Question

From the e-Activity, analyze the reasons why the short-term project that you have chosen might be ranked higher under the NPV criterion if the cost of capital is high, while the long-term project might be deemed better if the cost of capital is low. Determine whether or not changes in the cost of capital could ever cause a change in the internal rate of return (IRR) ranking of two (2) projects.

e activity: Use the Internet to research two (2) mutually exclusive investment projects to compare. The projects may involve any kind of investment, as long as the time frame for one (1) of the investments is a maximum of one (1) year (short term) and the time frame for the other investment is five (5) years minimum (long term). Be prepared to discuss.

Answer 1

To answer this question let us first know the formula for calculating the NPV.

NPV = - C₀  + C₁   /(1+ r) + C₂   /(1+ r)² + C3 /(1+ r)³  +.........+C_n   / (1+r)ⁿ

where C are the cash flows , r is the cost of capital and n is the number of years for which project is undertaken .

If we compare two projects with different time periods, the one with shorter period will have higher NPV than the one with longer period at same cost of capital. This is true mathematically because in a short-term project, cash flows are generated quickly and discounted lesser time than a long-term project to get the Net Present Value.

For a short-term project, if the cost of capital is high, it will be discounted less and ranked higher usually. The reason being the cash flows generated from this project are received sooner in near future and discounted less number of times. However, for a longer term project, the higher proportion of cash is expected in far away future. So lower the cost of capital, better for the total NPV of the project. NPV is sensitive to changes in the cost of capital for a long-term project than a short-term project. Therefore if a project generates good cash flow sooner, it can be used for re-investment for generating higher returns. But if cash flow is generated in many years to come, it gets discounted multiple times and lesser the NPV that is generated. It can be concluded that high cost of capital will render short-term projects more attractive to an investor and low cost of capital renders long-term projects as more attractive.

No ,changes in the cost of capital would not change the internal rate of return (IRR) ranking of two (2) projects.

Mutually exclusive projects refer to those projects which are completely independent of each other and only one project can be accepted among so many projects. So it is concluded that project with higher NPV is accepted and other projects are rejected even though they have positive NPV.

Let's say that Amazon Inc. is considering two mutually exclusive projects . Project A is a 1-year project with cash flow of $ 17000,Initial investment is $10000 and cost of capital is 8%.

Project B is also a 5-year project the following cash flows in each of the 5years: $1,000, $3,000, $4,000, $6,750, $4000.The cost of capital is 8 % for each project and investment is $10,000. Let's calculate NPV for each project A and B ,

NPV of project A = -10000+ 17000/(1.08) = $5740.74

NPV of project B = -10000 + 1000/(1.08) +3000/(1.08)²  +4000/(1.08)³ +6750/(1.08)⁴ +4000/(1.08)⁵

  =-10000 + 925 + 2572 + 3175.32+4961.45+2722.332

= $4356.102

If we calculate the same cash flows of both projects at 2 % cost of capital you can find below

NPV of project A at 2 % cost of capital = -10000 + 17000/1.02 = -10000+16666.66= $ 6666.66

NPV of project B at 2 % cost of capital = -10000 +1000/(1.08) +3000/(1.08)²  +4000/(1.08)³ +6750/(1.08)⁴ +4000/(1.08)⁵

=10000+980.39+2883.50+3769.289+6235.956+3622.923 = 7492.046

So if we follow NPV Criterion , in a mutually exclusive projects, whoever's NPV is higher can be accepted.

Here NPV of project A is higher than NPV of project B in case where rate of interest is high i.e 8 % however NPV of project B is higher that project A when the cost of capital reduces to 2 %.So this proves cost of capital significantly affects the NPV when a short term project and long term project are evaluated exclusively.