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Consider the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 –$419,000 –$37,000 1 47,000 19,800 2 59,000 13,900 3 76,000 15,600 4 534,000 12,400 The required return on these investments is 11 percent. Required: (a) What is the payback period for each project? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).) Payback period Project A years Project B years (b) What is the NPV for each project? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).) Net present value Project A $ Project B $ (c) What is the IRR for each project? (Do not round intermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).) Internal rate of return Project A % Project B % (d) What is the profitability index for each project? (Do not round intermediate calculations. Round your answers to 3 decimal places (e.g., 32.161).) Profitability index Project A Project B (e) Based on your answers in (a) through (d), which project will you finally choose?

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Nonicorp1

Answer:

a. The payback period for project A=3.44 years, and the payback period for project B=2.21 years.

b. Net present value for project A=$78,560.951, and the Net present value for project B=$11,694.239

c. IRR  for Project A= 16.57% and IRR for Project B=25.72%

d. Probability index (P.I) for Project A=1.187 and the Probability index (P.I) for Project B=1.316

e. The final decision should be based on the NPV since it doesn't have the ranking problem that is usually associated with other capital budgeting techniques. I would choose Project A since it has a higher Net Present Value (NPV) as compared to Project B.

Explanation:

                   PROJECT A                 PROJECT B

Year            Cash flow                     Cash flow

0.                 $419,000                      $37,000

1.                  $47,000                       $19,800

2.                 $59,000                       $13,900

3.                 $76,000                        $15,600

4.                 $534,000                      $12,400

a.

The payback period for Project A can be determined as follows;

The cash flows at Year 0 represent the initial investment to the project. The payback period is the number of years it will take until the return on the project is equal to the initial investment. This can be calculated as shown;

419,000-(47,000+59,000+76,000)

=419,000-182,000=$237,000

After 3 years, the total cash flow will be=$182,000 which is still $237,000 less from the initial investment. Determine the number of months in the fourth year that it will take to cover the remainder;

(237,000/534,000)=0.44 years

Total number of years=3+0.44=3.44 years

The payback period for project A=3.44 years

The payback period for Project B can be determined as follows;

37,000-(19,800+13,900)

=37,000-33,700=$3,300

After 2 years, the total cash flow will be=$33,700 which is still $3,300 less from the initial investment. Determine the number of months in the third year that it will take to cover the remainder;

(3,300/15,600)=0.21 years

Total number of years=2+0.21=2.21 years

The payback period for project B=2.21 years

b.

Net present value for project A is;

NPV=-419,000+{47,000/(1+0.11)}+{59,000/((1+0.11)^2)}+{76,000/((1+0.11)^3)}+534,000/((1+0.11)^4)=-419,000+(42,342.342+47,885.724+55,570.545+351,762.340=$42,378,560.61

Net present value for project A=$78,560.951

Net present value for project B is;

NPV=-37,000+{19,800/(1+0.11)}+{13,900/((1+0.11)^2)}+{15,600/((1+0.11)^3)}+12,400/((1+0.11)^4)=-37,000+(17,837.837+11,281.552+11,406.586+8,168.264=$11,694.239

Net present value for project B=$11,694.239

c.

The IRR for each project A is:

$419,000 = $47,000 / (1 + IRR) + $59,000 / (1 + IRR)^2 + $76,000 / (1 + IRR)^3 + $534,000 / (1 + IRR)^4

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRR = 16.57%

The IRR for each project B is:

$37,000 = $19,800 / (1 + IRR) + $13,900 / (1 + IRR)^2 + $15,600 / (1 + IRR)^3 + $12,400 / (1 + IRR)^4

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRR = 25.72%

d.

Probability index (P.I) for Project A;

P.I=[{47,000/(1+0.11)}+{59,000/((1+0.11)^2)}+{76,000/((1+0.11)^3)}+534,000/((1+0.11)^4)]/419,000=(42,342.342+47,885.724+55,570.545+351,762.340=1.187

The Probability index (P.I) for Project A=1.187

Probability index (P.I) for Project B;

[{19,800/(1+0.11)}+{13,900/((1+0.11)^2)}+{15,600/((1+0.11)^3)}+12,400/((1+0.11)^4)]/37,000=(17,837.837+11,281.552+11,406.586+8,168.264=1.316

The Probability index (P.I) for Project B=1.316

e.

The final decision should be based on the NPV since it doesn't have the ranking problem that is usually associated with other capital budgeting techniques. I would choose Project A since it has a higher Net Present Value (NPV) as compared to Project B.

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