Question

Consider the following three stocks: a. Stock A is expected to provide a dividend of $11.90 a share forever. b. Stock B is expected to pay a dividend of $6.90 next year. Thereafter, dividend growth is expected to be 2.00% a year forever. c. Stock C is expected to pay a dividend of $4.10 next year Thereafter dividend growth is expected to be 18 00% a year for five years (ie, years 2 through 6 and zero thereafter a-1. If the market capitalization rate for each stock is 8.00%, what is the stock price for each of the stocks? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Stock Price Stock A Stock B Stock C a-2. Which stock is the most valuable? Stock C O Stock B O Stock A b-1. If the market capitalization rate for each stock is 5 00%, what is the stock price for each ofthe stocks? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Stock Price Stock A Stock B Stock C b-2. Which stock is the most valuable? Stock E O Stock A O Stock C

Answer 1

Answer:

Part a-1)

The stock price has been calculated as follows:

Stock Price (Stock A) = Annual Dividend/Capitalization Rate = 11.90/8% = $148.75 (it is a case of perpetuity having a constant stream of cash flows)

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Stock Price (Stock B) = Dividend Next Year/(Capitalization Rate - Growth Rate) = 6.90/(8% - 2%) = $115

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Price of Stock C can be calculated with the use of following formula:

Stock Price = D1/(1+Capitalization Rate)^1 + D2/(1+Capitalization Rate)^2 + D3/(1+Capitalization Rate)^3 + D4/(1+Capitalization Rate)^4 + D5/(1+Capitalization Rate)^5 + D5/(1+Capitalization Rate)^6 + D5/(Capitalization Rate - Growth Rate)*(1+Capitalization Rate)^6

Here D1 = 4.10, D2 = 4.10*(1+18%)^1, D3 = 4.10*(1+18%)^2, D4 = 4.10*(1+18%)^3, D5 = 4.10*(1+18%)^4 and D6 = 4.10*(1+18%)^5

Using these values in the above formula, we get,

Stock Price (Stock C) = 4.10/(1+8%)^1 + 4.10*(1+18%)^1/(1+8%)^2 + 4.10*(1+18%)^2/(1+8%)^3 + 4.10*(1+18%)^3/(1+8%)^4 + 4.10*(1+18%)^4/(1+8%)^5 + 4.10*(1+18%)^5/(1+8%)^6 + 4.10*(1+18%)^5/(8%-0)*(1+8%)^6 = $102.63

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Part a-2)

Based on the calculations in Part a-1, Stock A has the highest current value and therefore, it will be considered most valuable.

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Part b-1)

The stock price has been calculated as follows:

Stock Price (Stock A) = Annual Dividend/Capitalization Rate = 11.90/5% = $238 (it is a case of perpetuity having a constant stream of cash flows)

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Stock Price (Stock B) = Dividend Next Year/(Capitalization Rate - Growth Rate) = 6.90/(5% - 2%) = $230

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Price of Stock C can be calculated with the use of following formula:

Stock Price = D1/(1+Capitalization Rate)^1 + D2/(1+Capitalization Rate)^2 + D3/(1+Capitalization Rate)^3 + D4/(1+Capitalization Rate)^4 + D5/(1+Capitalization Rate)^5 + D5/(1+Capitalization Rate)^6 + D5/(Capitalization Rate - Growth Rate)*(1+Capitalization Rate)^6

Here D1 = 4.10, D2 = 4.10*(1+18%)^1, D3 = 4.10*(1+18%)^2, D4 = 4.10*(1+18%)^3, D5 = 4.10*(1+18%)^4 and D6 = 4.10*(1+18%)^5

Using these values in the above formula, we get,

Stock Price (Stock C) = 4.10/(1+5%)^1 + 4.10*(1+18%)^1/(1+5%)^2 + 4.10*(1+18%)^2/(1+5%)^3 + 4.10*(1+18%)^3/(1+5%)^4 + 4.10*(1+18%)^4/(1+5%)^5 + 4.10*(1+18%)^5/(1+5%)^6 + 4.10*(1+18%)^5/(5%-0)*(1+5%)^6 = $171.98

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Part b-2)

Based on the calculations in Part a-1, Stock A has the highest current value and therefore, it will be considered most valuable.