Mr Katlego Ndlovu is starting his studies in $2026$ and needs to purchase an updated laptop before

he starts. He will need R$15000$ on $1$ January $2026.$ His bank provides interest at $8\%$ per annum,

compounded annually $($unless otherwise stated$).$

Required:

Remember to show all formulas used and workings.

Q$\mathrm{.}1\mathrm{.}1$ How much must Katlego deposit on $1$ January $2023$ as a single premium investment

at his bank to accumulate a balance of R$15000$ by $1$ January $2026?$

$(4)$

Q$\mathrm{.}1\mathrm{.}2$ If Katlego wants to make equal payments at his bank every year on $1$ January,

starting on $1$ January $2023$ until $($and including$)1$ January $2026$ to accumulate the

R$15000,$ how large must each of the four payments be$?$

$(4)$

$222022$

$$ The Independent Institute of Education $($Pty$)$ Ltd $2022$

Page $3$ of $9$

Q$\mathrm{.}1\mathrm{.}3$ To help Katlego reach his R$15000$ goal, his uncle offers to give him R$4000$ on

$1$ January $2023.$ Katlego will make six additional payments of equal amounts every

six months, the first instalment on $1$ January $2023.$ If all this money is deposited in

another bank which pays $8\%$ interest, compounded semi$$annually $($biannually$),$ how

large must each of the six payments be$?$

$(12)$

PART B

Nqoko has inherited R$150000$ from her late dad$$s estate. She would like to use this money to

purchase a vehicle, with a current cost of R$180000,$ three years from now.

Required:

Q$\mathrm{.}1\mathrm{.}4$ Will Nqoko have enough money to buy the vehicle if she deposits the inheritance

into an account paying $10\%$ p$.$a$.($compounded quarterly$)?$ Ignore tax and assume

that vehicle prices escalate at $4\%$ per annum.

$(12)$

PART C

Hotel Inc is a group operating in different markets within the hospitality industry. They are

planning to acquire another hotel group in order to grow their market share, hence they need to

analyse how this could affect their finance structure. You are provided with the following

summary of the Statement of Financial Position of Hotel Inc.

Statement of financial position of Hotel Inc as at $31$ July $2022$

R R

Non$$current assets $1000000$ Ordinary share capital $400000$

Current assets $50000010\%$ preference shares $400000$

$15\%$ debentures $450000$

$20\%$ long term loans $250000$

$15000001500000$

Additional information:

The corporate tax rate is $28\%.$

$222022$

$$ The Independent Institute of Education $($Pty$)$ Ltd $2022$

Page $4$ of $9$

Required:

Q$\mathrm{.}1\mathrm{.}5$ Calculate the cost of equity if the profit after tax was R$300000.$ All the profit

attributable to the ordinary shareholders was distributed in the form of dividends.

$(4)$

Q$\mathrm{.}1\mathrm{.}6$ Determine the cost of preference shares in Rand value. $(3)$

Q$\mathrm{.}1\mathrm{.}7$ Determine the cost of debenture capital. $(3)$

Q$\mathrm{.}1\mathrm{.}8$ Determine the cost of long$$term loan capital. $(3)$

Q$\mathrm{.}1\mathrm{.}9$ Explain the factors that can affect a company$$s cost of capital. $(10)$

Question $2$

Navada Ltd is an upmarket restaurant in Sandton that introduced two new meals $($Sweet and

Savoury$)$ to its menu recently. These meals have the following revenue and costs per meal:

Sweet Savoury

Selling price per meal R$60$ R$75$

Variable cost per meal R$30$ R$40$

Fixed cost per meal R$15$ R$20$

Meal fixed costs are based on the following:

Sweet Savoury

Sales $($meals$)300000250000$

Required:

Calculate the aggregate break$$even meals and sales for Navada Ltd$.$

Round all answer to two decimals, where needed.

Set your answer out as follows in your answer booklet.

Sweet Savoury TOTAL

Contribution

Sales mix $($units$)$

Total sales

Average selling price per meal

Equivalent contribution

Total fixed costs

Break$$even point $($meals$)$

Break$$even point $($sales value$)2022$

$$ The Independent Institute of Education $($Pty$)$ Ltd $2022$

Page $6$ of $9$

Question $3($Marks: $30)$

The clerk working at EFC Gym would like a cost formula linking the costs involved in enrolling

members to the number of members enrolled during a month $($especially the colder months$).$ The

departmental costs and the number of members enrolled during the immediately preceding three

months are given in the following table:

Month Number of members enrolled Departmental costs $($R$)$

June $72056000$

July $65053500$

August $68054200$

Required:

Estimate the fixed and variable components of the departmental costs, using the data above and

formulas below, by applying the least squares regression method. Regression equations to assist

in your calculations are as follows:

y $=$ a $+$ bx

$$y $=$ na $+$ b$$x

$$xy $=$ a$$x $+$ b$$x$^2$

Start your answer with doing your calculations in the following format:

Month Number of members

enrolled $($X$)$

Departmental

costs $($R$)($Y$)$

X$^2$ XY

June $72056000$

July $65053500$

August $68054200$

Round all answers to the nearest number.

$22$