# Question 7 Test 4 2015

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reshown Nov 1, 2016

Siya is considering buying some shares in Big Company. She evaluates the equity risk premium for this company to be 3%and expects that the next dividend, payable 3 months from now, will be R24 per share. She thinks that the dividends will grow at 5% per annum after that. The risk-free rate of interest is 9% compounded annually.

(i) Calculate the value Siya puts on a Big Company share.

Big Company shares are currently trading at R350 per share.

(ii) State, giving a reason, whether Siya should buy this share based on the value calculated in (i).

(iii) Explain why there might be a difference in the underlying value and market price of equity.

Big Company financial results in the previous financial year:

• Net income of R1,400m

• R500m dividends due to preference share holders

• Number of issued ordinary shares in the market: 35m

(iv) Calculate Big Company’s P/E ratio.

(v) State if Big Company is more likely to be a “growth” or an “income” company and explain why.

answered Nov 1, 2016 by (340 points)
selected Mar 1, 2017 by Rowan

Please refer to the attached photo for the timeline I used to answer this question.

This question is mostly straight forward after summarising it on a timeline.  You can see how detailed my timeline is. It also has more than three cashflows so that a pattern can be easily recognised from it.

I will first find the value of the stock at time t0. I will then present value it. An easier method might be to find the value of the stock at time t-1 so that I will only have to work with the annuity in arrears formula. The value P is simply the present value of all future dividends in perpetuity.

P = 24 + 24(1.05)(1+3%+9%)-1 + 24(1.05)2(1+3%+9%)-2 + 24(1.05)3(1+3%+9%)-3 +…

P = 24[1 + (1.05)(1+3%+9%)-1 + (1.05)2(1+3%+9%)-2 + (1.05)3(1+3%+9%)-3 + …]

The effective interest rate used to present value the cashflows is the risk free interest rate plus the risk premium.

Now that I have P as an ordinary sum to infinity, I will use the formula for the annuity in advance to sum it up (the first receipt is on the time to which I am present valuing). Recall that the sum for the annuity in advance looks like the expression A as shown in the picture. I have to express P in the same way as A. I shall find a quantity "v" such that I have:

P = 24[1 + v + v2+ v3+ …]

Therefore, it must be that v = (1.05)(1+3%+9%)-1. I will simply take this v value and plug it into the formula A. I will then take the limit as n goes to infinite to find P. Please refer to the picture for this step. Therefore, P = R384. To find the value of the stock in the present, I simply present value P over 3 months:

The value of the stock = P(1+3%+9%)-3/12 % =  R373,27

Please refer to your module 1 notes on section 2.7, more specifically section 2.7.2

answered Nov 1, 2016 by (340 points)
edited Nov 1, 2016 by Lwazi

Answer to questions 7 (ii) - (v)

(ii) Siya should buy the share. The share is vastly undervalued by the market. Therefore, after some time, the market price of the share will catch up with underlying price. In that case, Siya will enjoy capital gains on her stock.

(iii) The main thing to understand here is that underlying values of stocks differ from market values because of information asymmetry. It must be that the market has a lag period for the absorption of information into share prices. Think of things that might result to this situation.

(iv) Earnings "distributable" to ordinary shareholders = R 1 400m - R 500m = R 900m. Remember that ordinary shareholders are the last to receive any share of profits. Preference shareholders and any other lenders have to get their dividends or interest payments first.

Therefore, earnings per ordinary share = R 900/35 = R 25.71

Then the P/E ratio = market price / earnings per ordinary share = R350/R25.71 = 13.611

(v) This company is probably a growth company. The P/E ratio tells us the "price" shareholders are willing to pay for a unit of earnings they're receiving from the company. In this case, shareholders are willing to pay R 13.61 for just R 1 of earnings. It must be that shareholders are expecting the company to pay very high dividends in the future. They are also expecting the company to increase profits rapidly in future.

A useful tip: A growth company is typically indicated by a high P/E ratio, whilst an income company is indicated by a low P/E ratio.