Question

Suppose your firm is considering investing in a project with the cash flows shown below, that the required rate of return on projects of this risk class is 12 percent, and that the maximum allowable payback and discounted payback statistic for the project are 2 and 3 years, respectively. Time 0 1 2 3 4 5 6 Cash Flow -1,030 130 470 670 670 270 670

Answer 1

IRR is the rate of return for which NPV = 0

NPV = Present value of cash inflows of the project - initial investment

Putting NPV = 0

Present value of cash inflows of the project = initial investment

[ (C1/(1+IRR)¹) + (C2/(1+IRR)²) + (C3/(1+IRR)³) + (C4/(1+IRR)⁴) + (C5/(1+IRR)⁵) + (C6/(1+IRR)⁶)] = c0

[ (130/(1+IRR)¹) + (470/(1+IRR)²) + (670/(1+IRR)³) + (670/(1+IRR)⁴) + (270/(1+IRR)⁵) + (670/(1+IRR)⁶)] = 1030

We have to find IRR by trial and error method

by assuming any value and substituting the assumed value in the above equation

we want IRR such that

Left Hand side of equation(LHS) = Right hand side of equation (RHS) = 1030

by following this method we find that for IRR = 33.7269% or 33.73% ( rounding off to 2 decimal places)

since IRR> required return (12%) , we will accept the project

since NPV is positive , the project should be accepted

payback period = 2.64 years , according to payback period the initial investment would be recovered in 2.64 years and since it is greater than the maximum allowable payback period of 2 years, the project should be rejected