Return calculation

Return calculation

15. As per the model of constant growth, we can say that

Stock Price (denoted as ‘P’) = DIV₁ / (r-g)

Where the given values are:

P = $40

DIV₁ (value of given next dividend) = $4

r (rate of discount) = x (unknown)

g (rate of growth) = rate of retention * investment return rate

= 0.40 X 0.15

= 0.03

Putting this value of ‘g’ in the equation of constant growth, we get,

P = DIV₁ / (r-g)

or, 40 = 4 / (r – 0.06)

or, r – 0.06 = 4 / 40

or, r – 0.06 = 0.1

or, r = 0.1+0.06 = 0.16

Therefore, rate of discount = 16%.

16. As per the model of constant growth, we can say that

Stock Price (denoted as ‘P’) = DIV₁ / (r-g)

Now, P₀ = DIV₁ / (r – g)

And, DIV₁ = DIV₀ X (1 + g)

1. Discount rate (r) = 15%

Replacing the values in the constant growth model equation, we get,

P₀ = DIV₁ / (r – g)

P₀ = {DIV₀ X (1 + g)} / (r-g)

= (3 X 1.05) / (0.15 – 0.05)

= 31.50

1. Discount rate (r) = 12%

Replacing the values in the constant growth model equation, we get,

P₀ = DIV₁ / (r – g)

P₀ = {DIV₀ X (1 + g)} / (r-g)

= (3 X 1.05) / (0.12 – 0.05)

= 45.

It can be seen that as the discount rate increases, the price of the stock decreases.

18. As per the model of constant growth, we can say that

Stock Price (denoted as ‘P’) = DIV₁ / (r-g)

The given values for the problem are,

DIV₁ = $2

r (rate of discount) = 12% or 0.12

g (growth rate) = 6% or 0.06

Putting the values in the equation, we get,

P = DIV₁ / (r-g)

= 2 / (0.12 – 0.06)

= 33.33

Answer to chapter 11 questions and problems

1. 11. The average return rate is stated to be 11.5% for the common US stock. It was the return rate at which the holders of the stocks had been getting returns on an average basis. However, this rate of return was more (7.6%) in comparison to the risk-free rate return rate on the treasury bills. This extra return thus obtained is described as the higher risk-reward.
   12. The US common stock average risk premium is identified to be 7.6%. It was the rate that brought in excess returns for the stockholders regularly. It implies that the average return rate had been 7.6% more when compared with the risk-free rates of returns applicable to the treasury bills. Thus, the larger stock average stock premium is 7.6%.
   13. The computation of standard deviation was done with the help of excel. The following formulae were used for the purpose.

Calculations

Standard Deviation = 5.693%

2. No investor would have made a bond investment id they could predict the negative average return earnings during the considered period. The results must have been induced by some unanticipated events, such as rising nominal rates of interest and inflation. It rose to such heights not witnessed in decades. The rise in these figures brought in losses in long-term large capital bonds. The investors had purchased the bonds prior to the concerned period could not anticipate such variations.

The period results explain the threats of measuring the normal risk premiums on the basis of historical data. Despite the fact that the long-term experience may be a great leader for normal premiums, the short period realized premiums might have minimal information about the future premium expectations.

3. In case the investors do not will to carry the investment risk, a premium of higher risk may be essential for them to compensate the holds of risky assets. The security amount for the risky investments have chances of failing if the expected return rates of the securities jump to now-higher return rate requirements.
4. Considering the fact that the -20% rate of return is low in comparison to the historical average return rate in the market, it will influence the market returns standard deviations on the positive side. The higher risk (derived from the standard deviation) is a direct leader towards higher premium market risks.
5. On the basis of the S&P 500 historical risk premium (7.4%) and its risk-free rate (2%), it is possible to make predictions on the expected return rate (9.4%). For the stock to have a similar systematic risk, it must also provide similar expected returns. The price of the stock is equal to the present cash flow value for the 1-year line.

P₀ = ($2 +$50) / 1.094

= $47.53