Question

​(​NPV, ​PI, and IRR calculations​) 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 ​$1,850,000​, and the project would generate incremental free cash flows of ​$500,000 per year for 6 years. The appropriate required rate of return is 6 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.)

b. What is the​ project's PI​?   ​(Round to three decimal​ places.)

c. What is the​ project's IRR​?

Answer 1

a) Calculation of NPV

Net Present Value (NPV) = Present value of cash inflows - Present value of cash outflows

Particulars	Period	Amount	PVF @ 6%	Present Value
Cash Outflows:
Initial Outlay	0	($1,850,000.00)	1	($1,850,000.00)
Cash Inflows:
Annual Cash Inflows	1-6	$500,000.00	4.917324326	$2,458,662.16
Net Present Value				$608,662.16

b) Calculation of Profitability index (PI)

Profitability index (PI) = Present value of future cash flows / Intial Investment

PI = $2,458,662.16 / $1,850,000.00

PI = 1.3290065 or 1.33

Profitability index (PI)  = 1.33

c) Calculation of IRR

IRR is the internal rate of return at which NPV = 0

At discount rate = 6%

NPV = $608,662.16

So, we need to discount the cash flows at a higher rate.

(i) Let Discount rate be 15%

Calculation of NPV at Discount rate be 15%

Particulars	Period	Amount	PVF @ 15%	Present Value
Cash Outflows:
Initial Outlay	0	($1,850,000.00)	1	($1,850,000.00)
Cash Inflows:
Annual Cash Inflows	1-6	$500,000.00	3.784482694	$1,892,241.35
Net Present Value				$42,241.35

The NPV is still positive so we need to further discount the cash flows at a higher rate

(ii) Let Discount rate be 16%

Calculation of NPV at Discount rate be 16%

Particulars	Period	Amount	PVF @ 16%	Present Value
Cash Outflows:
Initial Outlay	0	($1,850,000.00)	1	($1,850,000.00)
Cash Inflows:
Annual Cash Inflows	1-6	$500,000.00	3.684735908	$1,842,367.95
Net Present Value				($7,632.05)

The NPV at discount rate 16 % is negative. This means that IRR lies between 15% to 16%

Using Interpolation:

IRR = 15 % + 42,241.35 / (42,241.35 - (-$7,632.05))

IRR = 15 % + 42,241.35 / 49873.39

IRR = 15% + 0.84697

IRR = 15.84697 or 15.85%

d) Decision: Accept the project  

NPV	$608,662.16
PI	1.33
IRR	15.85%

Since NPV is Positive that means that present values of cash inflows is higher than the present value of cash outflows.Therefore, we should accept the project..

Since, PI >1 it indicates the  Present value of future cash flows is greater than initial investments.Therefore, we should accept the project..

Since IRR = 15.84% is higher than the required rate of return 6%. Therefore, we should accept the project..

Note :
PVF(r,t) = (1/(1+r))^n
PVAF = (1/(1+r))^1 + (1/(1+r))^2 +...+(1/(1+r))^n