Question

Assume you've generated the following information about the stock at Carmen's Burger House: The company' latest dividends of $4.46 a share are expected to grow to $4.82 next year to $5.21 the year after that, and to $5.63 in year 3. After that, you think dividends will grow at a constant 6% rate.

a. Use the variable growth version of the dividend valuation model and a required return of 15​% to find the value of the stock.

b. Suppose you plan to hold the stock for three​ years, selling it immediately after receiving the ​$5.63 dividend. What is the​stock's expected selling price at that​ time? As in part a​,assume a required return of 15​%.

c. Imagine that you buy the stock today paying a price equal to the value that you calculated in part a.You hold the stock for three​ years, receiving dividends as described above. Immediately after receiving the third​ dividend, you sell the stock at the price calculated in part b.Use the IRR approach to calculate the expected return on the stock over three years. Could you have guessed what the answer would be before doing the​ calculation?

d. Suppose the​ stock's current market price is actually ​$52.43. Based on your analysis from part a​, is the stock overvalued or​undervalued?

e. A friend of yours agrees with your projections of​ Carmen's future​ dividends, but he believes that in three​ years, just after the company pays the $5.63 ​dividend, the stock will be selling in the market for ​$56.79. Given that​ belief, along with the​stock's current market price from part d​, calculate the return that your friend expects to earn on the stock over the next three years.

Answer 1

Answer (a):

Dividend:

Year 1 = $4.82

Year 2 = $5.21

Year 3 = $5.63

After year 3 dividends grow at constant rate of 6%

Value of stock at the end of year 3 = Year 4 dividend / (Required return - Growth rate) = 5.63 * (1 + 6%) / (15% - 6%) = $66.30889

Current Value of share = 4.82 / (1 + 15%) + 5.21 / (1 + 15%) ² + 5.63 / (1 + 15%) ³ + 66.30889 / (1+15%) ³

= 55.4318

= $55.43

Current Value of share = $55.43

Answer (b):

As calculated above:

Value of stock at the end of year 3 = Year 4 dividend / (Required return - Growth rate) = 5.63 * (1 + 6%) / (15% - 6%) = $66.30889

Value of stock at the end of year 3 = $66.31

Answer (c):

As calculated above:

IRR = 15%

Yes, the answer can be guessed before doing the calculation. IRR will be same as required return (15%) based on which the share value is calculated.

Answer (d):

If the stock's current market price actually is ​$52.43, it is undervalued.

Current value of share as calculated in answer (a) above = $55.43

Answer (e):

Return that your friend expects to earn on the stock over the next three years = 12.35%