To calculate pricing at the end of 2022 using the formula, we can substitute the following values for t and r:

P = $1000 / (1 + 0.04)3, where t = 3 (since we wish to determine the price at the end of 2022, which is three years after the end of 2019) and r = 0.04. (the annual interest rate).

P = $862.61 (rounded to the nearest cent) (rounded to the nearest cent)

To calculate prices using the table method, we can utilize the interest factor table for a 4% interest rate over a three-year period. We look up the value in a table where the number of years corresponds to the row and the interest rate corresponds to the column.

The interest factor for a 4% interest rate over a three-year period is 0.8647.

To determine the price of the bond at the end of 2022, we multiply the face value of the bond ($1000) by the interest factor:

P = $1000 x 0.8647

P = $864.70 (rounded to the nearest cent) (rounded to the nearest cent)

Consequently, we obtain slightly different results using the two methods: $862.61 using the formula and $864.70 using the table method. Almost certainly, the difference is due to rounding errors.

Using the formula PV = (D1 / (1 + r)1) + (D2 / (1 + r)2) +... + (Dn / (1 + r)n) + (Pn / (1 + r)n), the potential energy is calculated.

D1, D2,..., Dn are the future dividends to be received in periods 1, 2,..., n Pn is the expected price of the stock at the end of period n r is the required rate of return, which we assume to be 10%

Using the following formula, we can determine the stock's price at the end of 2022:

PV = (1.25 / (1 + 0.1/4)^1) + (1.50 / (1 + 0.1/4)^2) + (1.75 / (1 + 0.1/4)^3) + (41.23 / (1 + 0.1/4)^4) = 1.189 + 1.338 + 1.479 + 32.452 = 36.458

Using the formula method, the price of the stock at the end of 2022 is approximately $36.46.

Using the table method:

We can also use a table to calculate the present value of the stock, based on the dividends and the required rate of return:

Summing up the Present Value column, we get:

PV = 1.22129 + 1.43331 + 1.62833 + 28.1236 = 32.40653

Hence, the price of the shares by the end of 2022, using the table technique, is roughly $32.41.

Thus, we receive slightly different outcomes utilizing these two strategies. The formula technique gives us a price of $36.46, whereas the table method gives us a price of $32.41. This is due to rounding errors and the fact that the formula technique calculates the present value of each payout and the final price separately, whereas the table method applies present value factors for each period.

CAPM

The Capital Asset Pricing Model (CAPM) is a commonly used method to calculate the cost of equity. The formula for the CAPM is:

r(e) = r(f) + (e) x [r(m) - r(f)]

where:

r(e) = cost of equity

r(f) = risk-free rate

(e) = beta of the stock

r(m) = expected return of the market

If the risk-free rate is 2%, and the projected return of the market is 8%, we need to compute the beta of the stock.

Beta is a measure of a stock's volatility in proportion to the wider market. It is commonly determined by regressing the stock's returns against the returns of the market. If we do not have access to historical data, we can utilize assumptions or industry averages. Let's say the beta of this stock is 1.2.

With these data, we can compute the cost of equity:

r(e) = 2% + 1.2 x (8% - 2%) r(e) = 2% + 1.2 x 6% r(e) = 2% + 7.2% r(e) = 9.2%

Therefore, the cost of equity for this stock using the CAPM is 9.2%.

Using the CAPM formula with the given MRP and risk-free rate:

Cost of Equity = Rf + beta * MRP

Cost of Equity = 0.03 + 1.2 * 0.07

Cost of Equity = 0.03 + 0.084

Cost of Equity = 0.114

Since we have quarterly cash flows, we need to adjust this cost of equity to a quarterly rate by dividing it by 4:

Quarterly Cost of Equity = 0.114 / 4

Quarterly Cost of Equity = 0.0285

Therefore, the quarterly cost of equity using the CAPM is 2.85%.

1 Estimate prices at the end of December 2023 and December 2024 using table method. Note that a price is a PV of all future CFs at the time of pricing. Assume that your cost of equity stays constant in the future.

2. Discuss similarity and discrepancy between the realized prices for the year-end 2022 and your estimated prices at the end of 2022 (You have a realized price for the year-end 2022 because you are doing this project in 2023)

3. What do you observe for the estimated prices for December 2023 and December 2024? If they are drastically different, why do you think they are? If they are similar, why do you think they are? Discuss fully. Dont try to be brief.