Question

A Suppose you are an investment analyst. One of your client is looking for 3 following different types of stocks If the market capitalization rate (required rate) for each of the following stocks is 10 percent, calculate the values and comment which stock is most valuable for your client. Stock A is expected to provide a dividend of $10 a share forever. ii. Stock B is expected to pay a dividend of $5 next year. Thereafter, dividend growth is expected to be 4 percent a year forever. Stock C is expected to pay a dividend of $5 next year. Thereafter, dividend growth is expected to be 20 percent a year for 5 years (i.e. until year 6) and zero thereafter. (18 marks) B. The present value of investing in a stock should not depend on how long the investor plans to hold it. Explain the statement. (7 marks)

Answer 1

Part i) Value of the stock = Expected dividend/market captalisation rate = 10/0.1 = $100

Part ii) Value of the stock = Expected dividend/(market captalisation rate-growth rate) = 5/(0.1-0.04) = 5/0.06 = 83.33

Part iii) Dividend for 1st year = $5,

Dividend for 2nd year = Dividend for 1st year*(1+growth rate) = $5*(1+0.2) = $5*1.2 = $6

Dividend for 3rd year = Dividend for 2nd year*(1+growth rate) = $6*(1+0.2) = $6*1.2 = $7.2

Dividend for 4th year = Dividend for 3rd year*(1+growth rate) = $7.2*(1+0.2) = $7.2*1.2 = $8.64

Dividend for 5th year = Dividend for 4th year*(1+growth rate) = $8.64*(1+0.2) = $8.64*1.2 = $10.368

Dividend for 6th year = Dividend for 5th year*(1+growth rate) = $10.368*(1+0.2) = $10.368*1.2 = $12.4416

Value of the stock = Dividend for 1st year/[(1+market captalisation rate)^1] + Dividend for 2nd year/[(1+market captalisation rate)^2] + Dividend for 3rd year/[(1+market captalisation rate)^3] + Dividend for 4th year/[(1+market captalisation rate)^4] + Dividend for 5th year/[(1+market captalisation rate)^5] + Dividend for 6th year/[(1+market captalisation rate)^6]

= 5/[(1+0.1)^1] + 6/[(1+0.1)^2] + 7.2/[(1+0.1)^3] + 8.64/[(1+0.1)^4] + 10.368/[(1+0.1)^5] + 12.4416/[(1+0.1)^6]

= 5/1.1 + 6/(1.1^2) + 7.2/(1.1^3) + 8.64/(1.1^4) + 10.368/(1.1^5) + 12.4416/(1.1^6)

= 4.5455 + 6/1.21 + 7.2/1.331 + 8.64/1.4641 + 10.368/1.61051 + 12.4416/1.771561

= 4.5455 + 4.9587 + 5.4095 + 5.9012 + 6.4377 + 7.0230 = 34.2755