### CFA Practice Question

Assume the following information about two individual projects.

Project A
Initial cash outflow: \$175,000
Expected cash inflows
t1: \$75,000
t2: \$65,000
t3: \$35,000
t4: \$35,000
t5: \$15,000

Project B
Initial cash outflow: \$100,000
Expected cash inflows
t1: \$15,000
t2: \$15,000
t3: \$18,000
t4: \$45,000
t5: \$45,000

Assuming these projects are not mutually exclusive, and the cost of capital is 10%, which of the two should be undertaken according to NPV? Additionally, which of the two projects has the steeper NPV profile?
A. Project A should be accepted, project A has a steeper NPV profile
B. Project A should be accepted, project B has a steeper NPV profile
C. Both projects should be accepted, project A has a steeper NPV profile
Explanation: The NPV of project B is found to be -\$1,766.21, and thus should not be accepted. However, project A has a positive NPV of \$6,416.14, and should be accepted. Project B is characterized as having the majority of its cash inflows occurring in later time periods, and thus is more sensitive to changes in the cost of capital. This is exemplified by a steeper NPV profile for project B.

### User Contributed Comments17

User Comment
shasha B behaves like lower coupon bond, with larger portion of cash flow at later stage.
KD101 Projects are NOT MUTUALLY EXCLUSIVE that means if you accept one you must accept another??? or none? So ideally - you need to look at the jointly investing in both
Franz Not mutually excluse - you must only accept one
Ebenezer Appears to be some confusion over the term 'not mutually exclusive'-which means you can accept both if both have postive NPV. Mutually exclusive means you can only accept one of it.
garachen "steeper" is a little vague
synner because they are not mutually exclusive, and they both give positive NPV, so both A and B should be accepted.
what does "steeper" mean?
murli No. Project B gives negative NPV and should not be accepted.
dimos NPV of project B is -1766.21 and that is why it should not be accepted.
danlan Steeper means sensitivity of NPV comparing to YTM. Since B has most cost at later stage, its NPV is more sensitive to YTM.
dimanyc Don't get it. Since B has majority of large inflows at the end of the period (and they are being discounted back by a larger number), it should have a less steep (flatter?!) profile. In other words, A should have a steeper profile.

Here's a proof by a test:
Project A:
20% coc: -24.2
10% coc: 6.42
5% coc: 26.17

Project B:
20% coc: -26.88
10% coc: -17.66
5% coc: 15.72

Any thoughts on that?
gerry No dimanyc. It's the opposite. Project B's NPV is more sensitive to changes in the discount rates and that's why it has a steeper NPV profile.
Bparsons Because project B's cash flows occur later in the life of the project, the present value of those cash flows is more sensitive to changes in the cost of capital.

Therefore, for every % increase in the cost of capital, the NPV of project B decreases more than that of A - it has a steeper NPV profile.
threedot I thought the NPV profile was the slope of the line plotted with NPV on the y-axis and disc. rate on x-axis?
jpducros - When 2 projects have positive NPV, the one with the highest NPV will have the steepest slope.
- Here, one project has + NPV and one has - NPV so one has a positive slope and one has a negative slope. Do we have to make abstraction of the sign to consider the steepness ?
tommyguard3 Is there a way to calculate the steepness of a slope or is it only looking at the time the cash flows are realized that will tell you that?
kritan tommyguard3: I just plotted the above out on a graph, with NPV on the Y axis and IRR on the X axis. once you have the NPV and IRR of both projects (from your calculator, natch), you can draw out each curve and see which is steeper.
wperge I agree with dimanyc, I did a sensitivity analysis for A and B and it seemed like B's NPV was more sensitive to a change in the discount rate
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