Question

Fijisawa Inc. is considering a major expansion of its product line and has estimated the following cash flows associated with such an expansion. The initial outlay would be

$2,000,000 ,

and the project would generate incremental free cash flows of

$500,000

per year for

6

years. The appropriate required rate of return is

7

percent.

a. Calculate the

NPV.

b. Calculate the

PI.

c. Calculate the

IRR.

d. Should this project be accepted?

a.

What

is the project's

NPV ?

(Round to the nearest​ dollar.)

Answer 1

Initial cash outflow = $2,000,000

Annual cash inflows = $500,000

Time = 6 years

Required rate of return = 7%

Present value of cash inflows = Annual cash inflow x Present value annuity factor (7%,6)

= 500,000 x 4.767

= $2,383,500

a)

NPV = Present value of cash inflows - Present value of cash outflows

= 2,383,500 - 2,000,000

= $383,500

b)

Profitability index = Present value of cash inflows/ Present value of cash outflows

= 2,383,500/2,000,000

= 1.19

c)

Since at 7% discount rate, NPV of the project is positive, we must take a higher discount rate so that NPV becomes negative.

Let second discount rate be 13%.

Present value of cash inflows (at 13%) = Annual cash inflows x PVAF(_{13% , 6} )

= 500,000 x 3.998

= $1,999,000

NPV (at 13%) = Present value of cash inflows - Present value of cash outflows

= 1,999,000 - 2,000,000

= - $1,000

Since at 7%, NPV is positive and at 13%, NPV is negative, hence the IRR of the project must lie between 7% to 13%. Exact IRR can be calculated as under:

IRR = Lower rate + {NPV at lower rate/(NPV at lower rate - NPV at higher rate)} x (Higher rate - lower rate)

= 7% + {383,500/(383,500 + 1,000)} x (13% - 7%)

= 7% + (383,500/384,500) x 6

= 7% + 5.98%

= 12.98%

Hence, IRR of the project is 12.98%(Approx.)

d)

The project can be accepted since it is producing positive NPV and it's IRR is more than the required rate of return.

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