A manufacturing company is considering buying a new machine to replace an old one. The new machine costs $400,000 and has a useful life of 10 years. The old machine has a book value of $100,000 and is expected to have a useful life of 5 more years. The company plans to sell the old machine for $50,000 at the end of its useful life. The new machine is expected to generate annual cost savings of $60,000 compared to the old machine. The company's required rate of return is 12%.

a) Should the company buy the new machine?

b) What is the net present value of the investment if the company decides to buy the new machine?

c) What is the internal rate of return of the investment?

d) What is the payback period of the investment?