Question

Recently, an analysis of Caterpillar Inc. found that it’s equity beta (the beta on its stock) is 1.03. The most recent annual dividend is $4.12/share. A survey of economist finds that the perceived market risk premium is around 6.5%. As of Oct 1, 2020, the yield on a 30-year U.S. Treasury was 1.45%. Given this information, answer the following questions.

a. Assuming dividends are NOT expected to grow in the future. What is the expected current share price given this information?

b. Assume dividends are expected to grow by 4% in perpetuity. Given this assumption, what is the expected current share price?

c. Assume that dividends are expected to grow abnormally for the next 3 years at a rate of 10%. Then, long-term dividend growth is expected to stabilize at 4% annually. Given this information, what is the expected current price?

d. The actual current price in mid-October is $168.75. Given this information and assuming a constant growth rate, what is the implied growth rate given this price?

e. Provide one or more possible explanations of why the actual price ($168.75) is so far above the prices calculated in parts (a), (b), and (c).

Answer 1

~ Required Rate of Return on Equity = 1.45% + 1.03 (6.5%) = 8.145%

Answer (a)

Expected Current Share Price

= D₀ (1+g) / (r - g)

= $4.12 (1.0) / (0.08145 - 0)

= $50.58

Therefore, expected current share price = $50.58

Answer (b)

Expected Current Share Price

= D₀ (1+g) / (r - g)

= $4.12 (1.04) / (0.08145 - 0.04)

= 4.2848 / 0.04145

= $103.37

Therefore, expected current share price = $103.37

Answer (c)

D1 = $4.12 x 1.10 = $4.53

D2 = $4.53 x 1.10 = $4.98

D3 = $4.98 x 1.10 = $5.48

Terminal Value as on Year 3 end = ($5.48)(1.04) / (0.08145 - 0.04) = $137.50

Expected Current Share Price:

= $4.53/1.08145¹  + $4.98/1.08145²  + ($5.48 + $137.50)/1.08145³

= $121.49

Therefore, expected current share price = $121.49

Answer (d)

Price = D₀ (1+g) / (r - g)

$168.75 = $4.12 (1+g) / (0.08145 - g)

$13.74 - 168.75g = $4.12 + 4.12g

9.62 = 172.87 g

g = 0.0556

Therefore, g = 5.56%

Therefore, implied growth rate = 5.56%

Answer (e)

~ The actual price of $168.75 is far above the price of $50.58 calculated in part (a) because the actual price has an implied growth rate of 5.56% in dividends, while the price calculated in part (a) has no growth of dividends. Hence, higher the dividend growth rate, higher the price of stock.

~ The actual price of $168.75 is far above the price of $103.37 calculated in part (b) because the price calculated in part (b) has a growth rate of 4% which is lower than 5.56%. The difference is a result of difference in perpetual growth rates.

~ The actual price of $168.75 is far above the price of $121.49 calculated in part (c) because the value of share has the majority weightage of the Terminal Value which is dependent on the perpetual growth rate. Since the actual price has a perpetual growth rate higher than 4%, the actual price is higher than the price calculated in part (c).