Question

A Corporation is deciding whether to engage in a 2-year project that requires an initial cash outflow of I (CF₀) = $2,000,000. CF₁ is expected to be a cash inflow of $4,670,000 and CF₂ is expected to be another cash outflow of $2,722,500. Altogether there are three cash flows—an initial cash outflow, followed by a cash inflow, followed by a second cash outflow at the end of the 2-year project life.

1. Determine the multiple IRR’s by plotting the project’s NPV Profile and observing where the profile crosses the horizontal axis. Label the axes and all the vertical and horizontal intercepts.
2. Should the corporation accept this project at:

1. k = 10%?
2. k = 15.5%?
3. k = 25%?

Explain your reasoning in each of these three cases.

Answer 1

A) The Project's NPV profile is as shown below for various discount rates

From the Profile, the IRR's can be determined as the Discount rates for which NPV is 0

It can be seen that NPV is 0 for two discount rates of 12.50% and 21%

So, the two IRR's of the project are 12.50% and 21%

B) If the discount rate is

i) k =10%

NPV = -2000000+4670000/1.1-2722500/1.1^2 = -$4545.45

So, the project should not be accepted as the NPV is negative

The present value of the year two cashoutflows makes the Net present values negative.  

ii)

k =15.5%

NPV = -2000000+4670000/1.155-2722500/1.155^2 = $2473.72

So, the project should be accepted as the NPV is positive

The discount rate is such that the present value of 1st year cashinflow is more than the present value of cashoutflows in this situation

iii)

k =25%

NPV = -2000000+4670000/1.25-2722500/1.25^2 = -$6400

So, the project should not be accepted as the NPV is positive

The discount rate is so high that the present value of 1st year cashinflow is not sufficient to keep the overall Net present value positive.

The above is also evident from the graph as the NPV is positive only for discount rates between 12.5% and 21%. For all other discount rates, the NPV is negative.