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In: Finance

Use the discounted payback method, the net present value method, and the profitability index method to...

Use the discounted payback method, the net present value method, and the profitability index method to evaluate the following project:

Year 0 Initial Investment 900,000

Year 1 Income 175,000

Year 2 Income 450,000

Year 3 Additional investment 100,000

Year 4 Income 630,000

Discount rate 7%

DPB __________ years

NPV ______________

PI ______________

Would you recommend that the board accept or reject this project? ________________ Accept or reject

Solutions

Expert Solution

Computation of Discounted payback period:

Year

Cash Flow

Calculation of PV factor

PV Factor @ 7 %

Discounted Cash Flow

'Cum Dis. Cash Flow

0

$ (900,000)

1/(1+0.07)^0

1

$   (900,000.00)

$   (900,000.00)

1

$    175,000

1/(1+0.07)^1

0.93457944

$      163,551.40

$   (736,448.60)

2

$    450,000

1/(1+0.07)^2

0.87343873

$      393,047.43

$    (343,401.17)

3

$   (100,000)

1/(1+0.07)^3

0.81629788

$      (81,629.79)

$     (425,030.96)

4

$    630,000

1/(1+0.07)^4

0.76289521

$      480,623.98

$      55,593.03

Payback Period = A +B/C

Where,

A= Last period with a negative cumulative discounted cash flow = 3

B = Absolute value of a cumulative discount cash flow at the end of the period A = $ 425,030.96

C = Total discounted cash flow during the period after A = $ 480,623.98

Discounted Payback Period = 3 +?$ (425,030.96) ?/$ 480,623.98

                           = 3 + $ 425,030.96/ $ 480,623.98

                           = 3 + 0.8843316 = 3.88 years

Computation of NPV:

Year

Cash Flow

Calculation of PV factor

PV Factor @ 7 %

PV

0

$        (900,000)

1/(1+0.07)^0

1

$   (900,000.00)

1

$           175,000

1/(1+0.07)^1

0.93457944

$      163,551.40

2

$           450,000

1/(1+0.07)^2

0.87343873

$      393,047.43

3

$        (100,000)

1/(1+0.07)^3

0.81629788

$      (81,629.79)

4

$           630,000

1/(1+0.07)^4

0.76289521

$      480,623.98

NPV

$        55,593.03

Computation of Profitability Index:

Profitability Index = 1 + Net Present Value/Initial Investment Required

                                 = 1 + $ 55,593.03/$ 900,000 + $ 81,629.79

                                 = 1 + $ 55,593.03/ $ 981,629.79

                                 = 1 + 0.056633393 = 1.06

Project should be accepted as NPV is positive and Profitability Index is greater than one.

jeff jeffy answered 1 year ago
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