosen.

Explanation of Solution

Find out the project to be chosen on the basis of accounting rate of return (ARR). Also, explain the reason for better performance of ARR in this setting than payback period.

Explanation of Solution

Calculate present value of the annuity to recommend that Person WG should accept the lump sum amount or annuity.

Explanation of Solution

Find out the NPV of the investment if the RRR is 8%. Also, recommend that Person D should invest or not.

Explanation of Solution

Find out the IRR for Person PF’s project. Also recommend that Person PF should acquire the equipment or not.

Explanation of Solution

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