1) Consider the following two mutually exclusive projects: What is the payback p

Question

1) Consider the following two mutually exclusive projects:

  

  

  

What is the payback period for each project? (Round your answers to 2 decimal places. (e.g., 32.16))

  

  

  

What is the discounted payback period for each project? (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

  

  

  

What is the NPV for each project? (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

  

  

  

What is the IRR for each project? (Round your answers to 2 decimal places. (e.g., 32.16))

  

  

  

What is the profitability index for each project? (Do not round intermediate calculations and round your final answers to 3 decimal places. (e.g., 32.161))

  

  

2) An investment under consideration has a payback of six years and a cost of $876,000. Assume the cash flows are conventional.

   If the required return is 12 percent, what is the worst-case NPV? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places. (e.g., 32.16))

Year Cash Flow (A) Cash Flow (B) 0 –$ 357,000 –$ 46,500 1 38,000 23,300 2 58,000 21,300 3 58,000 18,800 4 433,000 13,900

Explanation / Answer

1. Payback period:

A

B

Year

Cash flows

Cumulative cash flows

Cash flows

Cumulative cash flows

0

-357000

-357000

-46500

-46500

1

38000

-319000

23300

-23200

2

58000

-261000

21300

-1900

3

58000

-203000

18800

16900

4

433000

230000

13900

30800

Payback period

=3 + (203,000/433,000)

3+0.47 = 3.47years

=2+(1,900/18,800)

=2+0.10 = 2.10 years

a-2. Based on payback period, it is better to choose Project B because we can recover investment early.

b. Discounted payback period for each project:

A

B

Year

Cash flows

PV factor at 14%

PV of cash flows

Cumulative cash flows

Cash flows

PV factor at 14%

PV of cash flows

Cumulative cash flows

0

(357,000.00)

      1.0000

(357,000.00)

(357,000.00)

       (46,500.00)

               1.0000

       (46,500.00)

(46,500.00)

1

       38,000.00

      0.8772

       33,333.33

(323,666.67)

         23,300.00

               0.8772

         20,438.60

(26,061.40)

2

       58,000.00

      0.7695

     44,629.12

(279,037.55)

         21,300.00

               0.7695

         16,389.66

    (9,671.75)

3

       58,000.00

      0.6750

       39,148.35

(239,889.20)

         18,800.00

               0.6750

         12,689.46

       3,017.72

4

    433,000.00

      0.5921

    256,370.76

       16,481.56

         13,900.00

               0.5921

           8,229.92

    11,247.64

Discounted payback period:
A = 3+ (239,889.20/256,370.76)
= 3+ 0.94 = 3.94years
B = 2+ (9,671.75/ 12,689.46) = 2+ 0.76 = 2.76 years.
b.2: Based on Discounted payback period, it is better to choose Project B because we can recover investment early.

c. Computation of NPV:

A

B

Year

Cash flows

PV factor at 14%

PV of cash flows

Cash flows

PV factor at 14%

PV of cash flows

0

    (357,000.00)

      1.0000

        (357,000.00)

   (46,500.00)

               1.0000

           (46,500.00)

1

         38,000.00

      0.8772

             33,333.33

     23,300.00

               0.8772

             20,438.60

2

         58,000.00

      0.7695

             44,629.12

     21,300.00

               0.7695

             16,389.66

3

         58,000.00

      0.6750

             39,148.35

     18,800.00

               0.6750

             12,689.46

4

       433,000.00

      0.5921

           256,370.76

     13,900.00

               0.5921

               8,229.92

NPV

Sum of all PV of cash flows:

             16,481.56

             11,247.64

c-2: Based on NPV it is better to choose Project A because NPV is high for Project A when compare to Project B.

d. IRR for each project:
Project A: 16%
Project B: 26%

d-2: Based on IRR it is better to choose Project A because return is high for Project A when compare to Project B.

e. Computation of profitability index:
Formula for PI = Sum of PV of future cash flows / initial investment
Project A = 373,481.56 / 357,000 = 1.05
Project B = 57,747.64 / 46,500 = 1.24

e.2. Based on PI it is better to choose Project B because Profit is more for Project B when compare to Project A

f. Based on above all the calculations, I choose Project B, because it has less investment and we can recover early and PI also more while comparing to Project B.

2. The worst- case NPV:
Given, Initial cost = $876,000
Cash flows are conventional = sum of the cash flows from the project is at least $876,000
Period = 6 years
Required return = 12%
NPV = -876,000 + 876,000 / (1+12%)6
= -876,000 + 876,000 / 1.9738
= -876,000 + 443,813.96
=-432,186.04

A

B

Year

Cash flows

Cumulative cash flows

Cash flows

Cumulative cash flows

0

-357000

-357000

-46500

-46500

1

38000

-319000

23300

-23200

2

58000

-261000

21300

-1900

3

58000

-203000

18800

16900

4

433000

230000

13900

30800

Payback period

=3 + (203,000/433,000)

3+0.47 = 3.47years

=2+(1,900/18,800)

=2+0.10 = 2.10 years

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