In: Finance
Suppose a project requires an initial cash outflow of $34,900. The project will last for four years with the annual cash flows given below. The required rate of return is 12%.
(1) Compute the net present value of the project. Should the firm invest in this project based on net present value? Why?
Year |
Cash Flows |
1 |
$12,500 |
2 |
$19,700 |
3 |
0 |
4 |
$10,400 |
(2) Compute the internal rate of return. Should the firm invest in this project based on internal rate of return? Why?
(3) Use a graph to show why the firm’s decisions in (1) and (2) are consistent or inconsistent. Be specific.
(4) Now suppose another project’s future annual cash flows are given below with an initial cash outflow $14,900.00). The required rate of return is 12%. Using a graph to explain why you cannot use IRR for capital budgeting in this case. (You do not need to compute anything here.)
Y ear |
Cash Flow |
1 |
$12,500 |
2 |
$12,500 |
3 |
$12,500 |
4 |
$12,500 |
5 |
$12,500 |
6 |
$12,500 |
7 |
-$19,700 |
8 |
-$20,000 |
9 |
-$20,000 |
10 |
-$20,000 |
To find the NPV of the project, we discount the future cashflows to present value by using the discount factor. Discount Factor for each year = 1/ (1+R)^N for ef for year 1 ; 1/ (1+ 12%)^1 = 0.8928
IRR is the rate at which NPV is zero.
1)We observe that NPV is negative of -1425, hence we will not select the project
2) We find that IRR is 10%, which is lower than cost of capital, hence we will not select the project based on IRR
3) We find the NPV of the project at various cost of capital for our analysis
We find that NPV of the project becomes zero at cost of 10% (Which is also our IRR) and NPV is negative when cost is 12% which was also calculated above. Hence decision frpm (1) & (2) are consistent.
4)
Multiple IRRs occur when a project has more than one internal rate of return. The problem arises where a project has non-normal cash flow (non-conventional cash flow pattern).Non-conventional (also called non-normal cash flows) are cash flows that have non-continuous streams of net cash outflows and net cash inflows, i.e. net cash outflows may occur at the start of the project, followed by net cash inflows, followed by further net cash outflows.
We observe that @7% and 77%, NPV of the project is close to zero. Hence there are 2 IRRs of the project. Due to the multiple IRR problem and the unrealistic reinvestment rate assumption inherent in IRR methodology, net present value is the preferred capital budgeting tool.