b$)$ Critically discuss the merits of each investment appraisal method, then discuss the result of the evaluations you have made of the two projects and advise the company.Project A

Payback period:

Year $1=40$ Year $2=90(40+50)$ Year $3=150(90+60)$

So$,$ the Payback period is somewhere between $3$ years.

Accounting rate of return:

ARR$=\frac{\text{A}\text{v}\text{e}\text{r}\text{a}\text{g}\text{e}\text{a}\text{n}\text{n}\text{u}\text{a}\text{l}\text{a}\text{c}\text{c}\text{o}\text{u}\text{n}\text{t}\text{i}\text{n}\text{g}\text{p}\text{r}\text{o}\text{f}\text{i}\text{t}}{\text{A}\text{v}\text{e}\text{r}\text{g}\text{e}\text{i}\text{n}\text{v}\text{e}\text{t}\text{m}\text{e}\text{n}\text{t}}100$

$\frac{55}{67\mathrm{.}5}100=81\mathrm{.}48$

Net Present Value $($NPV$)$:

$\frac{40}{1+0\mathrm{.}12}+\frac{50}{(1+0\mathrm{.}12)2}+\frac{60}{(1+0\mathrm{.}12)3}+\frac{50}{(1+0\mathrm{.}12)4}+\frac{75}{(1+0\mathrm{.}12)5}-135=42\mathrm{.}85$

$1$

Project B

Payback period:

Year $1=80$ Year $2=140(80+60)$ Year $3=190(140+50)$

So$,$ the Payback period is somewhere between $3$ years.

Accounting rate of return:

ARR$=\frac{\text{A}\text{v}\text{e}\text{r}\text{a}\text{g}\text{e}\text{a}\text{n}\text{n}\text{u}\text{a}\text{l}\text{a}\text{c}\text{c}\text{o}\text{u}\text{n}\text{t}\text{i}\text{n}\text{g}\text{p}\text{r}\text{o}\text{f}\text{i}\text{t}}{\text{A}\text{v}\text{e}\text{r}\text{g}\text{e}\text{i}\text{n}\text{v}\text{e}\text{t}\text{m}\text{e}\text{n}\text{t}}100$

$\frac{44}{74}100=59\mathrm{.}45$

Net Present Value $($NPV$)$:

$\frac{80}{1+0\mathrm{.}12}+\frac{60}{(1+0\mathrm{.}12)2}+\frac{50}{(1+0\mathrm{.}12)3}+\frac{20}{(1+0\mathrm{.}12)4}+\frac{10}{(1+0\mathrm{.}12)5}-148=25\mathrm{.}24$