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Multiple Choice
In the context of evaluating two investment projects, what does the 'crossover rate' represent?
A
The interest rate at which the payback periods of both projects are the same.
B
The rate of return at which a project's internal rate of return (IRR) equals zero.
C
The discount rate at which the net present values (NPVs) of both projects are equal.
D
The required rate of return used to calculate the future value of an investment.
Verified step by step guidance
1
Understand the concept of the crossover rate: The crossover rate is the discount rate at which the net present values (NPVs) of two investment projects are equal. It is used to compare the financial viability of two projects under varying discount rates.
Identify the formula for NPV: The NPV of a project is calculated using the formula: , where 't' is the time period, 'r' is the discount rate, and 'Cash Flowt' represents the cash inflow at time 't'.
Set up the equation for the crossover rate: To find the crossover rate, equate the NPV formulas of both projects. This means: . Substitute the cash flows and initial investments of both projects into the formula.
Solve for the discount rate 'r': Rearrange the equation to isolate 'r', which represents the crossover rate. This may involve algebraic manipulation and solving for 'r' using numerical methods or financial calculators.
Interpret the result: The crossover rate indicates the discount rate at which both projects are equally attractive in terms of their NPVs. If the actual discount rate is below the crossover rate, one project may be preferred; if above, the other project may be preferred.