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

Problem 1:

Dividend at time 0 = 1

Dividend at time 1 = 1 * 1.25 = 1.25

Dividend at time 2 = 1.25 * 1.25 = 1.5625

Dividend at time 3 = 1.5625 * 1.25 = 1.953125

Dividend at time 4 = 1.953125 * 1.05 = 2.0507813

The dividedn paid at the end of year will increase constantly. Therefore we can find the price at year 2 by applying constant growth model.

The expected price at year 2, P2 = D3 / K - G

P2 =  1.953125 / (0.2 - 0.05) = $13.02

The present value of expected price = 13.02 / ( 1.2)² = $9.04

The present value of expected dividends 1 = 1.25 / 1.2 = 1.042

The present value of expected dividends in year 2 = 1.5625 / (1.20)² = 1.085

Current price = 1.085 + 1.042 + 9.04 = $11.17

Expected dividend yield = 1.25 / 11.17 = 0.1119 or 11.2%

The expected price one year from now is the PV at that time of P2 and D2:

P1= (D2+ P2)/1.20

P1 = (1.5625 + 13.02)/1.20 = $12.15

Capital gain = (P1– P0)/P0

Capital gain = (12.15 – 11.17) / 11.17 = 0.088 = 8.8%

The sum of dividend yield and capital gain is equal to market capitilization rate. This is consistent with dividend discount model

Problem 2:

a)

Th follwing formula is used to compute industry's estimated P/E:

P0 / E1 = payout ratio / ( r - g)]

g = ROE * retention rate

g = 0.4 * 0.25 = 0.10

r = Risk free rate + beta ( risk premium)

r = 0.06 + 1.2 ( 0.05) = 0.12

Therefore:

P0 / E1 = 0.6 / ( 0.12 - 0.10) = 30

b)

Higher expected growth in GDP implies higher earnings growth and a higher P/E. Therefore, forecasted growth in real GDP would cause P/E ratios to be generally higher for Country A.

Government bond yield would cause P/E ratios to be generally higher for Country B. A lower government bond yield implies a lower risk-free rate and therefore a higher P/E.

Equity risk premium would cause P/E ratios to be generally higher for Country B. A lower equity risk premium implies a lower required return and a higher P/E.

Problem 3:

ROE = (1 – Tax rate) [ROA + (ROA – Interest rate) Debt/Equity]

0.03 = (1 – 0.35) [ROA + (ROA – 0.06)0.5]

0.03 = (0.65) [ROA + (0.5ROA – 0.03)

0.03 = (0.65) [1.5 ROA - 0.03)

0.046154 = 1.5ROA - 0.03

0.076154 = 1.5ROA

0.05 = ROA

ROA = 5%