Answer:
Answer: c) 12.22%
Step-by-step explanation:
IRR is the annual rate of growth that an investment is expected to generate. The formula is shown below:
[tex]NPV= \sum\limits_{n=0}^N \frac {C_n}{(1+r)^n}[/tex]
NPV= Net Present Value
N = total number of periods
n = number of the year
Cn = cash flow at year n
r = internal rate of return
The formula can also be written as:
[tex]NPV= \sum\limits_{n=0}^N {C_n}(1+r)^{-n}[/tex]
The internal rate of return is a discount rate that makes the net present value (NPV) of all cash flows equal to zero in a discounted cash flow analysis.
The cash flows for the project are expected to be:
C0= -4,000,000
C1 = 600,000
C2 = 800,000
C3 = 4,000,000
To have NPV=0, then the following equation must be satisfied:
[tex]{C_0}(1+r)^{-0}+{C_1}(1+r)^{-1}+{C_2}(1+r)^{-2}+{C_3}(1+r)^{-3}=0[/tex]
[tex]-4,000,000+600,000(1+r)^{-1}+800,000(1+r)^{-2}+4,000,000(1+r)^{-3}=0[/tex]
The value of r cannot be determined by algebraic methods. Only an approximate value can be found by some numerical method.
We are given four options, let's test them out and find which one is the best approximation. The one that produces a result closer to zero will be selected:
a) r = 11.52%=0.1152
[tex]-4,000,000+600,000(1+0.1152)^{-1}+800,000(1+0.1152)^{-2}+4,000,000(1+0.1152)^{-3}=65,320[/tex]
b) r = 11.84%=0.1184
[tex]-4,000,000+600,000(1+0.1184)^{-1}+800,000(1+0.1184)^{-2}+4,000,000(1+0.1184)^{-3}=35,420[/tex]
c) r = 12.22%=0.1222
[tex]-4,000,000+600,000(1+0.1222)^{-1}+800,000(1+0.1222)^{-2}+4,000,000(1+0.1222)^{-3}=330[/tex]
d) r = 12.71%=0.1271
[tex]-4,000,000+600,000(1+0.1271)^{-1}+800,000(1+0.1271)^{-2}+4,000,000(1+0.1271)^{-3}=-44260[/tex]
The IRR of 12.22% is the best approximation for the project.
Answer: c) 12.22%
