Question

1. Consider two projects, X and Y. Project X's IRR is 19% and Project Y's IRR is 17%. The projects have the same risk and the same lives, and each has constant cash flows during each year of their lives. If the cost of capital is 10%, Project Y has a higher NPV than X. Given this information, which of the following statements is CORRECT?   

	a.	The crossover rate must be greater than 10%.
	b.	If the cost of capital is 8%, Project X will have the higher NPV.
	c.	If the cost of capital is 18%, Project Y will have the higher NPV.
	d.	Project X is larger in the sense that it has the higher initial cost.
	e.	The crossover rate must be less than 10%.

I know A is correct, but just would like to know the logic to it as I have no idea how the answer is A. Thanks.

Answer 1

Answer: Option A is correct.

Explanation:
The rate of return at which the net present value (or NPV) of two projects are equal, is referred to as the crossover rate.
Internal rate of return (or IRR) of project Y=17%
IRR of Project X=19%
So, IRR of project Y is less than the IRR of project X

IRR is the rate of return at which the NPV is zero, if we increase this rate of return, NPV will become negative because NPV=-Initial cash outflow+Present value of future cash inflows and this present present value is discounted using the cost of capital (return rate) and IRR is a case at which present values of future cash flows becomes equal to initial cash outflow.

So, at 19% rate of return, NPV of Project Y will become negative.

Given that, if the cost of capital is 10%, project Y has a higher NPV than project X.

For crossover rate, the NPV of both the projects should be equal and they will have same NPV when the rate lies between 10% and 19% because above this range NPV of project Y will become negative (move down) and at 10%, project Y will have higher (move up) NPV than project X.

So, as per the options given, the crossover rate must be greater than 10%.