Question

1. Flynn, Inc. is considering a four-year project that has an initial after-tax outlay or after-tax cost of $80,000. The future after-tax cash inflows from its project for years one, two, three, and four are $40,000, $40,000, $30,000, and $30,000, respectively. Flynn uses the internal rate of return method to evaluate projects. What is the approximate IRR for this project?
   1. The IRR is less than 12%.
   2. The IRR is between 12% and 20%.
   3. The IRR is about 24.55%.
   4. The IRR is about 28.89%.

show work please aside from excel:)

Answer 1

So we know that the IRR is the rate at which the NPV is zero

So the Initial outlay = present values of cash inflows

If the IRR is r , then present values of cash inflows = 40000/(1+r) + 40000/(1+r)^2 + 30000 / (1+r)^3 + 30000/ (1+r)^4

There is no short formula for IRR other than trial and error or excel

So We will go by the options here,

when we put r = 12%,  then present values of cash inflows = 40000/(1+0.12) + 40000/(1+0.12)^2 + 30000 / (1+0.12)^3 + 30000/ (1+0.12)^4 = 108021 ... ( The value should be equal to 80000 for NPV to be zero, so we have to icrease the rate for the Present value to be lower)

when we put r = 24.55%,  then present values of cash inflows in similar way is 85894

when we put r = 28.89%,  then present values of cash inflows in similar way is close to 80000

So the correct choice is d)The IRR is about 28.89%