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9.2 One of the key features of the Discounted Dividend Model for valuing shares is that it can be used to predict the share price and the dividend at any time in the future.

This is because the model is based on the present value formula for a constant-growth perpetuity. In general, the formula shown in question 9.1 can be generalized as P_n = D_n+1 / (kg).

So, you can predict the price at any n, as long as the following conditions are satisfied:

• you know the dividend at the end of period n, and
• both k and g are constant forever.

To illustrate this, complete the following assignment problem:

Notation: For all n>0, let

• P_n = Price at time n
• D_n = Dividend at time n (i.e., the end of period n)
• Y_n = Earnings in period n
• r = retention ratio = (1 D_n) / Y_n
• E_n = Equity at the end of year n
• k = discount rate
• g = dividend growth rate = r x ROE
• ROE = Y_n / E_n-1

We will further assume that k and ROE are constant, and that r and g are constant after the first dividend is paid.

Answer (a d) based on the information given. (14 marks)

1. Using the Discounted Dividend Model, calculate the price P₀ if D₁ = 20, k = 0.15, and g = r x ROE = 0.8 x 0.15 = 0.12. (2 marks)
2. What will P₅ be if D₆ = 20, k = 0.15, and g = r x ROE = 0.8 x 0.15 = 0.12? (2 marks)

Note that this cannot be equal to the price at time 5 for the stock in part a, since in part a, D₁ = 20, and will grow every year at g = 0.12.( PAY ATTENTION TO THIS PLEASE)

3. Recall that the value of any stock is equal to the present value of all future cash flows (i.e., dividends). Note that P₅ in part b above captures the value at the end of year 5 of all dividends from D₆ onward into the future (i.e., D₇, D₈, D₉, et).

If P₅ = your result from part b, assuming no dividends are paid until D₆, what would the following share values be? (2 marks each)

i. P₀, the value now, at time 0?

ii. P₁, the value 1 year from now?

iii. P₂, the value 2 years from now?

4. In part c, what is the relationship between P₂ and P₁ (i.e., P₂/P₁)? Why? (4 marks)