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ABC Corporation has a machine that requires repairs or should be replaced. ABC has evaluated the...

Question:

ABC Corporation has a machine that requires repairs or should be replaced. ABC has evaluated the two options and calculated the cash flows resulting from each option as follows:

Option A: Repair the Machine

Year : Cash Flow

0 : -50,000

1 : 31,500

2 : 20,100

3 : 18,900

4 : 17,100

5 : 13,700

Option B: Buy a new Machine

Year : Cash Flow

0 : -400,000

1 : 91,300

2 : 155,000

3 : 127,800

4 : 126,900

5 : 125,100

You have recently been hired by ABC Corporation and your first assignment is to help them decide which of these two options should be pursued.

Conduct the analysis by calculating the following for each option:

1. Net Present Value (NPV)

2. Internal Rate of Return (IRR)

3. Profitability Index (PI)

4. Payback Period (PB)

5. Crossover Rate

The company has a Weighted Average Cost of Capital (WACC) (discount Rate) of 12%. For this analysis, your boss John Doe asked you to calculate NPV at three different discount rates: 12% (the current WACC), 14% and 16%.

Crossover rate:

In capital budgeting analysis exercises, the crossover rate is used to find the required rate of return where one investment project becomes superior to another. For example from mutually exclusive two projects A and B, if the cross over rate is R the if project A is superior for a cost of capital of <R then project B will be superior for the cost of capital >R. There will be a point of indifference at the cost of capital = R.

Answer and Explanation:

1. Net Present Value (NPV)

We calculate the NPV of each option for the discount rate of 12%, 14%, 16%

Option A

Year

Cash flow(CFA)

PV@12%= CFA/(1+r)^n; r = 12%,n 0 to 5

NPV = sum of PV

PV@14%

NPV@14%

PV@16%

NPV@16%

0

-$ 50,000

-$ 50,000

$ 26,242

-$ 50,000

$ 23,095

-$ 50,000

$ 20,168

1

$ 31,500

$ 28,125

$ 27,632

$ 27,155

2

$ 20,100

$ 16,024

$ 15,466

$ 14,938

3

$ 18,900

$ 13,453

$ 12,757

$ 12,108

4

$ 17,100

$ 10,867

$ 10,125

$ 9,444

5

$ 13,700

$ 7,774

$ 7,115

$ 6,523

Option B

Year

Cash flow(CFB)

PV@12%= CFB/(1+r)^n; r = 12%,n 0 to 5

NPV = sum of PV

PV@14%

NPV@14%

PV@16%

NPV@16%

0

-$ 4,00,000

-$ 4,00,000

$ 47,681

-$ 4,00,000

$ 25,725

-$ 4,00,000

$ 5,421

1

$ 91,300

$ 81,518

$ 80,088

$ 78,707

2

$ 155,000

$ 123,565

$ 119,267

$ 115,190

3

$ 127,800

$ 90,966

$ 86,261

$ 81,876

4

$ 126,900

$ 80,647

$ 75,135

$ 70,086

5

$ 125,100

$ 70,985

$ 64,973

$ 59,562

2. Internal Rate of Return (IRR)

We calculate the IRR for each option from Microsoft Excel as:

  • IRR(A) = 35.32%
  • IRR(B) = 16.56%

Syntax:

IRR(values, guess)

Values: is an array or a reference to cells that contain numbers for which the internal rate of return to be calculated.

Guess: is a number that you guess is close to the result of IRR, we take 0.5 as the default IRR

3. Profitability Index (PI)

We calculate the profitability index as PI = (NPV+ initial investment)/NPV

Rate of interest

PI(A)

PI(B)

12%

1.52

1.12

14%

1.46

1.06

16%

1.40

1.01

4. Payback Period (PB)

Year

Cash flow(CFA)

Cumulative Cash flow

Payback period (where the cumulative cash flow became zero)

0

-$ 50,000

-$ 50,000

 

1

$ 31,500

-$ 18,500

 

2

$ 20,100

$ 1,600

1.9 years

3

$ 18,900

$ 20,500

 

4

$ 17,100

$ 37,600

 

5

$ 13,700

$ 51,300

 

Year

Cash flow(CFB)

Cumulative Cash flow

Payback period (where the cumulative cash flow became zero)

0

-$ 4,00,000

-$ 4,00,000

 

1

$ 91,300

-$ 3,08,700

 

2

$ 155,000

-$ 1,53,700

 

3

$ 127,800

-$ 25,900

 

4

$ 126,900

$ 101,000

3.2 Years

5

$ 125,100

$ 226,100

 

5. Crossover Rate

We calculate the crossover rate as the discount rate that makes the NPV of the differential cash flow = 0

Year

Cash flow(CFA)

Cash flow(CFB)

CFD = (CFB-CFA)

0

-$ 50,000

-$ 4,00,000

-$ 3,50,000

1

$ 31,500

$ 91,300

$ 59,800

2

$ 20,100

$ 155,000

$ 134,900

3

$ 18,900

$ 127,800

$ 108,900

4

$ 17,100

$ 126,900

$ 109,800

5

$ 13,700

$ 125,100

$ 111,400

We calculate the IRR of the differential cash flow as:

IRR = 14.29%

So the crossover rate = 14.29%


Learn more about this topic:

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What Is Capital Budgeting? - Techniques, Analysis & Examples

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Chapter 3 / Lesson 13
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Capital budgeting is important to the growth and development of a business. In this lesson, you will learn what capital budgeting is, why it is important, and how it is used.


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