Question

NPV and IRR   Benson Designs has prepared the following estimates for a​ long-term project it is considering. The initial investment is

23,260

and the project is expected to yield​ after-tax cash inflows of

7000

per year for

5

years. The firm has a cost of capital of

11%.

a.  Determine the net present value​ (NPV) for the project.

b.  Determine the internal rate of return​ (IRR) for the project.

c.  Would you recommend that the firm accept or reject the​ project?

Answer 1

(a)-Net Present Value (NPV) of the Project

Year	Annual Cash flow ($)	Present Value factor at 11.00%	Present Value of Annual Cash flow ($)
1	7,000	0.900901	6,306.31
2	7,000	0.811622	5,681.36
3	7,000	0.731191	5,118.34
4	7,000	0.658731	4,611.12
5	7,000	0.593451	4,154.16
TOTAL			25,871.28

Net Present Value (NPV) of the Project = Present value of annual cash inflows – Initial investment costs

= $25,871.28 - $23,260

= $2,611.28

(b)-Internal rate of return​ (IRR) for the project.

The Present Value factor for determining IRR = Net Initial Investment / Net Annual Cash Inflow

= $23,260 / $7,000 per year

= 3.32286

From the Present Value Annuity Factor Table (PVAIF Table), the discount rate (IRR) corresponding to the factor of 3.32286 for 5 Years is 15.37%.

“Hence, the Internal rate of return (IRR) for the project will be 15.37%”

(c)-DECISION

“YES”. Benson Designs should accept the project, since the Net Present Value of the Project is positive $2,611.28 and the Internal rate of return for the project (15.37%) is greater than the firm’s cost of capital (11.00%).

NOTE

The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Discount Rate/Cost of capital and “n” is the number of years.