QUESTION 5 X Company is considering buying a new machine tha

QUESTION #5:

X Company is considering buying a new machine that will cost $150,000 and that will generate annual cash inflows of $31,470 for 6 years.

What is the approximate internal rate of return?

Solution

Internal rate of return is the rate at which Net Present value is zero. Discount rate and Present value of cash inflows has adverse relation. It means if discount rate increases , net present value decreases and vice versa. Suppose discount rate is 10% Present Value of annuity of 1 for 6 years @ 10% = (1-(1+i)^-n)/i Where, = (1-(1+0.10)^-6)/0.10 i 10% = 4.355260699 n 6 Present Value of annual cash inflows = Annual cash inflows x Present value of annuity of 1 = $     31,470.00 x 4.355261 = $ 1,37,060.05 Present value of annual cash inflows $ 1,37,060.05 Less cost of machine $ 1,50,000.00 Net Present Value $   -12,939.95 since in the above case, Net Present value is negative.It means Internal rate of return is lower than 10% to increase negative Net Present Value to Zero. Suppose discount rate is 5% Present Value of annuity of 1 for 6 years @ 5% = (1-(1+i)^-n)/i Where, = (1-(1+0.05)^-6)/0.05 i 5% =             5.07569 n 6 Present Value of annual cash inflows = Annual cash inflows x Present value of annuity of 1 = $     31,470.00 x    5.07569 = $ 1,59,732.03 Present value of annual cash inflows $ 1,59,732.03 Less cost of machine $ 1,50,000.00 Net Present Value $       9,732.03 At 5%, Net Present value , Net Present value is more than zero, It means Internal rate of return is more than 5%. Now, we can uderstand that Internal rate of return is between 5% and 10%, because zero Net Present value is coming within such rate. So, Approximate Internal rate of return = L+((H-L)*(A/(A-(A-B))) Where, = 5%+(5%*(9732.03/22671.98)) L 5% = 7.15% H 10% H-L 5% Thus, Approximate Internal rate of return is 7.15% or 7% A $     9,732.03 B $ -12,939.95 A-B $   22,671.98