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ABC Corp. has just paid a dividend of $0.45. ABC has an annual required return of 11.68%. Attempt 1/5 for 10 pts. Part 1 If dividends are annual and expected to be constant, what is the value of the stock? 3.85 Correct ✓ Attempt 1/5 for 10 pts. Part 2 What is ABC's dividend yield? 11.88% Correct ✓ Attempt 1/5 for 10 pts. Part 3 From now on, assume that the dividend of $0.45 was a quarterly dividend. What is the quarterly discount rate? 2.7732% Correct ✓ Attempt 2/5 for 9 pts. Part 4 What is the value if dividends are constant and quarterly? 16.2 Correct ✓ Attempt 1/5 for 10 pts. Part 5 We now think that dividends will grow by 0.5% from quarter to quarter. The firm just paid the quarterly dividend of $0.45. What is the value of the stock? 19.88 Correct ✓ Attempt 2/5 for 9 pts. Part 6 A different analyst thinks that ABC's dividends will grow by 5% for the next 4 quarters, and then grow by 0.5% thereafter. What is the value of the stock?

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Answer to a math question ABC Corp. has just paid a dividend of $0.45. ABC has an annual required return of 11.68%. Attempt 1/5 for 10 pts. Part 1 If dividends are annual and expected to be constant, what is the value of the stock? 3.85 Correct ✓ Attempt 1/5 for 10 pts. Part 2 What is ABC's dividend yield? 11.88% Correct ✓ Attempt 1/5 for 10 pts. Part 3 From now on, assume that the dividend of $0.45 was a quarterly dividend. What is the quarterly discount rate? 2.7732% Correct ✓ Attempt 2/5 for 9 pts. Part 4 What is the value if dividends are constant and quarterly? 16.2 Correct ✓ Attempt 1/5 for 10 pts. Part 5 We now think that dividends will grow by 0.5% from quarter to quarter. The firm just paid the quarterly dividend of $0.45. What is the value of the stock? 19.88 Correct ✓ Attempt 2/5 for 9 pts. Part 6 A different analyst thinks that ABC's dividends will grow by 5% for the next 4 quarters, and then grow by 0.5% thereafter. What is the value of the stock?

Expert avatar
Velda
4.5
110 Answers
To find the value of the stock when dividends are expected to grow at a rate of 5% for the next 4 quarters and then grow by 0.5% thereafter, we can use the Gordon Growth Model. This model assumes that the value of a stock equals the present value of its future dividends.

Step 1: Calculate the dividends for each quarter for the next 4 quarters.
- The first dividend is $0.45.
- The second dividend will be 5% more than the first dividend: $0.45 * (1 + 5%) = $0.4725.
- The third dividend will be 5% more than the second dividend: $0.4725 * (1 + 5%) = $0.496125.
- The fourth dividend will be 5% more than the third dividend: $0.496125 * (1 + 5%) = $0.52093125.

Step 2: Calculate the present value of the dividends for the first 4 quarters.
- We will discount the dividends at the quarterly discount rate (which we already calculated as 2.7732%).
- The present value of the first dividend is $0.45 / (1 + 2.7732%)^1 = $0.438171.
- The present value of the second dividend is $0.4725 / (1 + 2.7732%)^2 = $0.452972.
- The present value of the third dividend is $0.496125 / (1 + 2.7732%)^3 = $0.468501.
- The present value of the fourth dividend is $0.52093125 / (1 + 2.7732%)^4 = $0.483943.

Step 3: Calculate the future dividends beyond the next 4 quarters.
- We will assume that these dividends will grow at a rate of 0.5%.
- The fifth dividend will be 0.5% more than the fourth dividend: $0.52093125 * (1 + 0.5%) = $0.523569375.
- The sixth dividend will be 0.5% more than the fifth dividend: $0.523569375 * (1 + 0.5%) = $0.526322932.

Step 4: Calculate the present value of the future dividends beyond the next 4 quarters.
- We will discount these dividends at the quarterly discount rate (2.7732%).
- The present value of the fifth dividend is $0.523569375 / (1 + 2.7732%)^5 = $0.457496.
- The present value of the sixth dividend is $0.526322932 / (1 + 2.7732%)^6 = $0.461999.

Step 5: Calculate the total present value of all dividends.
- Add up the present values of the dividends for the first 4 quarters: $0.438171 + $0.452972 + $0.468501 + $0.483943 = $1.843587.
- Add up the present values of the future dividends beyond the next 4 quarters: $0.457496 + $0.461999 = $0.919495.
- The total present value of all dividends is $1.843587 + $0.919495 = $2.763082.

Step 6: Adding the present value of the dividends to the present value of the fifth dividend gives us the stock value.
- The value of the stock is $2.763082 + $0.523569375 = $3.286651.

Answer:
The value of the stock when dividends are expected to grow at a rate of 5% for the next 4 quarters and then grow by 0.5% thereafter is $3.286651.

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