The directors of your company are considering two mutually exclusive projects, which both require an investment of K$1\mathrm{.}2$ million. The cash flows of the two projects have different time patterns. Project M is a mining type of investment and the cost of removing the ore is lower at the entrance to the mine, where there is easier access. Project O is an Orchard type of investment where it takes a number of years for trees to mature and be fully fruit bearing. The projects$$ cash inflows are as follows:

Year $12345$

Project M $($K$000)700400300100100$

Project O $($K$000)100200300500800$

The projects$$ net present values have been calculated for a number of discount rates.

NET PRESENT VALUES

Discount rate Project M Project O

K K

$6\%222,000318,000$

$8\%170,750214,170$

$10\%122,710118,900$

$12\%77,74033,940$

$14\%35,490(44,310)$

$16\%(4,200)(115,910)$

$20\%(76,900)(241,510)$

Graph paper is not required for this question.

$($a$)$ Calculate the payback period for each project and comment on the usefulness of the figures that you have calculated. $(4$ Marks$)$

$($b$)$ Estimate the approximate internal rate of return of each project and indicate which project is better and why. $(6$ Marks$)$

$($c$)$ If the cost of capital was expected to be $9\%$ over the next five years, show which project should be selected and why. $(4$ Marks$)$

$($d$)$ Estimate the sensitivity of each project to changes in the cost of capital, and hence determine which project is more risky. $(6$ Marks$)$