Nobell Company is evaluating an investment of $1,000,000 which will yield net ca

Question

Nobell Company is evaluating an investment of $1,000,000 which will yield net cash inflows of $142,369 per year for 10 years with no residual value. What is the internal rate of return?

Present value of annuity of $1:

5%

6%

7%

8%

1

0.952

0.943

0.935

0.926

2

1.859

1.833

1.808

1.783

3

2.723

2.673

2.624

2.577

4

3.546

3.465

3.387

3.312

5

4.329

4.212

4.1

3.993

6

5.076

4.917

4.767

4.623

7

5.786

5.582

5.389

5.206

8

6.463

6.21

5.971

5.747

9

7.108

6.802

6.515

6.247

10

7.722

7.36

7.024

6.71

A. 7%

B. 9%

C. 8%

D. 6%

Explanation / Answer

Calculation of IRR:

IF we take IRR as discount rate, the Present value of Cash inflow should be equal to initial cash out flow

Present value of cash inflow= Annual Cash inflow* Present value of $1 Annuity (IRR, Period)

=   $142,369* Present value of $1 Annuity (IRR, 10 Years )

Initial cash out fllow = $1,000,000

Hence,

$142,369* Present value of $1 Annuity (IRR, 10 Years ) = $1,000,000

Present value of $1 Annuity (IRR, 10 Years ) = $1,000,000 / $142,369

Present value of $1 Annuity (IRR, 10 Years ) = 7.024

Now we shall find the Factor 7.024 in the present value of annuity table given (In the row of 10 years ):

Present value of annuity of $1:

Year

5%

6%

7%

8%

1

0.952

0.943

0.935

0.926

2

1.859

1.833

1.808

1.783

3

2.723

2.673

2.624

2.577

4

3.546

3.465

3.387

3.312

5

4.329

4.212

4.1

3.993

6

5.076

4.917

4.767

4.623

7

5.786

5.582

5.389

5.206

8

6.463

6.21

5.971

5.747

9

7.108

6.802

6.515

6.247

10

7.722

7.36

7.024

6.71

So the factor comes in the coumn of 7%

hence the IRR shall be 7%

Calculation of IRR:

IF we take IRR as discount rate, the Present value of Cash inflow should be equal to initial cash out flow

Present value of cash inflow= Annual Cash inflow* Present value of $1 Annuity (IRR, Period)

=   $142,369* Present value of $1 Annuity (IRR, 10 Years )

Initial cash out fllow = $1,000,000

Hence,

$142,369* Present value of $1 Annuity (IRR, 10 Years ) = $1,000,000

Present value of $1 Annuity (IRR, 10 Years ) = $1,000,000 / $142,369

Present value of $1 Annuity (IRR, 10 Years ) = 7.024

Now we shall find the Factor 7.024 in the present value of annuity table given (In the row of 10 years ):

Present value of annuity of $1:

Year

5%

6%

7%

8%

1

0.952

0.943

0.935

0.926

2

1.859

1.833

1.808

1.783

3

2.723

2.673

2.624

2.577

4

3.546

3.465

3.387

3.312

5

4.329

4.212

4.1

3.993

6

5.076

4.917

4.767

4.623

7

5.786

5.582

5.389

5.206

8

6.463

6.21

5.971

5.747

9

7.108

6.802

6.515

6.247

10

7.722

7.36

7.024

6.71

So the factor comes in the coumn of 7%

hence the IRR shall be 7%

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