Question

SUBJECT 1 B

4 years ago, Company A., paid dividends equal to €0.3858 per share. Today, the company paid dividends €0.80 per share (thus g1=20%). It plans to keep this growth rate steady for the next 3 years and then the company’s dividend growth rate (g2) is expected to be 8% flat for the foreseeable future. Considering that investors require a return of 12% to invest in the company’s stocks, you are required to answer the following questions:

a. What is the intrinsic value per share of Company A. if you choose to use the Dividend Discount Model?

Is this Solution right? D1 = D0 * (1+g1)1= 0,8 * (1+0.20)^1 = 0,96 / D2 = 0,8 * (1+0.20)^2 ≈ 1,15 and D3 = 0,8 * (1+0.20)^3 ≈ 1,38

Present value of future dividends’ market price for a required rate of return =12%: 1st yr: D01 = 0,96/(1+0,12)^1 ≈ 0,8571 / 2nd yr: D02 =1,15/(1+0,12)^2 ≈ 0,9168 / 3rd yr: D03 =1,38 /(1+0,12)^3 ≈ 0,9823. thus Present value of the first 3 years of dividends = (0,8571 + 0,9168 + 0,9823) = 2,7562 € and Expected Value_stock at beginning of 4th yr end of 3rd yr = D4/(k-g2) = [D3*(1+g2)]/(k-g2) = [1,38 * (1+0,08)] / (0,12-0,08) = 37,26 €, thus Present value of stock at 4th yr = Expected Value at 4th yr / (1+k)^3 thus, the PV of stock = 37,26/(1+0,12)^3=26,5215 €. Adding 26,522 value to the present value of all dividends to be received during the first 3 years, the intrinsic value is: 2,7562+26,5215 = 29,2777 € b.

b. If market currently prices Company's A share at €25, would you put your money in Company A?

Answer: Comparing Stock’s intrinsic value (29,27 €) with its suggested current market price (25 €) one can say that this stock is under-valuated and will provide the investor with a profit of (29,27-25) 4,27 € / share and thus should be preferred as an investment.

Please contribute to the rest sub-questions:

c. Company B is the main competitor of Company A. The stock of Company A has a beta coefficient of 1.2 and it pays out 40% of its earnings in dividends. The latest earnings announced by Company B were €10 per share. Dividends were just paid and are expected to be paid annually. Based on your analysis you expect Company B to earn a ROE of 20% per year on all reinvested earnings forever. Assuming that the risk-free rate of return is 8% and that the expected rate of return on the market portfolio is 15%, calculate the intrinsic value per share of Company B.

d. If the market price of Company B’s share is currently €60 would you invest in Company B or not?

e. If you had to choose between the two competitors, would the share of Company A or the share of Company B be your favorite? Explain briefly.

f. If a security is underpriced, then what is the relationship between its market capitalization rate and its expected rate of return? Discuss briefly.

Answer 1

c) Working 1 : Calculation of cost of equity

Cost of equity (Ke) = Rf + Beta (Rm - Rf)

Here,

Rf (Risk free rate) = 8% or 0.08

Beta = 1.2

Rm (Rate of market return) = 15% or 0.15

Now,

Cost of equity (Ke) = 0.08 + 1.2 (0.15 - 0.08)

Cost of equity (Ke) = 0.08 + 0.084 = 0.164 or 16.4%

Working 2 : Calculation of growth rate

Growth rate = ROE * Dividend payout ratio

Growth rate = 20% * 40% = 8% or 0.08

Working 3 : Dividend per share

Dividend per share = Earnings per share * Dividend payout ratio

Dividend per share = €10 * 40% = €4

Working 4 : Calculation of intrinsic value per share

Intrinsic value of share = Dividend per share (1 + Growth) / (Cost of equity - Growth rate)

Intrinsic value per share =( €4 *(1 + 0.08)) / (0.164 - 0.08)

Intrinsic value per share = €4.32 / 0.084

Intrinsic value per share = €51.43

d) Intrinsic value per share of company B is €51.43 & market price per share is €60.

Here share price is overvalued than it's intrinsic value & it will provide loss of €8.57 (60 - 51.43).

Hence it is recommended that not to invest in company B.

e) Share of company A is to be choosen than comapany A. As company A's share providing profit over intrinsic value whereas company B's share providing loss. Further, price of company A is lower @ 25 than price of company B @ 60.

f) If security is underpriced then expected rate of return is greater than market capitalisation rate.

Note : Solution for a & b is correct.