Palp $($PTY$)$ Ltd $($Palp$)$ is considering two machines that should produce considerable cost savings in its assembly operations. The cost of each machine is R$14000$ and neither is expected to have a salvage value at the end of a $4$ year useful life. Palp's required rate of return is $12\%$ and the company prefers that a project return its initial outlay within the first half of the project's life. The annual after$-$tax cash savings for each machine are provided as follows: Year $1$ to $4,$ Machine A $($ R$5000$ for each year$),$ Machine B $($ year $1-$ R$8000,$ Year $2-$ R$6000,$ Year $3-$ R$4000,$ and Year $4-$ R$2000).$ a$)$ Calculate the payback period for each machine. NB answer should be in $2$ decimal places. b$)$ Calculate the net present value for each machine. c$)$ Which machine should be purchased?