Question

Problem 1. The Duo Growth Company just paid a dividend of $1 per share. The dividend is expected to grow at a rate of 25% for the next 3 years and then level off to 5% per year forever. You think the appropriate market capitalization rate is 20% per year. (3 pts.)

What is your estimate of the intrinsic value of a share of stock?

If the market price of a share is equal to this intrinsic value, what is the expected dividend yield?

What do you expect its price to be 1 year from now? Is the implied capital gain consistent with your estimate of the dividend yield and the market capitalization rate?

Problem 2. Peninsular Research is initiating coverage of a mature manufacturing industry. John Jones, CFA, head of the research department, gathered the following fundamental industry and market data to help in his analysis (3 pts):

Forecast industry earnings retention rate	40%
Forecast industry return on equity	25%
Industry beta	1.2
Government bond yield	6%
Equity risk premium	5%

Compute the price-to-earnings (P₀/E₁) ratio for the industry based on the fundamental data.

Jones wants to analyze how fundamental P/E ratios differ among countries. He gathered the following economic and market data:

Fundamental factors	Country A	Country B
Forecast growth in real GDP	5%	2%
Government bond yield	10%	6%
Equity risk premium	5%	4%

Determine whether each of these fundamental factors would cause P/E ratios to be generally higher for Country A or higher for country B.

Problem 3. A firm has an ROE of 3%, a debt-to-equity ratio of 0.5, a tax rate of 35%, and pays an interest rate f 6% on its debt. What is its operating ROA? (3 pts)

Answer 1

Answer to Problem 1:

Answer a.

D0 = $1

Growth rate for first 3 years is 25%, followed by a constant growth rate (g) of 5% forever

D1 = $1.0000 * 1.25 = $1.2500
D2 = $1.2500 * 1.25 = $1.5625
D3 = $1.5625 * 1.25 = $1.9531
D4 = $1.9531 * 1.05 = $2.0508

Market Capitalization Rate, k = 20%

P3 = D4 / (k - g)
P3 = $2.0508 / (0.20 - 0.05)
P3 = $13.6720

P0 = $1.25/1.20 + $1.5625/1.20^2 + $1.9531/1.20^3 + $13.6720/1.20^3
P0 = $11.17

Intrinsic Value of Stock is $11.17

Answer b.

Expected Dividend Yield = D1 / P0
Expected Dividend Yield = $1.25 / $11.17
Expected Dividend Yield = 0.112 = 11.2%

P1 = $1.5625/1.20 + $1.9531/1.20^2 + $13.6720/1.20^2
P1 = $12.15

Implied Capital Gain Yield = (P1 - P0) / P0
Implied Capital Gain Yield = ($12.15 - $11.17) / $11.17
Implied Capital Gain Yield = 0.088 = 8.8%

Market Capitalization Rate = Implied Capital Gain Yield + Expected Dividend Yield
Market Capitalization Rate = 8.8% + 11.2%
Market Capitalization Rate = 20.0%

So, this is consistent with DDM.