1. Discuss the meaning of interest using your own experience and the other available resources.
2. Form a group of five members and discuss the various types of interest. Explain the different types of interest you
know in your presentation.
3. Explain the meaning of simple interest. Use the internet and the available text books in your school library.
Interest is the cost for use of borrowed funds. When you borrow a given amount of money from the bank (amount called principal), you will be charged a given amount per year (interest) at a specified rate (interest rate). The interest rate is usually expressed as a percentage of the principal. For example, interest may be stated as 10% per annum. This means that every year, you pay 10% of the borrowed amount (the principal) as interest.
T = Time or duration of repayment.
P = 65,000 R = 11% T = 6 years
1. Calculate; the simple interest on 125,000Rwf for 3½ years at 6½% p.a.
2. Find the time within which 76,800 Rwf increases to 89,600 Rwf at 5% p.a.
3. Find the principal on which a simple interest for 8 years at 2.5% is 2160 Rwf.
4. Kwizera borrowed a sum of money at 12% simple interest per annum. After 5 years he repaid 128,000Rwf. Calculate
the sum of money borrowed.
5. Form a group of five members and discuss the meaning of compound interest.For example, if a loan of 10,000Rwf earns interest 10% per month, after the first month, the total amount due will be the principal of 10,000Rwf plus the interest of 1000 which totals 11,000Rwf. The interest for the second month will be calculated basing on the new amount of 11,000Rwf.
A loan, for example, may have its interest compounded every month; in this case, a loan of 100Rwf initial principal and 1% interest per month would have an amount accumulated to 101Rwf at the end of the first month, 102.01 at the end of the second month and therefore the compound interest after two months will be:
= 102.01 – 100 = Rwf ..........................................................
TIGO Company deposited 980,000 Rwf with their bank for 2 years. If the bank offers an interest of 8% p.a and allows for interest to be added to the principal so that it also earns interest, find the interest after 2 years. Find also the amount after the second year.
We can use annuity method to determine the interest given the fact that the last or previous method is long and tedious in case you are given a long period under consideration. The formula for the amount after (n) years is given by;
Using the same example as above substitute the values of P, R, and n in the formula
1. Grace plans to buy a car after 3 years. The car is expected to cost 220,000Rwf. Grace deposits 80,000Rwf at the
beginning of the 1st year and 40,000Rwf at the beginning of the 2nd year. Calculate the amount which should be
deposited at the beginning of 3rd year if compound interest is paid at the rate of 10% in order to enable her buy the car.
2. Kanimba borrowed 18,000Rwf from a microfinance at 2% per month with the option that interest unpaid would be added
to principal to obtain the new amount for every successive month. How much would he pay after 6 months if he pays the
3. Nyange enterprise borrowed 2,000,000Rwf from a bank and was required to return 2,400,000Rwf. Given that interest earned
in the first year was 245,000Rwf and the interest at the end of each period was added on to principal, find;
b) The compound time it would take to obtain the amount 2.4 years.
Break-Even Point, Payback Period and Return on Investment, Return on Equity
1. Use the internet and textbook resources from your school library and discuss the meaning of break-even point
2. Form a group of 3-5 members; illustrate a break-even point using a graph for presentation by your group leader.
3. State the assumptions that were considered by your group to illustrate the break-even chart.
4. State the usefulness of a break-even point.
5. Enumerate the limitation of break-even charts.Break-Even Point (BEP) is that point of sales volume at which total
revenue is equal to total costs. It is a no-profit, no-loss point. Two approaches can be used to compute the BEP.
The formula and the chart approaches indicated below illustrate the two scenarios or situations of break-even point.
The break-even chart-cost-volume-profit charts
Key terms used in break-even point concept
1. Break-even point analysis: This is a tool used to determine the volume at which a company’s costs will exactly equal to
its revenue, therefore no profit made.
2. Fixed costs: These are costs that do not tend to vary or change based on sales/volume. For example rent, equipment,
3. Variable costs per unit (VC): These refer to costs that tend to fluctuate with the level of sales or costs that tend to change
with the level of sales. For example raw materials, sales commissions, and delivery expenses.
4. Contribution margin: This is defined as a product or service price minus variable costs for unit sold.
The importance of break-even point to a business/entrepreneur/company
1. It can help managers assess the effect of changing prices, sales volume and costs on profits.
2. It helps small business owners to make decisions regarding whether to expand their operation or hire new employees.
3. It helps a business owner to have a good handle on the quantity exported, the likely selling price and the variable costs
4. It equips the business owner with the potential application for basic business analysis, hence being able to make a good
Disadvantages of break-even point analysis
1. It only emphasises the supply side (ie the costs only). It does not tell an entrepreneur about what sales are likely to be for
the product at various prices.
2. It assumes that costs are constant.
3. It assumes that average variable costs are constant per unit output.
4. It assumes that the quantity of goods produced is equal to the quantity of goods sold, i.e., there is no change in the quantity
of goods held in inventory at the beginning of the period and quantity of goods held in inventory at the end.
5. In multi-product companies, it assumes that relative proportions of each product sold and produced are constant,
i.e., the sale mix is constant.
Break-even charts or cost-volume – profit charts
A break-even chart may be defined as a graph which shows profit or loss at different levels of activity within a limited range. The level of activity at which sales revenue is equal to total cost is known as break-even point. At this level of activity, there will be no profit or loss. In the break-even chart, the following curves are drawn: fixed cost curve, total cost curve and sales curve.
The break-even chart is also known as the cost volume profit chart. This graph shows the costs, sales and profit and loss within a specific level of activity. Before the break-even point, there is loss and after that point the level of activity shows profit. It is explained by the help of the following diagram.
The break-even formulae
The BEP can be computed in terms of units, or in terms of money value (dollars, francs, etc) of sales volume or as a percentage of estimated capacity, in units. The BEP may be calculated for single product firm in terms of units of product.
The BEP in terms of units will be reached when units sold create sufficient revenue to cover their total costs (that is fixed and variable). Each unit of the product sold will cover its own variable cost and leaves a remainder called contribution or marginal income to cover the fixed costs. The BEP will occur when enough units have been sold so that total contribution is just equal to total fixed costs.
Note: The contribution per unit is the difference between selling price per units and variable cost per unit total is equal to the contribution multiplied by units sold; and profit is derived when fixed cost is subtracted from total contribution. Thus;
Unit contribution = unit selling price – unit variable cost
Total contribution = unit contribution × units sold
Total contribution = total fixed cost + profit
At break-even points, profits will be zero and therefore total contribution will only cover the fixed cost.
Let us assume that a manufacturing firm produces a single product whose selling price is 20 Rwf per unit and the variable cost per unit is 12Rwf. The annual fixed costs of the firm estimated is 160,000 Rwf, to break-even the firm’s contribution from the sale of units of product should be equal to the fixed cost of 160,000 Rwf.
The sale of one unit of the product yields a contribution 8 Rwf (i.e. the difference between the selling price of 20 Rwf and the fact that the firm’s profit is equal to zero at a volume of 20,000 units is verified as follows;
Sales revenue (20,000units at 20 Rwf) 400,000 Rwf
Less: variable costs (20,000units at 12Rwf) 240,009 Rwf
Contribution 160,000 Rwf
Less: fixes costs 160,000 Rwf
Profit 0 Rwf
That is, BEP in terms of units can be computed by the formulae
BEP (units) = Total fixed cost (TFC) / Selling price – Variable cost per unit
In francs; the break-even point for a single product can also be calculated in terms of francs value of sales volume. If both sides of equal value are multiplied by the selling price, we will get break-even solution in terms of francs. Thus,
BEP (Francs) = total fixed cost1-(variable cost per unit/selling price per unit)
= 160,0001-(12/20) = 160,000(8/20) = 400,000 Rwf
BEP (Francs) = TF / CP–V× P
The same answer could be arrived at by multiplying the break-even units by selling price (20,000X20 Rwf) = 400,000 Rwf
The advantage of the second format is that it can be used with both per unit information as well as the total information. This is also because the variable cost of sales ratio will remain the same for any sales volume as both variable cost and sales revenue change in direct proportion to sales volume.
Using total sales and total variable cost information, format 2 is particularly significant for a multi-product firms. These firms find difficulties in measuring volume in terms of common units of products. For such firms, the break-even point will be calculated in terms of total francs sales.
A diversified firm has the following budget for the year ending December 2006.
Budgeted sales 5,000,000 Rwf
Budgeted variable costs 3,000,000 Rwf
Budgeted fixed costs 1,000,000 Rwf
The break-even point for the firm will be;
BEP (francs) = 1,000,000 / 1-(3,000,000/5,000,000)
= 1,000,000 / 1-(3/5)
= 1,000,000 / 1 – 0.6
Sales revenue 2,500,000 Rwf
Variable cost (2,500,000 X 0.6) 1,500,000 Rwf
Contribution (2,500,000 X 0.4) 1,000,000 Rwf
Fixed cost 1,000,000 Rwf
1. A firm manufactures and sales a standard product known as “chocolate”. The selling price per unit of the product is
1,500 Rwf. The variable cost of producing the product is as follows:
Direct material 400 Rwf per unit of the product
Direct labour 150 Rwf per unit of the product
Variable overheads 50 Rwf unit of the product
The fixed costs incurred by the firm per period is 1,800,000 Rwf
a) Determine the value of the variable cost.
b) Determine the BEP of the firm.
c) The quantity to be produced if the firm is targeting a profit of 900,000 Rwf.
d) What is the contribution per unit of the firm?
2. A manufacturing company dealing in plastic containers has the following costs and revenue information; price per
unit 80,000 Rwf, variable material costs per unit 25,000 Rwf, variable labour cost per unit 30,000 Rwf, fixed costs
75,000,000 per month. The total production capacity of a firm is 100,000 containers.
a) Determine the break-even point in units and sales.
b) Determine the number of containers that they must sale to earn a profit of 100,000 Rwf.
c) If the firm is selling 40,000 containers assuming (1) above; what would be its margin of safety in units and sales?
d) What is the firm’s contribution per unit?e) If the firm’s variable labour costs increases by 20%, and its selling price
reduces to 70,000 Rwf, what would be the new break-even quantity?
f) What is the percentage change in the contribution per unit?
g) If the firm decides to produce 60% of its production capacity, how much profit will it generate?
1. Using textbooks available and internet resource, brainstorm about the meaning of payback period.
2. State the advantages and disadvantages of payback period.
3. An investment whose initial cash outlay is 20,000,000 Rwf is expected to generate the following cash flow over its
useful life. Find the total investment.
Year Cash flow
1 8,000,000 Rwf
2 7,000,000 Rwf
3 9,000,000 Rwf
4 10,000,000 Rwf
This is the most popular and widely used method of evaluating investment proposals. This method uses the minimum period in which the cash flows anticipate on the investment completely cover the initial outlays and other outflows as the yardstick for determining the viability of the investment. Payback period is the minimum period required to recover the original cash outflow in the investment.
Accept or reject criteria
The decision rule here is to select from competing investment a proposal that has the shortest payback period. Though, sometimes the projects may have a minimum payback period such that every investment with payback period less than the investor’s payback period will be viable.
Ways of calculating payback period
There are two ways of calculating the payback period.
The first method can be applied when the cash flow stream is in the nature of annuity for each year of the project’s life, where cash flows are uniform. In such a situation, the initial cost of investment is divided by the constant annual cash flow.
Payback period when the investment generates uniform/constant cash inflows
Payback period = initial cash outlay / annual cash inflows
An investment has an initial outlay of 50m Rwf and it is projected to have a useful life of 8 years with a uniform cash flow stream of 7.5m Rwf.
Its payback period = initial cash outlay / annual cash inflow
= 50,000,000 / 7,500,000
= ............... years
= .............. × 12 = 8 months
= .............years and ...............months
The second method is used when a project’s cash flows are not equal, but vary from year to year. In such a situation, payback period is calculated by the process of accumulating cash flows till the time when cumulative cash flows are equal to original investment outlay.
When the cash flow is not uniform
A firm invests 2m Rwf in a project at the beginning of the first year, 800,000Rwf and 600,000Rwf at the beginning of second and third year, respectively. However, the firm expects returns at the end of the first, second, and third years of 1,000,000Rwf, 400,000Rwf and 1,000,000Rwf respectively. It expects to continue receiving 500,000Rwf after the third year. Determine the payback period.
Total investment = 2,000,000 + 800,000 + 600,000 = .................Rwf
1. Discuss the meaning of return on investment.
2. Discuss the meaning of return on equity and its components.
3. When choosing the right source of finance, a business needs to assess the different types of finance based on a criteria.
In a group of 5-10 members, discuss and present the criteria you would follow.
4. Discuss at least three main types of short term finance known to you.
5. Discuss the main types of long term finances that are available for a business and present them to your class.
6. Internal finance comes from the trading of the business. Give four examples of internal finance from the discussion above.
Returns on capital employed or investment
ROI = PBIT / Capita employed× 100%
ROI = PBIT / CE× 100
Where: ROI is a return on investments
PBIT is profit before interest and tax
CE is capital employed
Capital employed is sometimes referred to as equity plus long term debts. It’s usually calculated by the formula
Capital employed = Total fixed asset + working capital
CE = TFA + WC
Return on investments (ROI) is sometimes given by the shareholders ratio. Shareholders ratio measures a return on the shareholders’ investment in the business, which is normally expressed as the ratio of dividends declared by the business to the par/market. The value of shares held by the shareholders is calculated using this formula.
Dividend Yield = gross dividends (ordinary shares) / Market price of shares
It should be noted that as the business becomes more established and profitable, the market value of its shares appreciates and becomes significantly different from par/face value of the shares.The return on equity is defined as;
Equity earnings / Average equity
Illustrations showing return on Equity
The numerator of this ratio is equal to profit after tax less preference dividends. The denominator includes all contributions made by equity shareholders (paid-up-capital + reserves and surplus). This ratio is also called the return on net worth.
Horizon’s return on equity for 20 × 1 is;
34 ÷ [(262 + 256)/2] = 0.131 or 13.1%
The return on equity measures the profitability of equity funds invested in the firm. It is regarded as a very important measure because it reflects the productivity of the ownership (or risk) capital employed in the firm. It is influenced by several factors of earning power, debt-equity ratio, average cost of debt funds, and tax rate.
In judging all the profitability measures it should be borne in mind that the historical valuation of assets imparts an upward bias to profitability measures during an inflationary period. This happens because the numerator of these measures represents current values, whereas the denominator represents historical values.
Valuation ratios indicate how equity stock of the company is assessed in the capital market. Since the market value of equity reflects the combined influence of risk and return, valuation ratios are the most comprehensive measures of a firm’s performance. The important valuation ratios are; price-earnings ratio, yield, and market value to book value ratio.
Price-earnings ratio; perhaps the most popular financial statistic in stock market discussion, the price-earnings ratio is defined as;
Market price per share / Earnings per share
The market price per share may be the price prevailing on a certain day or the average price over a period of time. The earnings per share is; profit after tax less preference dividend divided by the number of outstanding equity shares.
Horizon’s price-earnings ratio at the end of 20 × 1 is;
21.0/2.37 = 9.25
The price-earnings ratio (or the price earnings multiple as it is commonly referred to is a summary measure which primarily reflects the following factors; growth prospects, risk characteristics, shareholder orientation, corporate image, and degree of liquidity.
Yield; this is a measure of the rate of return earned by shareholders. It is defined as;
Dividend + Price change / Initial price
This may be split into two parts;
Dividend / Initial price Dividend yield + Price change / Initial price capital gains/loss yield
For horizon the dividend yield and the capital gains for 20 × 1 are as follows;
dividend yield = 1.8/20.0 = 9% capital yield = 11.0/20.0 = 5%
Hence, the total yield for 20 × 1 was 14%.
Generally companies with low growth prospects offer a high dividend yield and a low capital gains yield. On the other hand, companies with superior growth prospects offer a low dividend yield and a high capital gains yield.
Market value to book value ratio is another popular stock market statistic, the market value to book is defined as;
Market value per share / Book value per share
Horizon’s market value book value at the end of 20 × 1 was;
21.00/17.47 = 1.20
In a way, this ratio reflects the contribution of a firm to the wealth of society. When this ratio exceeds 1 it means that the firm has contributed to the creation of wealth in the society. If this ratio is, say, 2, the firm has created a wealth of one franc for every franc invested in it. When this ratio is equal to 1, it implies that the firm has neither contributed to nor detracted from the wealth of society.
1. Profit margin ratios of Horizon limited are somewhat higher than the industry average. The rate of return measures of
horizon limited is also higher than the industry average.
2. The valuation ratio of Horizon limited compare slightly favourably in relation to industry average.
- Business finance: Is defined as those activities which deal with the provision and management of funds for the satisfactory conduct of business.
- Financial management: Is concerned with the efficient acquisition and development of both short term and long term resources to ensure that the objectives of the enterprise are achieved.
- Money: Is something that is accepted as a form of payment for products or services, or the payment of obligations.
- Functions of money:
- Functions of financial management: Determining the volume of financial resource, ascertain the cash available in the business,consideration of the need of the providers of finance.
- Business Capital: It is the money needed to start and run a business.
- Sources of business capital: Grants, partners, retained profits, personal savings.
- Break-even point: This is a point of sales volume at which total revenue is equal to total cost.
- Payback period: It is the minimum time required to recover the original cash outflow in the investment.
- Return on Investment: It is the anticipated profits on investment.
- Return on Equity: Measures the profitability of equity funds invested in the firm.
1. a) Explain the meaning of finance, financial systems and financial management.
b) Explain the functions of financial management.
2. a) Which precautions should one consider when choosing sources of finance to their business activities?
b) Identify the various sources of capital and their advantages and disadvantages.
3. a) Find the simple interest on 80,000Rwf for five 10 years at 6% p.a.
b) Find the simple interest on 40,000Rwf for 4 month at 2% p.a.
c) VISION 2020 enterprises deposited 1,200,000 Rwf with their bank for 4 years. If the bank offers an interest rate
of 16% p.a and allows the interest to be added to the principal so that it also earns interest, find the interest after
4. a) Define the following concepts:
(i) Break-even point
(ii) Payback period
(iii) Returns on investment.
b) A manufacturing firm is considering investing 100,000 Rwf in new machinery. The equipment is expected to increase the
c) Umutako company limited makes dresses. In 2015 the company sold 124,000 Rwf pieces of dress at a price of 5,000 Rwf
per dress, the expenses of this company can be divided into:
- Total variable cost 100,500 Rwf excluding tax
- Fixed costs 670,000Rwf excluding tax.Calculate the break-even of the above business.