Youth $($Pty$)$ Ltd $($Youth$)$ is a dermatological practice in Cape Town$$s Central Business

District. The entity employs specialised, well$-$trained dermatologists, and the majority

of its client base is middle to high$-$income earners. Currently, Youth is considering

introducing a new product range to be sold in its practice. The entity is deciding

between two product ranges, $$Bright$$ and $$Elastic$.$

While Bright will be an affordable skincare range, Elastic will be more expensive but

offers more benefits to the user as it has more proteins and minerals. Consequently,

choosing Elastic as the product range to be introduced is riskier, whilst it is known that

Bright will be bought by customers. Elastic may not be as successful amongst the

customers due to the higher price. However, should Elastic succeed, the returns to

Youth will be higher due to the higher selling price and consequential profit.

In order to perform an evaluation of which product range to choose, Youth has

conducted research on the probability of each product range$$s success and the returns

they will receive in each of the various outcomes.

PRODUCT LINE: BRIGHT

A sensitivity analysis and market research have been conducted which delivered the

following results: Should the Bright product line fail, a loss of $14\mathrm{.}8\%$ will be

experienced. The chance of this product line failing is $8\mathrm{.}6\%.$ However, should it be

successful above average a $56\mathrm{.}1\%$ return will be obtained and, if highly successful, a

$68\mathrm{.}2\%$ return. The chances of these are $57\mathrm{.}2\%$ and $24\mathrm{.}2\%$ respectively. In the case of

the Bright product line achieving average success, a $51\mathrm{.}5\%$ return will still be obtained.

PRODUCT LINE: ELASTIC

The sensitivity analysis and market research for this product line indicated the

following: Should this product be successful above average, a $77\mathrm{.}4\%$ return will be

received. The chance of this is $33\mathrm{.}6\%.$ If the product line is only average in this success

a $59\mathrm{.}8\%$ return will be generated of which the chance is $30\mathrm{.}1\%.$ In the extreme cases

of a failure or a high success, the outcomes will be a loss of $19\%$ and a return of $80\mathrm{.}5\%$

respectively. A $21\mathrm{.}2\%$ probability can be assigned to the first and $15\mathrm{.}1\%$ to the latter. REQUIRED:

$2\mathrm{.}1.$ Calculate the return that Youth $($Pty$)$ Ltd could expect from the Bright product

line and Elastic product line, respectively.

$(8$ marks$)$

$2\mathrm{.}2.$ Calculate the risk that Youth $($Pty$)$ Ltd can expect from the Bright product line

and Elastic product line, respectively.

$(21$ marks$)$

$2\mathrm{.}3.$ The directors of Youth $($Pty$)$ Ltd pointed out that the research indicated that the

Elastic product line will generate a return of $59\mathrm{.}8\%$ even if it only achieves an

average success, whereas the Bright product line will only generate a $51\mathrm{.}5\%$

return if the same outcome prevails.

Advise the directors of Youth $($Pty$)$ Ltd as to what the chances are of the Bright

product line generating a return of $59\mathrm{.}8\%$

$(6$ marks$)$

$2\mathrm{.}4.$ Indicate the range in which the Elastic product line$$s return could be expected

to fall within, should the directors require to know with $99\mathrm{.}7\%$ accuracy what the

actual return will be$.$

Assume the Elastic product line$$s variance was calculated as $16\%$ and the

expected return as $53\mathrm{.}5\%$

$(6$ marks$)$