# Consider the following cash flow [-100, + 230, -132]. We want to decide under what range of discount rate this is an advantageous investment.

1.Consider the following cash flow [-100, + 230, -132]. We want to decide under what range of discount rate this is an advantageous investment. But noting the change in sign, we conclude IRR is not a suitable instrument. (10 marks)a.Write the expression for NPV using the unknown r as discount rate. b.Write this expression as a function of [1/(1+r)].c.Show that the expression in (b) as a quadratic equation. Look this up if necessary.d.Solve the quadratic equation for its two roots.e.Prepare a table of NPV vs. r for r= 0,10,20,40,100%.f.Draw the graph of NVP vs. r.g.Under what range of r values is this an acceptable investment?h.Noting that NPV increases then declines as r grows from 0 to 40%, determine at what level of r NPV is a maximum (recall that d(NPV)/ds = 0, where NPV is a maximum). If you have sufficient background, solve this using calculus. If not, graphically find the top of the NPV hill (where slope = 0). What is the maximum value of NPV? (There is one bonus point for the correct answer using calculus