SU (SelviaUtama): Corporate Finance: Essay Quiz Expected Return 04

What is the expected return on a portfolio which comprised of RM 4,000 in stock M and RM 6,000 in stock N if the economy enjoys a boom period?

state of economy	probability of State of Economy	Return if State Occurs
		Stock M	Stock N
Boom	10%	18%	10%
Normal	75%	7%	8%
Recession	15%	-20%	6%

Answer:

To calculate the expected return on a portfolio comprised of RM 4,000 in Stock M and RM 6,000 in Stock N, we will follow these steps:

Calculate the total value of the portfolio.
Determine the expected return for each stock based on the given probabilities and returns.
Calculate the weighted expected return for the portfolio.

Step 1: Calculate Total Portfolio Value

The total value of the portfolio is:

Total Portfolio Value = Investment in Stock M + Investment in Stock N

Total Portfolio Value = R M 4, 000 + R M 6, 000 = R M 10, 000

Step 2: Calculate Expected Returns for Each Stock

We will calculate the expected return for each stock using the formula:

Expected Return = \sum (Probability of State \times Return if State Occurs)

For Stock M:

Boom: Probability = 10%, Return = 10%
Normal: Probability = 75%, Return = 7%
Recession: Probability = 15%, Return = -20%

Calculating the expected return for Stock M:

E (R_{M}) = (0.10 \times 0.10) + (0.75 \times 0.07) + (0.15 \times - 0.20)

Calculating each term:

Boom: $0.10 \times 0.10 = 0.01$
Normal: $0.75 \times 0.07 = 0.0525$
Recession: $0.15 \times - 0.20 = - 0.03$

Now summing these values:

E (R_{M}) = 0.01 + 0.0525 - 0.03 = 0.0325 or 3.25 %

For Stock N:

Boom: Probability = 10%, Return = 18%
Normal: Probability = 75%, Return = 8%
Recession: Probability = 15%, Return = 6%

Calculating the expected return for Stock N:

E (R_{N}) = (0.10 \times 0.18) + (0.75 \times 0.08) + (0.15 \times 0.06)

Calculating each term:

Boom: $0.10 \times 0.18 = 0.018$
Normal: $0.75 \times 0.08 = 0.06$
Recession: $0.15 \times 0.06 = 0.009$

Now summing these values:

E (R_{N}) = 0.018 + 0.06 + 0.009 = 0.087 or 8.7 %

Step 3: Calculate Weighted Expected Return for the Portfolio

Now we can calculate the overall expected return for the portfolio based on the investments in each stock.

Weights of Each Stock in the Portfolio

Weight of Stock M:

w_{M} = \frac{4, 000}{10, 000} = 0.40

Weight of Stock N:

w_{N} = \frac{6, 000}{10, 000} = 0.60

Portfolio Expected Return

Using the weights and expected returns calculated:

E (R_{p}) = w_{M} \cdot E (R_{M}) + w_{N} \cdot E (R_{N})

Substituting in the values:

E (R_{p}) = (0.40 \cdot 3.25 %) + (0.60 \cdot 8.7 %)

Calculating each term:

For Stock M: $E (R_{M})_{w e i g h t e d} = 0.40 \cdot 3.25 % = 1.30 %$
For Stock N: $E (R_{N})_{w e i g h t e d} = 0.60 \cdot 8.7 % = 5.22 %$

Now summing these values to find the total expected return for the portfolio:

E (R_{p}) = E (R_{M})_{w e i g h t e d} + E (R_{N})_{w e i g h t e d} = 1.30 % + 5.22 % = 6.52 %

The expected return on your portfolio is approximately 6.52% under the given economic conditions and probabilities for Stocks M and N.

The rate of return on the common stock of Flora Flowers is expected to be 14% in a boom economy, 8% in a normal economy, and only 2% in recessionary economy. The probabilities of these economic states are 20% for a boom, 70% for a normal economy, and 10% for a recession. What is the variance of a return on the common stock of Flora Flowers?

Answer:

To calculate the variance of the return on the common stock of Flora Flowers, we will follow these steps:

Calculate the expected return (mean return) based on the probabilities and returns for each economic state.
Calculate the variance using the expected return and the returns in each state.

Step 1: Calculate Expected Return

The expected return

E (R)

is calculated using the formula:

E (R) = \sum (Probability of State \times Return if State Occurs)

Given Data

Boom: Probability = 20% (0.20), Return = 14% (0.14)
Normal: Probability = 70% (0.70), Return = 8% (0.08)
Recession: Probability = 10% (0.10), Return = 2% (0.02)

Calculating the expected return:

E (R) = (0.20 \times 0.14) + (0.70 \times 0.08) + (0.10 \times 0.02)

Calculating each term:

Boom: $0.20 \times 0.14 = 0.028$
Normal: $0.70 \times 0.08 = 0.056$
Recession: $0.10 \times 0.02 = 0.002$

Now summing these values:

E (R) = 0.028 + 0.056 + 0.002 = 0.086 or 8.6 %

Step 2: Calculate Variance

Variance

σ^{2}

is calculated using the formula:

σ^{2} = \sum (Probability \times (Return - E (R))^{2})

Calculating each term:

For Boom:
- Return = 14% (or 0.14)
- Deviation from mean: $(0.14 - 0.086)^{2} = (0.054)^{2} = 0.002916$
- Contribution to variance: $0.20 \times 0.002916 = 0.0005832$
For Normal:
- Return = 8% (or 0.08)
- Deviation from mean: $(0.08 - 0.086)^{2} = (- 0.006)^{2} = 0.000036$
- Contribution to variance: $0.70 \times 0.000036 = 0.0000252$
For Recession:
- Return = 2% (or 0.02)
- Deviation from mean: $(0.02 - 0.086)^{2} = (- 0.066)^{2} = 0.004356$
- Contribution to variance: $0.10 \times 0.004356 = 0.0004356$

Now summing these contributions to find the total variance:

σ^{2} = 0.0005832 + 0.0000252 + 0.0004356

Calculating this gives:

σ^{2} = 0.001044

Assuming the CAPM or one – factor model holds, what is the cost of equity for a firm if the firm’s equity has a beta of 1.2, the risk – free rate of return is 2%, the expected return on the market is 9%, the the return to the company debt is 7%?

Answer:

To calculate the cost of equity for a firm using the Capital Asset Pricing Model (CAPM), we can use the following formula:

Cost of Equity (K_{e}) = R_{f} + β \times (R_{m} - R_{f})

Where:

$R_{f}$ = Risk-free rate
$β$ = Beta of the firm’s equity
$R_{m}$ = Expected return on the market

Given Data

Beta ( $β$ ): 1.2
Risk-Free Rate ( $R_{f}$ ): 2% or 0.02
Expected Return on the Market ( $R_{m}$ ): 9% or 0.09

Step 1: Calculate the Market Risk Premium

The market risk premium is calculated as:

R_{m} - R_{f} = 0.09 - 0.02 = 0.07 or 7 %

Step 2: Calculate the Cost of Equity

Now we can substitute the values into the CAPM formula:

K_{e} = R_{f} + β \times (R_{m} - R_{f})

Substituting in the values:

K_{e} = 0.02 + 1.2 \times 0.07

Calculating

1.2 \times 0.07

1.2 \times 0.07 = 0.084

Now adding this to the risk-free rate:

K_{e} = 0.02 + 0.084 = 0.104 or 10.4 %

SU (SelviaUtama)

Corporate Finance: Essay Quiz Expected Return 04

Step 1: Calculate Total Portfolio Value

Step 2: Calculate Expected Returns for Each Stock

For Stock M:

For Stock N:

Step 3: Calculate Weighted Expected Return for the Portfolio

Weights of Each Stock in the Portfolio

Portfolio Expected Return

Step 1: Calculate Expected Return

Given Data

Step 2: Calculate Variance

Given Data

Step 1: Calculate the Market Risk Premium

Step 2: Calculate the Cost of Equity

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