dividend valuation

The dividend valuation formula gives the market value 'now' (time 0) when the first dividend is in 1 years time. If the first dividend is in 4 years time, then it is 3 years later than in 1 years time, therefore it gives a MV three years later - time 3 instead of time 0. So we need to discount for 3 years to get the value now.

Sorry to be a pain, John - the timings really confuse me :( So, basically the question is “what is the mv of all expected dividends for the next 4 years?” / “how much are theses future dividends worth ‘now’ "? Correct? First dividend will be in Y1 = 0.6x1/1.10 = 0.55 Second in Y2: 0.60 x 1/1.10^2 = 0.50 Third in Y3: 0.60 x 1/1.10^3 = 0.45 And then the forth incl. growth of 4% = 0.60 x 1/1.10^4 = 0.41 x 1.04 / (0.10 - 0.04) = 7.10 That’s how I understand it. or alternatively: First dividend will be paid in Y0 = 0.60 Second in Y2: 0.6x1/1.10 = 0.55 Third in Y3: 0.60 x 1/1.10^2 = 0.50 And then the forth incl. growth of 4% = 0.60 x 1/10^3 = 0.45 x 1.04 / (0.10 - 0.04) = 7.80 But neither is correct. I’m sorry to bother you with something that is probably so simple, but I just don’t get it ?

The question is asking for the MV of the expected dividends for ever - not just the next 4 years. First dividend will be at time 1 = 0.6×1/1.10 = 0.55 Second at time 2: 0.60 x 1/1.10^2 = 0.50 Third at time 3: 0.60 x 1/1.10^3 = 0.45 What you have done there is correct (although it would have been quicker to use the 3 year annuity discount factor at 10% !!! For the dividends from time 4 onwards, we use the dividend valuation formula: 0.60 x 1.04 / (0.10 – 0.04) = 10.4 However, the dividend valuation formula gives the present value of the dividends when the first dividend is in 1 years time. Here, the first dividend is in 4 years time, which is 3 years later. So the answer of 10.4 is the PV in 3 years time. Therefore we need to discount the 10.4 for 3 years at 10%, which is 10.4 x 1/1.1^3 (although again it would be more sensible to use the tables provided!!!) = 7.80 Therefore the total MV = 0.55 + 0.50 + 0.45 + 7.80 = $9.30 I do suggest that you watch my free lectures on the valuation of securities, because I do go through a similar example and explain. (The lectures are a complete free course for Paper F9 and cover everything needed to be able to pass the exam well.)

Ah, thank you so much!!! Really appreciate your quick reply! I have watched all your lectures already, but will re-watch this one. Thanks for all your help :)

NOT SURE WHERE YOU GET 9.30 , It could well be right , but see below - this is how i would calculate and i get 8.81 - Any one able to comment CF DF at 10% NPV Y1 0.6 0.090 0.0540 Y2 0.6 0.826 0.4956 Y3 0.6 0.751 0.4506 Y3 (End) 10.4 7.8104 8.8106 For 4 years onward, we are calculating at the end of Y3 60(1.04) 62.4 1040 Cents or 10.40 0.1-0.04 0.1-.04

Corrected Y1 DF CF DF at 10% NPV Y1 0.6 0.909 0.5454 Y2 0.6 0.826 0.4956 Y3 0.6 0.751 0.4506 Y3 (End) 10.4 7.8104 9.3020 For 4 years onward, we are calculating at the end of Y3 60(1.04) 62.4 1040 Cents or 10.40 0.1-0.04 0.1-.04

9.3 is correct, you need to discount Y4 10.4 0.751 7.8 see John's answer: "The dividend valuation formula gives the present value of the dividends when the first dividend is in 1 years time. Here, the first dividend is in 4 years time, which is 3 years later. So the answer of 10.4 is the PV in 3 years time. Therefore we need to discount the 10.4 for 3 years at 10%, which is 10.4 x 1/1.1^3 (although again it would be more sensible to use the tables provided!!!) = 7.80" Therefore the total MV = 0.55 + 0.50 + 0.45 + 7.80 = $9.30

Thanks Jenny :-)