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A company is considering a two-year project, which has two annual
internal rates of return, namely 10% and 25%. The sum of the
undiscounted cash flows is positive.
The project will necessarily have a positive net present value,
when the annual cost of capital is
A More than 25%
B More than 10%
C Between 10% and 25%
D Less than 25%I was not able to understand this question at all.
Can you please explain this questionHere is the solution as well i was not able to understand the solution as well:
Answer A
The graph would be U-shaped with a negative NPV between 10% and
25% and positive NPVs at less than 10% or more than 25%.The project in question has two internal rates of return (IRRs) at 10% and 25%. When a project has multiple IRRs, it indicates that the cash flows change signs more than once, which is typical for non-conventional cash flows.
In this case, the sum of the undiscounted cash flows is positive, meaning that at a 0% discount rate, the NPV is positive. As the cost of capital increases, the NPV decreases.
So:
The NPV is positive when the cost of capital is below 10% and also when it is above 25%. Between 10% and 25%, the NPV is negative. This creates a U-shaped curve when plotting NPV against the cost of capital.
The NPV curve crosses the horizontal axis (NPV = 0) at the two IRRs: 10% and 25%. Therefore, the NPV is positive for costs of capital less than 10% and greater than 25%.
The correct answer is A) more than 25%. This is because, at any cost of capital above 25%, the NPV will be positive, while it will be negative for costs between 10% and 25%.
U-shaped graph illustrates the project is viable at both low and high discount rates, but not in the middle range.Thank you for the detailed explanation but here i have a one more doubt that as you said as cost of capital increases the NPV decreases so why after 25% the NPV is increasing ??
Think about a u shape
When there is an outflow followed by inflows and then more outflows, with two changes of sign and therefore potentially two IRR’s.
If it is an outflow first, then the curve will be u-shaped.
If on the other hand it was an inflow first, then it would be an inverted u-shape.
So again, having two internal rates of return (IRRs) indicates that the cash flows change signs more than once.
In this case, the cash flows are negative at time 0, positive at time 1, and then negative again at time 2.
Therefore, the NPV will be positive below the lower IRR of 10% and will become negative above the higher IRR of 25%.
Thus, for the project to have a positive NPV, the cost of capital must be more than 25%.
Watch John’s videos on IRR
You will either understand or not, if not just accept and move on from this 2 mark question
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