Introduction
Determining the most effective investment strategy is a critical aspect of financial management. When dealing with investments, understanding how to allocate your capital across various companies to achieve optimal returns is paramount. In the following section, we will explore a real-world scenario where a self-help group of ten young men invests in two companies, A and B, to determine the optimal allocation of their capital based on the dividend rates provided.Scenario Overview
A self-help group of ten young men invests a total of Shs. 72,000 in two companies, A and B, with predefined dividend rates. Company A pays a dividend of 22.5%, and Company B pays a dividend of 21%. Through a series of calculations, we aim to determine how much money was invested in each company to achieve a total return of 21.5% on the total investment.Step-by-Step Analysis
To solve the problem, we will use algebraic and financial mathematical methods to find the investment amounts in both companies.Investment in Company A
Let's denote the investment in Company A as (A) (in Shillings). Consequently, the investment in Company B will be (72,000 - A).The dividend received from Company A is (A times 0.225).The dividend received from Company B is ((72,000 - A) times 0.21).The total dividend received from both companies is 21.5% of the total investment, which is 72,000 Shs. Thus, the total dividend is:[text{Total Dividend} 72,000 times 0.215 15,480 text{ Shs.}]The equation for the total dividend can be written as:[A times 0.225 (72,000 - A) times 0.21 15,480]Let's simplify this equation step-by-step:[0.225A 72,000 times 0.21 - 0.21A 15,480][0.225A 15,120 - 0.21A 15,480][0.015A 15,120 15,480]Subtract 15,120 from both sides:[0.015A 360]Divide both sides by 0.015:[A frac{360}{0.015} 24,000 text{ Shs.}]Investment in Company B
With the amount invested in Company A known, we can now determine the investment in Company B:[72,000 - A 72,000 - 24,000 48,000 text{ Shs.}]Validation
Let's validate the results by calculating the dividends from both companies and ensuring they sum up to the total dividend.Dividend from Company A: (24,000 times 0.225 5,400 text{ Shs.})
Dividend from Company B: (48,000 times 0.21 10,080 text{ Shs.})
Total Dividend: (5,400 10,080 15,480 text{ Shs.})
The total investment is (72,000 times 0.215 15,480 text{ Shs.}), confirming the accuracy of our calculations.