Question

In: Accounting

A new machine that costs $80,800 is expected to save annual cash operating costs of $20,000...

A new machine that costs $80,800 is expected to save annual cash operating costs of $20,000 over each of the next seven years. The machine's internal rate of return is (see choices below the present value tables):

Present Value of $1

Periods

4%

6%

8%

10%

12%

14%

16%

1

.962

.943

.926

.909

.893

.877

.862

2

.925

.890

.857

.826

.797

.769

.743

3

.889

.840

.794

.751

.712

.675

.641

4

.855

.792

.735

.683

.636

.592

.552

5

.822

.747

.681

.621

.567

.519

.476

6

.790

.705

.630

.564

.507

.456

.410

7

.760

.665

.583

.513

.452

.400

.354

8

.731

.627

.540

.467

.404

.351

.305

9

.703

.592

.500

.424

.361

.308

.263

10

.676

.558

.463

.386

.322

.270

.227

Present Value of a Series of $1 Cash Flows

Periods

4%

6%

8%

10%

12%

14%

16%

1

0.962

0.943

0.926

0.909

0.893

0.877

0.862

2

1.886

1.833

1.783

1.736

1.690

1.647

1.605

3

2.775

2.673

2.577

2.487

2.402

2.322

2.246

4

3.630

3.465

3.312

3.170

3.037

2.914

2.798

5

4.452

4.212

3.993

3.791

3.605

3.433

3.274

6

5.242

4.917

4.623

4.355

4.111

3.889

3.685

7

6.002

5.582

5.206

4.868

4.564

4.288

4.039

8

6.733

6.210

5.747

5.335

4.968

4.639

4.344

9

7.435

6.802

6.247

5.759

5.328

4.946

4.607

10

8.111

7.360

6.710

6.145

5.650

5.216

4.833

Group of answer choices:

A. approximately 14%

B. some other value than the choices shown

C. approximately 16%

D. approximate 12%

Solutions

Expert Solution

IRR means rate at which NPV is zero.
Let us calculate NPV at 10% rate and 16% rate
10% 16%
a Annual Cash Inflow $         20,000 $         20,000
b PV annuity factor for 7 years 4.868 4.039
c PV of cash inflow (a*b) $         97,360 $         80,780
d Initial investment $         80,800 $         80,800
e NPV (c-d) $         16,560 $                -20
We can directly conclude that IRR is 16% (approx) because NPV at
16% rate is very close to 0.
therefore corrct option : C

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