Consider the following two mutually exclusive projects: Year Cash Flow (X) Cash
ID: 2743954 • Letter: C
Question
Consider the following two mutually exclusive projects:
Year
Cash Flow (X)
Cash Flow (Y)
What is the IRR of Project X? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)
What is the IRR of Project Y? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)
What is the crossover rate for these two projects? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)
Year
Cash Flow (X)
Cash Flow (Y)
0 $16,900 $16,900 1 6,610 7,090 2 7,190 7,830 3 4,710 3,430Explanation / Answer
For Calculation of IRR, Take two discount rate. One rate at which Present Value of Cash inflow is greater than the Present Value of Cash outflow and other rate at which Present Value of Cash inflow is lesser than the Present Value of Cash outflow.
a) IRR of Project X
At 3 % Discount Rate
Present Value of Cash inflow = 6610 * Present Value Factor @ 3 % for first year + 7190 * Present Value Factor @ 3 % for second year + 4710 * Present Value Factor @ 3 % for third year
Present Value of Cash inflow = 6610 * 0.971 + 7190 * 0.943 + 4710 * 0.915
Present Value of Cash inflow = $ 17508.13
Present Value of Cash outflow = $ 16900
At 10 % Discount Rate
Present Value of Cash inflow = 6610 * Present Value Factor @ 10 % for first year + 7190 * Present Value Factor @ 10 % for second year + 4710 * Present Value Factor @ 10 % for third year
Present Value of Cash inflow = 6610 * 0.909 + 7190 * 0.826 + 4710 * 0.751
Present Value of Cash inflow = $ 15484.64
Present Value of Cash outflow = $ 16900
IRR (By inter-polation) = 3 + (17508.13 - 16900) * (10 - 3) / (17508.13 - 15484.64)
= 3 + 608.13 * 7 / 2023.49
= 3 + 4256.91 / 2023.49
= 3 + 2.10
= 5.10 %
Conclusion:- IRR of Project X = 5.10 %.
b) IRR of Project Y
At 2 % Discount Rate
Present Value of Cash inflow = 7090 * Present Value Factor @ 2 % for first year + 7830 * Present Value Factor @ 2 % for second year + 3430 * Present Value Factor @ 2 % for third year
Present Value of Cash inflow = 7090 * 0.980 + 7830 * 0.961 + 3430 * 0.942
Present Value of Cash inflow = $ 17703.89
Present Value of Cash outflow = $ 16900
At 5 % Discount Rate
Present Value of Cash inflow = 7090 * Present Value Factor @ 5 % for first year + 7830 * Present Value Factor @ 5 % for second year + 3430 * Present Value Factor @ 5 % for third year
Present Value of Cash inflow = 7090 * 0.952 + 7830 * 0.907 + 3430 * 0.864
Present Value of Cash inflow = $ 16815.01
Present Value of Cash outflow = $ 16900
IRR (By inter-polation) = 2 + (17703.89 - 16900) * (5 - 2) / (17703.89 - 16815.01)
= 2 + 803.89 * 3 / 888.88
= 2 + 2411.67 / 888.88
= 2 + 2.71
= 4.71 %
Conclusion:- IRR of Project Y = 4.71 %
a) IRR of Project X 5.10 %. b) IRR of Project Y 4.71 %.