# CMA Study Group

View Only #### Royline Gonsalves07-07-2023 11:54 AM #### Gautham Krishnan M07-09-2023 02:51 PM • #### 1.  please help in understanding this. also is there an alternate way to solve ?

Posted 07-07-2023 11:54 AM
Company A is offering a common stock that is expected to pay the following dividends: \$10 next year, \$20 the following year, and after that grow in perpetuity of 2%. Meanwhile, Company B offers a preferred stock with a par value of \$200 and a 12% dividend rate. Both companies have an 8% cost of capital. If both stocks are being offered at \$300, which is a better investment?

Answer----Computation of Company A stock price: [10 ÷ (1 + 8%)] + {20 ÷ [(1 + 8%)2]} + {[20 × (1 + 2%)] ÷ [(1 + 8%)3]} + {[20 × (1 + 2%)2] ÷ [(1 + 8%)3]} ÷ (8% − 2%) ÷ [(1 + 8%)3] = \$318 Computation of Company B stock price: (200 × 12%) ÷ (8% − 0%) = 300.

TO find value of company, as answer is A

• #### 2.  RE: please help in understanding this. also is there an alternate way to solve ?

Posted 07-09-2023 02:51 PM

Hello Royline,

The above question seems to have been answered in the following manner. They must have used a Variable Dividend Growth Model to assess the value of the stock and adjust it for time value of money.

Company A - Equity Stock

At first the approach was to find out the dividends for the years and adjust them for the present values

First Year - \$ 10 - Adjust it for the present value of the required rate of return (for this question it will be the 8% cost of Capital) - 10/((1.08)^1) = \$9

Second Year - \$ 20 - Adjust for time value - 20/((1.08)^2)) = \$17

Third Year - \$20*(1+.02) = \$ 20.4 (Dividend in third year is after 2% increase) - Adjust for time value - 20.04/((1.08)^3)) = \$16

As per the variable growth model it will be appropriate to find out the stock price at the end of the third year. After finding it adjust for time value - We get the value as \$347 before time value adjustment and \$ 275 after adjusting for time value.

The formula is P3 = D4(1+g)/(ks-g)

P3 = Price for the third year

D3 = Dividend in the fourth year = 20.04*1.02 =  \$20.80

g = Growth rate of dividend = 0.02

ks = Required rate of return = 0.08

Total all the values = \$9+\$17+\$16+\$275 = \$318 which is the estimated stock price.

Here we calculated the dividend for all three years and discounted them for the present values for required rate of return. Then we found the estimated price at the end of year 3 and discounted the same for the present value for required rate of return.

Company B - Preferred Stock

In case of preferred stock the dividend is given as a fixed amount of \$ 200*12%

For preferred stock the forumula is fairly straight forward as the dividend is fixed

Vp= D/k

Vp = Market value of preferred stock

D = Constant annual dividend per share = 200*12% = \$24

k =  Market rate of interest or effective rate of interest ( in this case 8% which is the cost of capital)

Thus V = 24/8% = \$ 300.

On the whole while comparing the values of option A and option B with respect to the prices at which they are offered option A has a higher value in comparison to Option B. Therefore it makes sense to choose option A.

Hope this helps.

Thanks.

Regards,

Gautham Krishnan

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Gautham Krishnan M
Director/Manager
Ernakulam
India
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• #### 3.  RE: please help in understanding this. also is there an alternate way to solve ?

Posted 09-20-2023 05:10 AM

Hello,<o:p></o:p>

I am sure many of us have gotten stuck with this question, please go through this explanation and move forward with your preparations.<o:p></o:p>

First let us understand the question well, <o:p></o:p>

If both stocks are offered for \$300 (at present), which is the better investment?<o:p></o:p>

Preferred stock<o:p></o:p>

We already know the par value, so we use Gordon's dividend discount/Growth model formula (For Market price analysis).<o:p></o:p>

MPS=D1/Ke – g<o:p></o:p>

Where, D1 = Next year dividend, Ke = Cost of Equity, g = Growth rate.<o:p></o:p>

Dividend @ 12% on \$200 par value preferred stock <o:p></o:p>

MPS=24/0.08-0<o:p></o:p>

MPS=\$300 (Preferred stock market value)<o:p></o:p>

Common stock<o:p></o:p>

Let us see what's given in the question,<o:p></o:p>

Expected dividend next year = \$10
Expected dividend (Following next year) =\$20
Thereafter, dividend grow in perpetuity (Forever) = 2%
Cost of capital (Ke)= 8%
Growth in the dividend from 3rd Year<o:p></o:p>

With this information, we are required to find the present value of the common stock and present value of the dividend payments.<o:p></o:p>

To convert the future dividend to the present value, we use "present value of annuity" formula it helps us discount future cash flow to the present value.<o:p></o:p>

PV=CF/(1+r) n<o:p></o:p>

Where, CF= Cash flow, r=Ke, n = number of years<o:p></o:p>

<o:p> </o:p>

1.       Dividend next year (Y1) to present value <o:p></o:p>

PV=10(No growth in dividend)/ (1.08)1 = \$9.25<o:p></o:p>

2.       Dividend following year (Y2) to present value.<o:p></o:p>

PV=20(No growth in dividend)/ (1.08)2 = \$14.14<o:p></o:p>

3.       Dividend thereafter, (From Y3) to the present value<o:p></o:p>

PV=20*(1+growth rate 2%) = 20.40/ (1.08)3 = \$16.19<o:p></o:p>

We calculated the present value of all the future dividends, now we need to calculate the present value of the stock price.<o:p></o:p>

4.       Fine the market price of the stock in the 4th year<o:p></o:p>

We use Gordon's dividend discount/Growth model formula (For Market price analysis).  For common stock, previously we used the same formula to calculate preferred stock market value.<o:p></o:p>

MPS=D4/Ke – g<o:p></o:p>

Where, D1 = 4th year dividend, Ke = Cost of Equity, g = Growth rate.<o:p></o:p>

MPS=20.40(1.02 Growth included)/0.08-0.02 = \$346.80 (Future value)<o:p></o:p>

5.       Find the market price of the stock's future value to the present value.<o:p></o:p>

To convert the future stock to the present value, we use "present value of annuity" formula it helps us discount future cash flow to the present value. (Same was used for the dividend above)<o:p></o:p>

PV=CF/(1+r) n<o:p></o:p>

Where, CF= Cash flow, r=Ke, n = number of years<o:p></o:p>

<o:p> </o:p>

PV=346.80/ (1.08)3 = \$275.30<o:p></o:p>

So, adding all the dividends and stock price discounted to present value, we come up with below number. <o:p></o:p>

Common stock value = (\$9.25+\$14.14+\$16.19+\$275.30) = \$318<o:p></o:p>

We can conclude that common stock present value of \$318 is more attractive than preferred stock value of \$300.<o:p></o:p>

<o:p> </o:p>

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SHAIBAN AHMED HAJI FAQUIH
Accountant
DUBAI
United Arab Emirates
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