Answer :
Answer:
The IRR of this investment is 5.5%
Explanation:
First we need to express the present value of this investment
[tex][/tex]
[tex]PV=-12+\frac{0.3}{1+r} +\frac{0.3*1.03}{(1+r)^2}+\frac{0.3*1.03^2}{(1+r)^3}+... +\frac{0.3*1.03^{k-1}}{(1+r)^k}[/tex]
From the second term we have a perpetuity with growth rate, which we resolve as
[tex]\frac{0.3}{1+r} +\frac{0.3*1.03}{(1+r)^2}+\frac{0.3*1.03^2}{(1+r)^3}+... +\frac{0.3*1.03^{k-1}}{(1+r)^k}=\frac{0.3}{r-0.03}[/tex]
Then we can replace r by IRR and PV equal to zero and we have
[tex]PV=0=-12+\frac{0.3}{IRR-0.03}\\ \\\frac{0.3}{IRR-0.03}=12\\\\IRR=0.03+0.3/12=0.03+0.025=0.055[/tex]
The IRR of this investment is 0.055 or 5.5%