- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 2. Time Value of Money in Finance
- Subject 3. Equity Instruments and the Time Value of Money
CFA Practice Question
A stock is not expected to pay dividends until three years from now. The dividend is then expected to be $2.00 per share, the dividend payout ratio is expected to be 40%, and the return on equity is expected to be 15%. If the required rate of return is 12%, the value of the stock today is closest to ______.
A. $27
B. $53
C. $67
User Contributed Comments 21
| User | Comment |
|---|---|
| kalps | Ans: 2(0.12-0.09) = 66.67 Discount factor = 1/1.12(2) = 53 |
| kaym | ans is 66.666 calculated as- 2/(0.12-0.09) |
| kalps | no your answer is wrong as the div starts in two years time you have not discounted it |
| KD101 | Well I think here how is goes - PV of $2 after 2 years is (remember you use expected dividends so use t-1 years) 1.5944 Now 1.5944 / (0.12-0.09) = $53.14 |
| mm04 | It says '3 years from now'. So: 2/0.12-0.09 = 66.67 This is the price at the beginning of the 3rd year/end of the 2nd year. Discount back for 2 years: 66.67/1.12^2 = 53 |
| llgoms | thanks mm04 -that's the clearest explanation |
| ThePessimist | Remember the distinction between dealing with a perpetual growth calculation and an individual dividend. If you were calculating the value of that first dividend, you'd discount by three years. When you calculate the GGM as mm04 showed, you're calculating the value of dividends as of the year *before* the first dividend is paid, and thus it only gets discounted by two years. (V0 is based on D1.) |
| NinaB | CF0 = 0, CF1 = 0, CF2 = 67, I = 12, NPV cpt = 53 |
| Bibhu | In case of delayed dividends, g = ROE*(1 - dividend payout ratio)= .15*.6=.09 . So CF2= D2/k-g= 2/(.12-.09)= 67. Then before starting in BA II plus CF + 2nd + Clear work. Then follow up what is given by NinaB |
| lazio | Thanks a lot, Bibhu, this is much of a relief. |
| miene | Ok, I think this is the most logic answer: Growth Rate (g)= ROE x Retention Rate Retention Rate = 1- Div.Payout Ratio Therefore: g = 0.15 x (1-0.4) g = 0.09 Now 2.00/0.12-0.09 = 66.67 Now we need to discount 66.67 to get to t0 (note its only 2 periods discounting) 66.67/(1.12)(1.12) = 53.14 |
| copus | why are there only two discounting periods and not three? |
| dcfa | this is how i did it: D= 2/1.12(3) = 1.4236 g=0.15x0.6=0.09 after 3years it is supposed to grow at 0.09 P3=D4/k-g=2(1.09)/(0.12-0.09)=72.667 (remember P0=D1/k-g) discount P3 term to now = 72.667/1.12(3)=51.7227 V0=51.7227+1.4236=53.1463 |
| Jurrens | At copus: It's only two periods because that formulas uses the NEXT dividend to calculate the price, therefore, if it had only been one year, it would be calculating the stock price at the beginning of the year. Hope that helps. |
| maria15 | Where did .09 come from? |
| maria15 | Never mind. I got it. Thanks! |
| dipu617 | It says "until three years from now"!! Does it mean at the end of 2nd year or at the end of 3rd year?? Anybody!! |
| DaniD13 | You do discount 3 years, but you also have to multiply the dividend first by 1.09 to get D1 not D0 2.18/(.12-.09) then discount by 1.12^3 |
| gill15 | Dani - No Dividend starts Year 3 and it is 2 at that point. When using Gordon the dividends are discounted back to Time = 2. At time = 2 P = 2/(.12 - .09) Now we're at time two and discount it back two more years and you got 53 |
| liana | Is the answer correct? check example from pg 283 CFA! |
| jgonzalez | Thanks miene! |