9-18: Dimond Hill Jewelers considering the following independent Project:
Expected Net Cashflows |
||
Year | Project D |
Project Q |
0 |
($2,500) |
($2,500) |
1 |
$2,000 |
$0 |
2 |
$900 |
$1,800 |
3 |
$100 |
$1,000 |
4 |
$100 |
$900 |
Q. Which project(s) should be accepted if the required rate of return for the Project is 10 percent? Compute the NPV and the IRR for both projects.
Solution
NPV Calculation for the project:
IRR calculation:
The following table represents different NPV at a different discount rate for both projects.
NPV |
||
RRR | Project D | Project Q |
10% | $205.42 | $253.63 |
12% | $137.92 | $218.70 |
14% | $73.61 | $92.89 |
16% | $12.28 | ($24.59) |
17% | ($17.33) | ($80.42) |
Decision:
If we are able to assume that projects D and Q are independent and the budget of the firm is high enough, then we can conclude that the firm will accept both projects Q and D simultaneously based on their positive NPVs.
9-20: Derek’s Donuts is considering two mutually exclusive investments. The projects’ expected net cash flows are as follows:
Expected net cash flows |
||
Time | Project A | Project B |
0 | ($300) | ($405) |
1 | ($387) | $134 |
2 | ($193) | $134 |
3 | ($100) | $134 |
4 | $500 | $134 |
5 | $500 | $134 |
6 | $850 | $134 |
7 | ($100) | $0 |
(a) NPV Profile for Project A and B:
Before we graph the NPV Profile for the projects, we must create a data table of projects NPV relative to different discount rates.
RRR |
NPV (Project A) |
NPV(Project B) |
0% | $970 | $399.00 |
2% | $797.47 | $345.59 |
4% | $646.67 | $297.45 |
6% | $514.57 | $253.92 |
8% | $398.62 | $214.47 |
10% | $296.63 | $178.60 |
12% | $206.77 | $145.93 |
14% | $127.46 | $116.08 |
16% | $57.34 | $88.75 |
(a) NPV Profile for Project A and B:
Before we graph the NPV Profile for the projects, we must create a data table of projects NPV relative to different discount rates.
RRR | NPV (Project A) | NPV(Project B) |
0% | $970 | $399.00 |
2% | $797.47 | $345.59 |
4% | $646.67 | $297.45 |
6% | $514.57 | $253.92 |
8% | $398.62 | $214.47 |
10% | $296.63 | $178.60 |
12% | $206.77 | $145.93 |
14% | $127.46 | $116.08 |
16% | $57.34 | $88.75 |
18% | $-4.73 | $63.68 |
20% | $-59.76 | $40.62 |
22% | $-108.61 | $19.37 |
24% | $-152.02 | $-0.26 |
26% | $-190.63 | $-18.41 |
28% | $-225.01 | $-35.24 |
30% | $-255.65 | $-50.87 |
Based on the above date the following NPV Profile can be drawn:
b) What is each project’s IRR?
So, Project B’s Internal Rate of Return (IRR) is higher than the IRR of Project A.
C) If you were told that each project’s required rate of return was 12 percent, which project should be selected? If the required rate of return was 15 percent, what would be the proper choice?
When each project’s required rate of return was 12 percent:
So, NPV (Project A)= $206.77
So, NPV (Project B)= $145.93
If each project’s required rate of return was 15 percent:
NPV (Project A)= $16.14
NPV (Project B)= $102.12
So, at a cost of capital of 12%, Project A should be selected. However, if the cost of capital rises to 15%, then the choice is reversed, and Project B should be accepted.
D. Looking at the NPV profiles constructed in part a, what is the approximate crossover rate, and what is its significance?
Time | Cash Flow Differential |
0 | $105 |
1 | ($521) |
2 | ($327) |
3 | ($234) |
4 | $366 |
5 | $366 |
6 | $716 |
7 | $100 |
Cross Over Rate | =14.50% |
Therefore, Cross Over Rate= 14.5%
The crossover rate represents the cost of capital at which the two projects have the same net present value (NPV). In this scenario, that common net present value, at a cost of capital of 14.50% is $109
Related Article: How RRR and IRR helps to select a project
Derek’s Donuts is considering