LeBlanc Inc. currently has earnings of $10 per share, and investors expect that the earnings per share will grow by 3 percent per year. Furthermore, the mean PE ratio of all other firms in thesame industry as LeBlanc Inc. is 15. LeBlanc is expected to pay a dividend of $3 per share over the next four years, and an investor in LeBlanc requires a return of 12 percent. What is the forecasted stock price of LeBlanc in four years, using the adjusted dividend discount model?
A) $150.00
B) $163.91
C) $45.00
D) $168.83
E) none of the above

Question

Quizplus · Accepted Answer

Step 1: Calculate the terminal value. 
- Using the formula for the terminal value in the dividend discount model, we get: 
    TV = (D5 x (1 + g)) / (r - g) 
    where D5 is the dividend in year 5, g is the growth rate, and r is the required return. 
- We know that: 
    D1 = $3 
    g = 3% 
    r = 12% 
- We can use the formula for the dividend growth rate to find D5: 
    D5 = D1 x (1 + g)^4 = $3 x 1.03^4 = $3.63 
- Plugging in these values, we get: 
    TV = ($3.63 x 1.03) / (0.12 - 0.03) = $46.39

Step 2: Calculate the stock price in year 4. 
- Using the formula for the adjusted dividend discount model, we get: 
    P4 = (D1 x (1 + g)) / (r - g) + (TV / (1 + r)^4) 
- Plugging in the values we know, we get: 
    P4 = ($3 x 1.03) / (0.12 - 0.03) + ($46.39 / (1 + 0.12)^4) = $29.25 + $98.58 = $127.83

Step 3: Calculate the stock price in year 4 using the PE ratio. 
- Using the P/E ratio, we can find the expected price in year 4: 
    P4 = E4 x PE4 
- We know that: 
    E1 = $10 
    g = 3% 
- Using the formula for the earnings in year 4, we get: 
    E4 = E1 x (1 + g)^3 = $10 x 1.03^3 = $11.26 
- Plugging in these values, we get: 
    P4 = $11.26 x 15 = $168.90

Since the adjusted dividend discount model gives a price of $127.83 and the PE ratio approach gives a price of $168.90, we choose the closest answer, which is D: $168.83.