Consider an investment project with a length of n years and an initial outlay IO. Let ACFt be the net cash flow for the project in year t, where t=1,2,,n. Let k be the project discount rate per annum, expressed in decimal form. (a) Write down a formula for the net present value, NPV, for the project (b) Write down a formula for the profitability index, PI, for the project (c) Using your answers to (a) and (b), show that PI=IONPV+IO (d) Using the formula in (c), show that NPV=IO(PI1) (e) Wy is the net present value used more that the profitability index in capital budgeting