Suppose that you had paid $ 300,000 for an investment that pays the following cash flows....

Suppose that you had paid $ 300,000 for an investment that pays the following cash flows. What will be your internal rate of return? a. $45,000 b. $38,000 c. $52,000 d. $320,000

Expert Solution

Ans:

IRR is found using trial and error method.

we found out whether the value of cash flows becomes zero at a particular rate , if not we out the value at another rate. we will find the difference between the rate and value and found at what rate the value will be equal to zero .

Step 1: Find the present value of cash flows at 10 % rate.

Present value factor (1/(1+rate)^n	Present value factor	Cash flows	Present value
1/(1.10)	0.909090909	45000	40909.09091
1/(1.10)^2	0.826446281	38000	31404.95868
1/(1.10)^3	0.751314801	52000	39068.36965
1/(1.10)^4	0.683013455	320000	218564.3057
		Present value of cash flows	329947
		Initial investment	300000
			29947

Step 1: Find the present value of cash flows at 15 % rate.

Present value factor (1/(1+rate)^n	Present value factor	Cash flows	Present value
1/(1.15)	0.869565217	45000	39130.43478
1/(1.15)^2	0.756143667	38000	28733.45936
1/(1.15)^3	0.657516232	52000	34190.84409
1/(1.15)^4	0.571753246	320000	182961.0386
		Present value of cash flows	285016
		Initial investment	300000
			-14984

Step 3. The value at the both rates are subtracted to find the amount at 1%

29947- ( 14984) = 44,931. This is for (10-15) = 5%

44,931 is for 5 %

for 1%, $ 8986.189.

The value of present value of cash flows left a balance of 29947 at 10% rate.

we need to find what more the rate should be to make this balance to zero , 29,947 / 8986.189 = 3.3325 %

The rate to be increased from 10% by 3.3325 % so the cash flows will be zero, 10 + 3.3325 = 13.3325 %

IRR = 13.3325 %

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