Corporate Finance: Essay Quiz Dividend Yield, Capital Gain Yield and Total IRR 03


  • Joven industries sold for RM1.90 on 1st January and ended the year at a price of RM2.50. in addition, the stock paid dividends of RM 0.20 per share. Calculate Joven dividend yield, capital gain yield, and total rate of return for the year.

Answer: 

Given Data

  • Beginning Price (P0): RM 1.90
  • Ending Price (P1): RM 2.50
  • Dividends Paid (D): RM 0.20

1. Dividend Yield

The dividend yield is calculated as follows:
Dividend Yield=DP0
Substituting the values:
Dividend Yield=0.201.900.1053 or 10.53%

2. Capital Gain Yield

The capital gain yield is calculated using the change in price:
Capital Gain Yield=P1P0P0
Substituting the values:
Capital Gain Yield=2.501.901.90=0.601.900.3158 or 31.58%

3. Total Rate of Return

The total rate of return combines both the dividend yield and the capital gain yield:
Total Rate of Return=Dividend Yield+Capital Gain Yield
Substituting the previously calculated yields:
Total Rate of Return=0.1053+0.31580.4211 or 42.11%
You earn a total return of -5% on Dolly.com this year, earned -40% last years, and earned 30% two years ago. Calculate both the three year holding period return and the average three year return.

Answer:

To calculate the three-year holding period return and the average three-year return for Dolly.com, we will use the following formulas:

Given Returns

  • Year 1: -5%
  • Year 2: -40%
  • Year 3: 30%

1. Three-Year Holding Period Return

The holding period return (HPR) over multiple periods can be calculated using the formula:
HPR=(1+r1)×(1+r2)×(1+r3)1
Where 
r1,r2,r3
 are the returns for each year expressed as decimals.
Substituting in the values:
HPR=(10.05)×(10.40)×(1+0.30)
Calculating each term:
HPR=(0.95)×(0.60)×(1.30
Calculating step-by-step:
  1. 0.95×0.60=0.57
  2. 0.57×1.30=0.741
Now, subtracting 1:
HPR=0.7411=0.259 or 25.9%

2. Average Three-Year Return

The average return over the three years can be calculated using the arithmetic mean of the annual returns:
Average Return=r1+r2+r33
Substituting in the values:
Average Return=5%+(40%)+30%3
Calculating step-by-step:
  1. Convert percentages to decimals:
    • 5%=0.05
    • 40%=0.40
    • 30%=0.30
  2. Sum the returns:
    0.05+(0.40)+0.30=0.050.40+0.30=0.15
  3. Divide by the number of years:
    Average Return=0.153=0.05 or 5%
  • Three-Year Holding Period Return-25.9%
  • Average Three-Year Return-5%

These calculations indicate that while the average annual return was negative, the holding period return reflects a more significant loss over the three years due to the compounding effects of negative returns in the first two years followed by a positive return in the last year.

  • Your portfolios is comprised of 30% of stock R, 50% of the stock S, and 20% of stock T. stock R has a beta of 0.64, stock S has a beta of 1.48 and stock T has a beta of 1.04. What is the beta of your portfolio?
Answer:

To calculate the beta of your portfolio, you can use the weighted average of the betas of the individual stocks in the portfolio. The formula for the portfolio beta (βp) is:
βp=wRβR+wSβS+wTβT
Where:
  • wR,wS,wT are the weights of stocks R, S, and T in the portfolio, respectively.
  • βR,βS,βT are the betas of stocks R, S, and T, respectively.

Given Data

  • Weight of Stock R (wR): 30% or 0.30
  • Weight of Stock S (wS): 50% or 0.50
  • Weight of Stock T (wT): 20% or 0.20
  • Beta of Stock R (βR): 0.64
  • Beta of Stock S (βS): 1.48
  • Beta of Stock T (βT): 1.04

Calculation

Now we can substitute the values into the formula:
βp=(0.300.64)+(0.501.48)+(0.201.04
Calculating each term:
  1. For Stock R:
    0.300.64=0.192
  2. For Stock S:
    0.501.48=0.740
  3. For Stock T:
    0.201.04=0.208

Summing Up

Now add these values together to find the portfolio beta:
βp=0.192+0.740+0.208=1.140
  • What is the difference between systematic and unsystematic risk? Which type of risk is eliminated with well diversified portfolio?
Answer:

The difference between systematic and unsystematic risk is fundamental in understanding investment risks and portfolio management.

Systematic Risk

Systematic risk, also known as market risk, affects the entire market or a significant portion of it. This type of risk is caused by macroeconomic factors that cannot be avoided or diversified away. Examples of systematic risk include:
  • Economic recessions
  • Changes in interest rates
  • Inflation
  • Political instability
  • Natural disasters

Since systematic risk impacts all investments in the market, it is non-diversifiable. Investors cannot eliminate this risk through diversification; instead, they can manage it through strategies like asset allocation and hedging.

Unsystematic Risk

Unsystematic risk, also referred to as specific or diversifiable risk, is unique to a particular company or industry. This type of risk arises from internal factors that affect a specific organization, such as:
  • Poor management decisions
  • Product recalls
  • Labor strikes
  • Competitive pressures
Unsystematic risk can be reduced or eliminated through diversification. By holding a well-diversified portfolio of assets across different industries and sectors, investors can mitigate the impact of any single investment's poor performance on their overall portfolio.

Summary of Differences

  • Scope: Systematic risk affects the entire market; unsystematic risk affects specific companies or industries.
  • Diversifiability: Systematic risk cannot be eliminated through diversification; unsystematic risk can be mitigated by diversifying investments.
  • Examples: Systematic risks include economic downturns and interest rate changes, while unsystematic risks include company-specific issues like management failures or product failures.

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