The MIRR (Modified Internal Rate of Return ) for the project utilizing all three methods. Introduction: MIRR is the Modified Internal Rate of Return; it is a financial measure of attracting investments. It is utilized in capital budgeting to rank the alternative investments of the same size.

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Answer 1

Question

Chapter 8, Problem 22QP

Summary Introduction

To calculate: The MIRR (Modified Internal Rate of Return) for the project utilizing all three methods.

Introduction:

MIRR is the Modified Internal Rate of Return; it is a financial measure of attracting investments. It is utilized in capital budgeting to rank the alternative investments of the same size.

Expert Solution & Answer

Answer to Problem 22QP

The MIRR for the project using the discounted approach is 19.21%, reinvestment approach is 14.49%, and combination approach is 14.14%.

Explanation of Solution

Given information:

Company M is assessing a project where the cash flows are $10,430, $13,850, $11,270, $9,830, and -$4,050 for year 1, 2, 3, 4, and 5 respectively. The initial cost is $27,500.

Discounted approach:

In this approach, compute the negative cash outflows value at year 0. On the other hand, the positive cash flows remain at its time of occurrence. Hence, discount the cash outflows to year 0.

$Time 0 cash flow=Initial cost+−Cash outflows(1+r)t=−$27,500+−$4,050(1+0.10)5=−$30,014.73$

Hence, the discounted cash flow at time 0 is -$30,014.73.

Equation of MIRR in a discounted approach:

$0=−$30,014.73+$10,430(1+MIRR)+$13,850(1+MIRR)2+$11,270(1+MIRR)3+$9,830(1+MIRR)4$

Compute MIRR using a spreadsheet:

Step 1:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 1

Type the equation of NPV in H6 in the spreadsheet and consider the MIRR value as H7.

Step 2:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 2

Assume the MIRR value as 0.10%.

Step 3:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 3

In the spreadsheet, go to data and select the what-if analysis.
In the what-if analysis, select goal seek.
In set cell, select H6 (the formula).
The “To value” is considered as 0 (the assumption value for NPV).
The H7 cell is selected for the by changing cell.

Step 4:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 4

Following the previous step click OK in the goal seek. The goal seek status appears with the MIRR value.

Step 5:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 5

Thevalue appears to be 19.2108278981048%.

Hence, the MIRR value is 19.21%.

Reinvestment approach:

In this approach, compute the future value of all the cash flows excluding the initial cost at the closure of the project. Hence, compute the reinvesting cash flows to year 5 is:

$Time 5 cash flow=Cash flows (year 1(1+r)4+year 2(1+r)3+year 3(1+r)2+year 4(1+r)+year 5)=($10,430(1+0.10)4+$13,850(1+0.10)3+$11,270(1+0.10)2+$9,830(1+0.10)−$4,050)=$10,430(1.4641)+$13,850(1.331)+$11,270(1.21)+$9,830(1.10)−$4,050=$54,104.61$

Hence, the reinvesting cash flow at time 5 is $54,104.61.

Equation of MIRR in reinvestment approach:

$0=−$27,500+$54,104.61(1+MIRR)5$

Compute the MIRR:

$0=−$27,500+$54,104.61(1+MIRR)5$54,104.61$27,500=(1+MIRR)5MIRR=($54,104.61$27,500)1/5−1MIRR=0.1449 or 14.49%$

Hence, the MIRR is 14.49%.

Combination approach:

In this approach, compute all the cash outflows at year 0 and all the cash inflows at the closure of the project. Hence, the value of the cash flows is as follows:

$Time 0 cash flow=Initial cost+−Cash outflows(1+r)t=−$27,500+−$4,050(1+0.10)5=−$30,014.73$

Hence, the total cash outflow at year 0 is -$30,014.73.

$Time 5 cash flow=Cash flows (year1(1+r)4+year2(1+r)3+year3(1+r)2+year4(1+r)+year5)=($10,430(1+0.10)4+$13,850(1+0.10)3+$11,270(1+0.10)2+$9,830(1+0.10))=$10,430(1.4641)+$13,850(1.331)+$11,270(1.21)+$9,830(1.10)=$58,154.61$

Hence, the value of total cash inflows is $58,154.61.

Equation of MIRR in combination approach:

$0=−$30,014.73+$58,154.61(1+MIRR)5$

Compute the MIRR:

$0=−$30,014.73+$58,154.61(1+MIRR)5$58,154.61$30,014.73=(1+MIRR)5MIRR=($58,154.61$30,014.73)1/5−1MIRR=0.1414 or 14.14%$

Hence, the MIRR is $14.14%.

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Answer 2

Question

Chapter 8, Problem 22QP

Summary Introduction

To calculate: The MIRR (Modified Internal Rate of Return) for the project utilizing all three methods.

Introduction:

MIRR is the Modified Internal Rate of Return; it is a financial measure of attracting investments. It is utilized in capital budgeting to rank the alternative investments of the same size.

Expert Solution & Answer

Answer to Problem 22QP

The MIRR for the project using the discounted approach is 19.21%, reinvestment approach is 14.49%, and combination approach is 14.14%.

Explanation of Solution

Given information:

Company M is assessing a project where the cash flows are $10,430, $13,850, $11,270, $9,830, and -$4,050 for year 1, 2, 3, 4, and 5 respectively. The initial cost is $27,500.

Discounted approach:

In this approach, compute the negative cash outflows value at year 0. On the other hand, the positive cash flows remain at its time of occurrence. Hence, discount the cash outflows to year 0.

$Time 0 cash flow=Initial cost+−Cash outflows(1+r)t=−$27,500+−$4,050(1+0.10)5=−$30,014.73$

Hence, the discounted cash flow at time 0 is -$30,014.73.

Equation of MIRR in a discounted approach:

$0=−$30,014.73+$10,430(1+MIRR)+$13,850(1+MIRR)2+$11,270(1+MIRR)3+$9,830(1+MIRR)4$

Compute MIRR using a spreadsheet:

Step 1:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 1

Type the equation of NPV in H6 in the spreadsheet and consider the MIRR value as H7.

Step 2:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 2

Assume the MIRR value as 0.10%.

Step 3:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 3

In the spreadsheet, go to data and select the what-if analysis.
In the what-if analysis, select goal seek.
In set cell, select H6 (the formula).
The “To value” is considered as 0 (the assumption value for NPV).
The H7 cell is selected for the by changing cell.

Step 4:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 4

Following the previous step click OK in the goal seek. The goal seek status appears with the MIRR value.

Step 5:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 5

Thevalue appears to be 19.2108278981048%.

Hence, the MIRR value is 19.21%.

Reinvestment approach:

In this approach, compute the future value of all the cash flows excluding the initial cost at the closure of the project. Hence, compute the reinvesting cash flows to year 5 is:

$Time 5 cash flow=Cash flows (year 1(1+r)4+year 2(1+r)3+year 3(1+r)2+year 4(1+r)+year 5)=($10,430(1+0.10)4+$13,850(1+0.10)3+$11,270(1+0.10)2+$9,830(1+0.10)−$4,050)=$10,430(1.4641)+$13,850(1.331)+$11,270(1.21)+$9,830(1.10)−$4,050=$54,104.61$

Hence, the reinvesting cash flow at time 5 is $54,104.61.

Equation of MIRR in reinvestment approach:

$0=−$27,500+$54,104.61(1+MIRR)5$

Compute the MIRR:

$0=−$27,500+$54,104.61(1+MIRR)5$54,104.61$27,500=(1+MIRR)5MIRR=($54,104.61$27,500)1/5−1MIRR=0.1449 or 14.49%$

Hence, the MIRR is 14.49%.

Combination approach:

In this approach, compute all the cash outflows at year 0 and all the cash inflows at the closure of the project. Hence, the value of the cash flows is as follows:

$Time 0 cash flow=Initial cost+−Cash outflows(1+r)t=−$27,500+−$4,050(1+0.10)5=−$30,014.73$

Hence, the total cash outflow at year 0 is -$30,014.73.

$Time 5 cash flow=Cash flows (year1(1+r)4+year2(1+r)3+year3(1+r)2+year4(1+r)+year5)=($10,430(1+0.10)4+$13,850(1+0.10)3+$11,270(1+0.10)2+$9,830(1+0.10))=$10,430(1.4641)+$13,850(1.331)+$11,270(1.21)+$9,830(1.10)=$58,154.61$

Hence, the value of total cash inflows is $58,154.61.

Equation of MIRR in combination approach:

$0=−$30,014.73+$58,154.61(1+MIRR)5$

Compute the MIRR:

$0=−$30,014.73+$58,154.61(1+MIRR)5$58,154.61$30,014.73=(1+MIRR)5MIRR=($58,154.61$30,014.73)1/5−1MIRR=0.1414 or 14.14%$

Hence, the MIRR is $14.14%.

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Answer 3

Question

Chapter 8, Problem 22QP

Summary Introduction

To calculate: The MIRR (Modified Internal Rate of Return) for the project utilizing all three methods.

Introduction:

MIRR is the Modified Internal Rate of Return; it is a financial measure of attracting investments. It is utilized in capital budgeting to rank the alternative investments of the same size.

Expert Solution & Answer

Answer to Problem 22QP

The MIRR for the project using the discounted approach is 19.21%, reinvestment approach is 14.49%, and combination approach is 14.14%.

Explanation of Solution

Given information:

Company M is assessing a project where the cash flows are $10,430, $13,850, $11,270, $9,830, and -$4,050 for year 1, 2, 3, 4, and 5 respectively. The initial cost is $27,500.

Discounted approach:

In this approach, compute the negative cash outflows value at year 0. On the other hand, the positive cash flows remain at its time of occurrence. Hence, discount the cash outflows to year 0.

$Time 0 cash flow=Initial cost+−Cash outflows(1+r)t=−$27,500+−$4,050(1+0.10)5=−$30,014.73$

Hence, the discounted cash flow at time 0 is -$30,014.73.

Equation of MIRR in a discounted approach:

$0=−$30,014.73+$10,430(1+MIRR)+$13,850(1+MIRR)2+$11,270(1+MIRR)3+$9,830(1+MIRR)4$

Compute MIRR using a spreadsheet:

Step 1:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 1

Type the equation of NPV in H6 in the spreadsheet and consider the MIRR value as H7.

Step 2:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 2

Assume the MIRR value as 0.10%.

Step 3:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 3

In the spreadsheet, go to data and select the what-if analysis.
In the what-if analysis, select goal seek.
In set cell, select H6 (the formula).
The “To value” is considered as 0 (the assumption value for NPV).
The H7 cell is selected for the by changing cell.

Step 4:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 4

Following the previous step click OK in the goal seek. The goal seek status appears with the MIRR value.

Step 5:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 5

Thevalue appears to be 19.2108278981048%.

Hence, the MIRR value is 19.21%.

Reinvestment approach:

In this approach, compute the future value of all the cash flows excluding the initial cost at the closure of the project. Hence, compute the reinvesting cash flows to year 5 is:

$Time 5 cash flow=Cash flows (year 1(1+r)4+year 2(1+r)3+year 3(1+r)2+year 4(1+r)+year 5)=($10,430(1+0.10)4+$13,850(1+0.10)3+$11,270(1+0.10)2+$9,830(1+0.10)−$4,050)=$10,430(1.4641)+$13,850(1.331)+$11,270(1.21)+$9,830(1.10)−$4,050=$54,104.61$

Hence, the reinvesting cash flow at time 5 is $54,104.61.

Equation of MIRR in reinvestment approach:

$0=−$27,500+$54,104.61(1+MIRR)5$

Compute the MIRR:

$0=−$27,500+$54,104.61(1+MIRR)5$54,104.61$27,500=(1+MIRR)5MIRR=($54,104.61$27,500)1/5−1MIRR=0.1449 or 14.49%$

Hence, the MIRR is 14.49%.

Combination approach:

In this approach, compute all the cash outflows at year 0 and all the cash inflows at the closure of the project. Hence, the value of the cash flows is as follows:

$Time 0 cash flow=Initial cost+−Cash outflows(1+r)t=−$27,500+−$4,050(1+0.10)5=−$30,014.73$

Hence, the total cash outflow at year 0 is -$30,014.73.

$Time 5 cash flow=Cash flows (year1(1+r)4+year2(1+r)3+year3(1+r)2+year4(1+r)+year5)=($10,430(1+0.10)4+$13,850(1+0.10)3+$11,270(1+0.10)2+$9,830(1+0.10))=$10,430(1.4641)+$13,850(1.331)+$11,270(1.21)+$9,830(1.10)=$58,154.61$

Hence, the value of total cash inflows is $58,154.61.

Equation of MIRR in combination approach:

$0=−$30,014.73+$58,154.61(1+MIRR)5$

Compute the MIRR:

$0=−$30,014.73+$58,154.61(1+MIRR)5$58,154.61$30,014.73=(1+MIRR)5MIRR=($58,154.61$30,014.73)1/5−1MIRR=0.1414 or 14.14%$

Hence, the MIRR is $14.14%.

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Answer 4

Question

Chapter 8, Problem 22QP

Summary Introduction

To calculate: The MIRR (Modified Internal Rate of Return) for the project utilizing all three methods.

Introduction:

MIRR is the Modified Internal Rate of Return; it is a financial measure of attracting investments. It is utilized in capital budgeting to rank the alternative investments of the same size.

Expert Solution & Answer

Answer to Problem 22QP

The MIRR for the project using the discounted approach is 19.21%, reinvestment approach is 14.49%, and combination approach is 14.14%.

Explanation of Solution

Given information:

Company M is assessing a project where the cash flows are $10,430, $13,850, $11,270, $9,830, and -$4,050 for year 1, 2, 3, 4, and 5 respectively. The initial cost is $27,500.

Discounted approach:

In this approach, compute the negative cash outflows value at year 0. On the other hand, the positive cash flows remain at its time of occurrence. Hence, discount the cash outflows to year 0.

$Time 0 cash flow=Initial cost+−Cash outflows(1+r)t=−$27,500+−$4,050(1+0.10)5=−$30,014.73$

Hence, the discounted cash flow at time 0 is -$30,014.73.

Equation of MIRR in a discounted approach:

$0=−$30,014.73+$10,430(1+MIRR)+$13,850(1+MIRR)2+$11,270(1+MIRR)3+$9,830(1+MIRR)4$

Compute MIRR using a spreadsheet:

Step 1:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 1

Type the equation of NPV in H6 in the spreadsheet and consider the MIRR value as H7.

Step 2:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 2

Assume the MIRR value as 0.10%.

Step 3:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 3

In the spreadsheet, go to data and select the what-if analysis.
In the what-if analysis, select goal seek.
In set cell, select H6 (the formula).
The “To value” is considered as 0 (the assumption value for NPV).
The H7 cell is selected for the by changing cell.

Step 4:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 4

Following the previous step click OK in the goal seek. The goal seek status appears with the MIRR value.

Step 5:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 5

Thevalue appears to be 19.2108278981048%.

Hence, the MIRR value is 19.21%.

Reinvestment approach:

In this approach, compute the future value of all the cash flows excluding the initial cost at the closure of the project. Hence, compute the reinvesting cash flows to year 5 is:

$Time 5 cash flow=Cash flows (year 1(1+r)4+year 2(1+r)3+year 3(1+r)2+year 4(1+r)+year 5)=($10,430(1+0.10)4+$13,850(1+0.10)3+$11,270(1+0.10)2+$9,830(1+0.10)−$4,050)=$10,430(1.4641)+$13,850(1.331)+$11,270(1.21)+$9,830(1.10)−$4,050=$54,104.61$

Hence, the reinvesting cash flow at time 5 is $54,104.61.

Equation of MIRR in reinvestment approach:

$0=−$27,500+$54,104.61(1+MIRR)5$

Compute the MIRR:

$0=−$27,500+$54,104.61(1+MIRR)5$54,104.61$27,500=(1+MIRR)5MIRR=($54,104.61$27,500)1/5−1MIRR=0.1449 or 14.49%$

Hence, the MIRR is 14.49%.

Combination approach:

In this approach, compute all the cash outflows at year 0 and all the cash inflows at the closure of the project. Hence, the value of the cash flows is as follows:

$Time 0 cash flow=Initial cost+−Cash outflows(1+r)t=−$27,500+−$4,050(1+0.10)5=−$30,014.73$

Hence, the total cash outflow at year 0 is -$30,014.73.

$Time 5 cash flow=Cash flows (year1(1+r)4+year2(1+r)3+year3(1+r)2+year4(1+r)+year5)=($10,430(1+0.10)4+$13,850(1+0.10)3+$11,270(1+0.10)2+$9,830(1+0.10))=$10,430(1.4641)+$13,850(1.331)+$11,270(1.21)+$9,830(1.10)=$58,154.61$

Hence, the value of total cash inflows is $58,154.61.

Equation of MIRR in combination approach:

$0=−$30,014.73+$58,154.61(1+MIRR)5$

Compute the MIRR:

$0=−$30,014.73+$58,154.61(1+MIRR)5$58,154.61$30,014.73=(1+MIRR)5MIRR=($58,154.61$30,014.73)1/5−1MIRR=0.1414 or 14.14%$

Hence, the MIRR is $14.14%.

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Answer 5

Chapter 8, Problem 22QP

Summary Introduction

To calculate: The MIRR (Modified Internal Rate of Return) for the project utilizing all three methods.

Introduction:

MIRR is the Modified Internal Rate of Return; it is a financial measure of attracting investments. It is utilized in capital budgeting to rank the alternative investments of the same size.

Expert Solution & Answer

Answer to Problem 22QP

The MIRR for the project using the discounted approach is 19.21%, reinvestment approach is 14.49%, and combination approach is 14.14%.

Explanation of Solution

Given information:

Company M is assessing a project where the cash flows are $10,430, $13,850, $11,270, $9,830, and -$4,050 for year 1, 2, 3, 4, and 5 respectively. The initial cost is $27,500.

Discounted approach:

In this approach, compute the negative cash outflows value at year 0. On the other hand, the positive cash flows remain at its time of occurrence. Hence, discount the cash outflows to year 0.

$Time 0 cash flow=Initial cost+−Cash outflows(1+r)t=−$27,500+−$4,050(1+0.10)5=−$30,014.73$

Hence, the discounted cash flow at time 0 is -$30,014.73.

Equation of MIRR in a discounted approach:

$0=−$30,014.73+$10,430(1+MIRR)+$13,850(1+MIRR)2+$11,270(1+MIRR)3+$9,830(1+MIRR)4$

Compute MIRR using a spreadsheet:

Step 1:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 1

Type the equation of NPV in H6 in the spreadsheet and consider the MIRR value as H7.

Step 2:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 2

Assume the MIRR value as 0.10%.

Step 3:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 3

In the spreadsheet, go to data and select the what-if analysis.
In the what-if analysis, select goal seek.
In set cell, select H6 (the formula).
The “To value” is considered as 0 (the assumption value for NPV).
The H7 cell is selected for the by changing cell.

Step 4:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 4

Following the previous step click OK in the goal seek. The goal seek status appears with the MIRR value.

Step 5:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 5

Thevalue appears to be 19.2108278981048%.

Hence, the MIRR value is 19.21%.

Reinvestment approach:

In this approach, compute the future value of all the cash flows excluding the initial cost at the closure of the project. Hence, compute the reinvesting cash flows to year 5 is:

$Time 5 cash flow=Cash flows (year 1(1+r)4+year 2(1+r)3+year 3(1+r)2+year 4(1+r)+year 5)=($10,430(1+0.10)4+$13,850(1+0.10)3+$11,270(1+0.10)2+$9,830(1+0.10)−$4,050)=$10,430(1.4641)+$13,850(1.331)+$11,270(1.21)+$9,830(1.10)−$4,050=$54,104.61$

Hence, the reinvesting cash flow at time 5 is $54,104.61.

Equation of MIRR in reinvestment approach:

$0=−$27,500+$54,104.61(1+MIRR)5$

Compute the MIRR:

$0=−$27,500+$54,104.61(1+MIRR)5$54,104.61$27,500=(1+MIRR)5MIRR=($54,104.61$27,500)1/5−1MIRR=0.1449 or 14.49%$

Hence, the MIRR is 14.49%.

Combination approach:

In this approach, compute all the cash outflows at year 0 and all the cash inflows at the closure of the project. Hence, the value of the cash flows is as follows:

$Time 0 cash flow=Initial cost+−Cash outflows(1+r)t=−$27,500+−$4,050(1+0.10)5=−$30,014.73$

Hence, the total cash outflow at year 0 is -$30,014.73.

$Time 5 cash flow=Cash flows (year1(1+r)4+year2(1+r)3+year3(1+r)2+year4(1+r)+year5)=($10,430(1+0.10)4+$13,850(1+0.10)3+$11,270(1+0.10)2+$9,830(1+0.10))=$10,430(1.4641)+$13,850(1.331)+$11,270(1.21)+$9,830(1.10)=$58,154.61$

Hence, the value of total cash inflows is $58,154.61.

Equation of MIRR in combination approach:

$0=−$30,014.73+$58,154.61(1+MIRR)5$

Compute the MIRR:

$0=−$30,014.73+$58,154.61(1+MIRR)5$58,154.61$30,014.73=(1+MIRR)5MIRR=($58,154.61$30,014.73)1/5−1MIRR=0.1414 or 14.14%$

Hence, the MIRR is $14.14%.

Answer 6

Chapter 8, Problem 22QP

Summary Introduction

To calculate: The MIRR (Modified Internal Rate of Return) for the project utilizing all three methods.

Introduction:

MIRR is the Modified Internal Rate of Return; it is a financial measure of attracting investments. It is utilized in capital budgeting to rank the alternative investments of the same size.

Expert Solution & Answer

Answer to Problem 22QP

The MIRR for the project using the discounted approach is 19.21%, reinvestment approach is 14.49%, and combination approach is 14.14%.

Explanation of Solution

Given information:

Company M is assessing a project where the cash flows are $10,430, $13,850, $11,270, $9,830, and -$4,050 for year 1, 2, 3, 4, and 5 respectively. The initial cost is $27,500.

Discounted approach:

In this approach, compute the negative cash outflows value at year 0. On the other hand, the positive cash flows remain at its time of occurrence. Hence, discount the cash outflows to year 0.

$Time 0 cash flow=Initial cost+−Cash outflows(1+r)t=−$27,500+−$4,050(1+0.10)5=−$30,014.73$

Hence, the discounted cash flow at time 0 is -$30,014.73.

Equation of MIRR in a discounted approach:

$0=−$30,014.73+$10,430(1+MIRR)+$13,850(1+MIRR)2+$11,270(1+MIRR)3+$9,830(1+MIRR)4$

Compute MIRR using a spreadsheet:

Step 1:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 1

Type the equation of NPV in H6 in the spreadsheet and consider the MIRR value as H7.

Step 2:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 2

Assume the MIRR value as 0.10%.

Step 3:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 3

In the spreadsheet, go to data and select the what-if analysis.
In the what-if analysis, select goal seek.
In set cell, select H6 (the formula).
The “To value” is considered as 0 (the assumption value for NPV).
The H7 cell is selected for the by changing cell.

Step 4:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 4

Following the previous step click OK in the goal seek. The goal seek status appears with the MIRR value.

Step 5:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 5

Thevalue appears to be 19.2108278981048%.

Hence, the MIRR value is 19.21%.

Reinvestment approach:

In this approach, compute the future value of all the cash flows excluding the initial cost at the closure of the project. Hence, compute the reinvesting cash flows to year 5 is:

$Time 5 cash flow=Cash flows (year 1(1+r)4+year 2(1+r)3+year 3(1+r)2+year 4(1+r)+year 5)=($10,430(1+0.10)4+$13,850(1+0.10)3+$11,270(1+0.10)2+$9,830(1+0.10)−$4,050)=$10,430(1.4641)+$13,850(1.331)+$11,270(1.21)+$9,830(1.10)−$4,050=$54,104.61$

Hence, the reinvesting cash flow at time 5 is $54,104.61.

Equation of MIRR in reinvestment approach:

$0=−$27,500+$54,104.61(1+MIRR)5$

Compute the MIRR:

$0=−$27,500+$54,104.61(1+MIRR)5$54,104.61$27,500=(1+MIRR)5MIRR=($54,104.61$27,500)1/5−1MIRR=0.1449 or 14.49%$

Hence, the MIRR is 14.49%.

Combination approach:

In this approach, compute all the cash outflows at year 0 and all the cash inflows at the closure of the project. Hence, the value of the cash flows is as follows:

$Time 0 cash flow=Initial cost+−Cash outflows(1+r)t=−$27,500+−$4,050(1+0.10)5=−$30,014.73$

Hence, the total cash outflow at year 0 is -$30,014.73.

$Time 5 cash flow=Cash flows (year1(1+r)4+year2(1+r)3+year3(1+r)2+year4(1+r)+year5)=($10,430(1+0.10)4+$13,850(1+0.10)3+$11,270(1+0.10)2+$9,830(1+0.10))=$10,430(1.4641)+$13,850(1.331)+$11,270(1.21)+$9,830(1.10)=$58,154.61$

Hence, the value of total cash inflows is $58,154.61.

Equation of MIRR in combination approach:

$0=−$30,014.73+$58,154.61(1+MIRR)5$

Compute the MIRR:

$0=−$30,014.73+$58,154.61(1+MIRR)5$58,154.61$30,014.73=(1+MIRR)5MIRR=($58,154.61$30,014.73)1/5−1MIRR=0.1414 or 14.14%$

Hence, the MIRR is $14.14%.

Answer 7

Chapter 8, Problem 22QP

Summary Introduction

To calculate: The MIRR (Modified Internal Rate of Return) for the project utilizing all three methods.

Introduction:

MIRR is the Modified Internal Rate of Return; it is a financial measure of attracting investments. It is utilized in capital budgeting to rank the alternative investments of the same size.

Answer 8

Expert Solution & Answer

Answer to Problem 22QP

The MIRR for the project using the discounted approach is 19.21%, reinvestment approach is 14.49%, and combination approach is 14.14%.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Given information:

Company M is assessing a project where the cash flows are $10,430, $13,850, $11,270, $9,830, and -$4,050 for year 1, 2, 3, 4, and 5 respectively. The initial cost is $27,500.

Discounted approach:

In this approach, compute the negative cash outflows value at year 0. On the other hand, the positive cash flows remain at its time of occurrence. Hence, discount the cash outflows to year 0.

$Time 0 cash flow=Initial cost+−Cash outflows(1+r)t=−$27,500+−$4,050(1+0.10)5=−$30,014.73$

Hence, the discounted cash flow at time 0 is -$30,014.73.

Equation of MIRR in a discounted approach:

$0=−$30,014.73+$10,430(1+MIRR)+$13,850(1+MIRR)2+$11,270(1+MIRR)3+$9,830(1+MIRR)4$

Compute MIRR using a spreadsheet:

Step 1:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 1

Type the equation of NPV in H6 in the spreadsheet and consider the MIRR value as H7.

Step 2:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 2

Assume the MIRR value as 0.10%.

Step 3:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 3

In the spreadsheet, go to data and select the what-if analysis.
In the what-if analysis, select goal seek.
In set cell, select H6 (the formula).
The “To value” is considered as 0 (the assumption value for NPV).
The H7 cell is selected for the by changing cell.

Step 4:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 4

Following the previous step click OK in the goal seek. The goal seek status appears with the MIRR value.

Step 5:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 8, Problem 22QP , additional homework tip 5

Thevalue appears to be 19.2108278981048%.

Hence, the MIRR value is 19.21%.

Reinvestment approach:

In this approach, compute the future value of all the cash flows excluding the initial cost at the closure of the project. Hence, compute the reinvesting cash flows to year 5 is:

$Time 5 cash flow=Cash flows (year 1(1+r)4+year 2(1+r)3+year 3(1+r)2+year 4(1+r)+year 5)=($10,430(1+0.10)4+$13,850(1+0.10)3+$11,270(1+0.10)2+$9,830(1+0.10)−$4,050)=$10,430(1.4641)+$13,850(1.331)+$11,270(1.21)+$9,830(1.10)−$4,050=$54,104.61$

Hence, the reinvesting cash flow at time 5 is $54,104.61.

Equation of MIRR in reinvestment approach:

$0=−$27,500+$54,104.61(1+MIRR)5$

Compute the MIRR:

$0=−$27,500+$54,104.61(1+MIRR)5$54,104.61$27,500=(1+MIRR)5MIRR=($54,104.61$27,500)1/5−1MIRR=0.1449 or 14.49%$

Hence, the MIRR is 14.49%.

Combination approach:

In this approach, compute all the cash outflows at year 0 and all the cash inflows at the closure of the project. Hence, the value of the cash flows is as follows:

$Time 0 cash flow=Initial cost+−Cash outflows(1+r)t=−$27,500+−$4,050(1+0.10)5=−$30,014.73$

Hence, the total cash outflow at year 0 is -$30,014.73.

$Time 5 cash flow=Cash flows (year1(1+r)4+year2(1+r)3+year3(1+r)2+year4(1+r)+year5)=($10,430(1+0.10)4+$13,850(1+0.10)3+$11,270(1+0.10)2+$9,830(1+0.10))=$10,430(1.4641)+$13,850(1.331)+$11,270(1.21)+$9,830(1.10)=$58,154.61$

Hence, the value of total cash inflows is $58,154.61.

Equation of MIRR in combination approach:

$0=−$30,014.73+$58,154.61(1+MIRR)5$

Compute the MIRR:

$0=−$30,014.73+$58,154.61(1+MIRR)5$58,154.61$30,014.73=(1+MIRR)5MIRR=($58,154.61$30,014.73)1/5−1MIRR=0.1414 or 14.14%$

Hence, the MIRR is $14.14%.

Answer 12

Ch. 8.1 - Prob. 8.1ACQ Ch. 8.1 - Prob. 8.1BCQ Ch. 8.2 - Prob. 8.2ACQ Ch. 8.2 - Prob. 8.2BCQ Ch. 8.3 - Prob. 8.3ACQ Ch. 8.3 - What are the weaknesses of the AAR rule?Ch. 8.4 - Prob. 8.4ACQ Ch. 8.4 - Prob. 8.4BCQ Ch. 8.5 - What does the profitability index measure?Ch. 8.5 - Prob. 8.5BCQ

The MIRR (Modified Internal Rate of Return ) for the project utilizing all three methods. Introduction: MIRR is the Modified Internal Rate of Return; it is a financial measure of attracting investments. It is utilized in capital budgeting to rank the alternative investments of the same size.

Answer to Problem 22QP

Explanation of Solution

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