The before-tax IRR is 37.93%
The after-tax IRR is 19.32%
The internal rate of return (IRR) is defined as the return rate on a project investment project over a periodic lifespan.
It is also referred to as the net present value of an investment project which is zero. It can be expressed by using the formula:
[tex]\mathbf{0= NPV \sum \limits ^{T}_{t=1} \dfrac{C_t}{(1+1RR)^t}- C_o}[/tex]
where;
- [tex]\mathbf{C_t}[/tex] = net cash inflow for a time period (t)
- [tex]\mathbf{C_o=}[/tex] Total initial investment cost
(a)
For the before-tax IRR:
The cash outflow = $120000
Cash Inflow for the first three years = $60000
Cash inflow for the fourth year = $60000 + $20000 = $80000
∴
Using the above formula, we have:
[tex]\mathbf{0 = \dfrac{60000}{(1+r)^1}+ \dfrac{60000}{(1+r)^2}+ \dfrac{60000}{(1+r)^3}+ \dfrac{80000}{(1+r)^4}}[/tex]
By solving the above equation:
r = 37.93%
(b)
For the after-tax IRR:
The cash outflow = $120000
Recall that:
- Cash Inflow = Cash inflow × Tax rate
∴
For the first three years; the cash inflow is:
[tex]\mathbf{=60000 -(60000\times 0.3) } \\ \\ \mathbf{ = 60000 -18000} \\ \\ \mathbf{ = 42000}[/tex]
For the fourth year, the cash inflow is
[tex]\mathbf{=80000 -(60000\times 0.3) } \\ \\ \mathbf{ = 80000 -18000} \\ \\ \mathbf{ = 62000}[/tex]
Using the above IRR formula:
[tex]\mathbf{0 = \dfrac{42000}{(1+r)^1}+ \dfrac{42000}{(1+r)^2}+ \dfrac{42000}{(1+r)^3}+ \dfrac{62000}{(1+r)^4}}[/tex]
By solving the above equation:
r = 19.32%
Learn more about the internal rate of return (IRR) here:
https://brainly.com/question/24301559
