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Internal rate of return and modified internal rate of return. Quark Industries has three potential​ projects,...

Internal rate of return and modified internal rate of return.

Quark Industries has three potential​ projects, all with an initial cost of ​$1,600,000.

Given the discount rate and the future cash flow of each project in the following​ table,

 Cash Flow   Project M Project N Project O

  Year 1   $400,000   $500,000 $900,000

  Year 2   ​$400,000   ​$500,000   $700,000

  Year 3   $400,000 $500,000 $500,000

  Year 4   $400,000 $500,000 $300,000

  Year 5 $400,000   $500,000 $100,000

Discount rate 9​% 14%   17%

Solutions

Expert Solution

Computation of IRR using trial and error method:

Project M:

Let’s compute NPV of project M using discount rate of 7 %:

Year

Cash Flow (CM)

PV Factor Computation

PV Factor @ 7 % (F)

PV (CM x F)

0

-$1,600,000

1/ (1+0.07) ^0

1

-$1,600,000

1

$400,000

1/ (1+0.07) ^1

0.934579439

$373,831.77570

2

$400,000

1/ (1+0.07) ^2

0.873438728

$349,375.49131

3

$400,000

1/ (1+0.07) ^3

0.816297877

$326,519.15076

4

$400,000

1/ (1+0.07) ^4

0.762895212

$305,158.08482

5

$400,000

1/ (1+0.07) ^5

0.712986179

$285,194.47179

NPV M1

$40,078.97438

As NPV is positive let’s compute NPV at discount rate of 8 %.

Year

Cash Flow (CM)

PV Factor Computation

PV Factor @ 8 % (F)

PV (CM x F)

0

-$1,600,000

1/ (1+0.08) ^0

1

-$1,600,000

1

$400,000

1/ (1+0.08) ^1

0.925925926

$370,370.37037

2

$400,000

1/ (1+0.08) ^2

0.85733882

$342,935.52812

3

$400,000

1/ (1+0.08) ^3

0.793832241

$317,532.89641

4

$400,000

1/ (1+0.08) ^4

0.735029853

$294,011.94112

5

$400,000

1/ (1+0.08) ^5

0.680583197

$272,233.27881

NPV M2

-$2,915.985169

IRR M = R1 + [NPV M1 x (R2 – R1)/ (NPV M1 – NPV M2)]

     = 7 % + [$40,078.97438 x (8 % - 7 %)]/ [$40,078.97438 – (-$2,915.985169)]

     = 7 % + ($40,078.97438 x 1 %)/ ($40,078.97438 + $2,915.985169)

    = 7 % + ($400.7897438 / $42,994.95955)

     = 7 % + 0.009321784

      = 7 % + 0.9321784 %

      = 7.93 %

Project N:

Let’s compute NPV of project N using discount rate of 16 %:

Year

Cash Flow (CN)

PV Factor Computation

PV Factor @ 16 % (F)

PV (CN x F)

0

-$1,600,000

1/ (1+0.16) ^0

1

-$1,600,000

1

$500,000

1/ (1+0.16) ^1

0.8620689655172

431034.48276

2

$500,000

1/ (1+0.16) ^2

0.7431629013080

371581.45065

3

$500,000

1/ (1+0.16) ^3

0.6406576735414

320328.83677

4

$500,000

1/ (1+0.16) ^4

0.5522910978805

276145.54894

5

$500,000

1/ (1+0.16) ^5

0.4761130154142

238056.50771

NPV N1

$37,146.82683

As NPV is positive let’s compute NPV at discount rate of 17 %.

Year

Cash Flow (CN)

PV Factor Computation

PV Factor @ 17 % (F)

PV (CN x F)

0

-$1,600,000

1/ (1+0.17) ^0

1

-$1,600,000

1

$500,000

1/ (1+0.17) ^1

0.93457943925234

427,350.42735

2

$500,000

1/ (1+0.17) ^2

0.87343872827321

365,256.77551

3

$500,000

1/ (1+0.17) ^3

0.81629787689085

312,185.27822

4

$500,000

1/ (1+0.17) ^4

0.76289521204753

266,825.02412

5

$500,000

1/ (1+0.17) ^5

0.71298617948367

228,055.57617

NPV N2

-$326.91864

IRR N = R1 + [NPV N1 x (R2 – R1)/ (NPV N1 – NPV N2)]

     = 16 % + [$37,146.82683 x (17 % - 16 %)]/ [$37,146.82683 – (-$326.91864)]

     = 16% + ($37,146.82683 x 1 %)/ ($37,146.82683+ $326.91864)

    = 16 % + ($371.4682683/ $37,473.74547)

      = 16 % + 0.009912761

      = 16% + 0.9912761%

      = 16.93 %

Project O:

Let’s compute NPV of project O using discount rate of 24 %:

Year

Cash Flow (CO)

PV Factor Computation

PV Factor @ 24 % (F)

PV (CO x F)

0

-$1,600,000

1/ (1+0.24) ^0

1

-$1,600,000.00

1

900,000

1/ (1+0.24) ^1

0.8064516129032

725,806.45161

2

700,000

1/ (1+0.24) ^2

0.6503642039542

455,254.94277

3

500,000

1/ (1+0.24) ^3

0.5244872612534

262,243.63063

4

300,000

1/ (1+0.24) ^4

0.4229735977850

126,892.07934

5

100,000

1/ (1+0.24) ^5

0.3411077401492

34,110.77401

NPV O1

$4,307.87836

As NPV is positive let’s compute NPV at discount rate of 25 %.

Year

Cash Flow (CO)

PV Factor Computation

PV Factor @ 25 % (F)

PV (CO x F)

0

-$1,600,000

1/ (1+0.25) ^0

1

-$1,600,000

1

900,000

1/ (1+0.25) ^1

0.800000

720,000

2

700,000

1/ (1+0.25) ^2

0.640000

448,000

3

500,000

1/ (1+0.25) ^3

0.512000

256,000

4

300,000

1/ (1+0.25) ^4

0.409600

122,880

5

100,000

1/ (1+0.25) ^5

0.327680

32,768

NPV O2

-$20,352

IRR O = R1 + [NPV O1 x (R2 – R1)/ (NPV O1 – NPV O2)]

     = 24 % + [$4,307.87836 x (25 % - 24 %)]/ [$4,307.87836– (-$20,352)]

     = 24 % + ($4,307.87836 x 1 %)/ ($4,307.87836 + $20,352)

    = 24 % + ($43.0787836/ $24659.87836)

      = 24 % + 0.001746918

      = 24 % + 0.1746918 %

      = 24.17 %

Computation of MIRR:

MIRR = n√ (Future value of positive cash flow/Present value of negative cash flow) – 1

Project M:           

Year

Cash Flow

(CM)

Computation of FV Factor

FV Factor @ 9 % (F)

FV

(CM x F)

1

$400,000

(1+0.09) ^4

1.41158161

564632.644

2

$400,000

(1+0.09) ^3

1.295029

518011.600

3

$400,000

(1+0.09) ^2

1.1881

475240.000

4

$400,000

(1+0.09) ^1

1.09

436000.000

5

$400,000

(1+0.09) ^0
jeff jeffy answered 1 year ago
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