Calculation Problems for Project Selection

$1.$ Your firm is trying to decide whether or not to invest in a new project opportunity based on the following information. The initial cash outlay will total $$250,000$ over two years. The firm expects to invest $$200,000$ immediately and the final $$50,000$ in one year$$s time. The company predicts that the project will generate a stream of earnings of $$50,000,$ $$100,000,$ $$200,000,$ and $$75,000$ per year, respectively, starting in Year $2.$ The required rate of return is $12\%,$ and the expected rate of inflation over the life of the project is forecast to remain steady at $3\%.$ Should you invest in this project?

$2.$ Sean, a new graduate at a telecommunications firm, faces the following problem on his first day at the firm: What is the average rate of return for a project that costs $$200,000$ to implement and has an average annual profit of $$30,000?$

$3.$ A four$-$year financial project has net cash flows of $$20,000$; $$25,000$; $$30,000$; and $$50,000$ in the next four years. It will cost $$75,000$ to implement the project. If the required rate of return is $0\mathrm{.}2.$

$($a$)$ Conduct a discounted cash flow calculation to determine the NPV$.$

$($b$)$ What would happen to the NPV of the above project if the inflation rate was expected to be $4$ percent in each of the next four years?

$($c$)$ Calculate the benefit$-$Cost ratio.

$4.$ Your company is seriously considering investing in a new project opportunity but cash flow is tight these days. Top management is concerned about how long it will take for this new project to pay back the initial investment of $$50,000.$ You have determined that the project should generate inflows of $$30,000,$ $$30,000,$ $$40,000,$ $$25,000,$ and $$15,000$ for the next five years. Your firm$$s required rate of return is $15\%.$ How long will it take to pay back the initial investment?