Question

Consider an asset expected to generate the following finite set of cash flows.

            0                      1                      2                      3                      4                      5          years

            |---------------     |----------------   |----------------   |----------------   |----------------- |

            -$11500           $1500              $7500              $1200              $1200              $4800

As shown on the timeline, the cost of the asset is $11,500. Assume a required rate of return of 10% per year, compounded annually.

A.        Calculate the net present value (NPV) of this set of cash flows.

B.        Calculate the internal rate of return (IRR) of the set of cash flows.

C.        Based on the NPV, should the company invest in this asset? Why or why not?

D.        Based on the IRR, should the company invest in this asset? Why or why not?

Answer 1

a)

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

NPV = -11,500 + 1,500 / (1 + 0.1)¹ + 7,500 / (1 + 0.1)² + 1,200 / (1 + 0.1)³ + 1,200 / (1 + 0.1)⁴ + 4,800 / (1 + 0.1)⁵

NPV = $763.60

b)

IRR is the rate of return that makes NPV equal to 0.

NPV = -11,500 + 1,500 / (1 + R)¹ + 7,500 / (1 + R)² + 1,200 / (1 + R)³ + 1,200 / (1 + R)⁴ + 4,800 / (1 + R)⁵

Using trial and error method, i.e., after trying various values for R, lets try R as 12.55%

NPV = -11,500 + 1,500 / (1 + 0.1255)¹ + 7,500 / (1 + 0.1255)² + 1,200 / (1 + 0.1255)³ + 1,200 / (1 + 0.1255)⁴ + 4,800 / (1 + 0.1255)⁵

NPV = 0

Therefore IRR is 12.55%

c)

Company should invest as the project has a positive NPV.

d)

Company should invest as the IRR is greater that cost of capital