A stock is expected to pay annual dividends of $1.20 and sell for $42.60 three years from today. Which of these is the correct formula for computing the value of the stock today if the discount rate is 9 percent

Price of the stock today=$35.9

Explanation:

The value of a stock, using the dividend valuation model, is the Present value (PV) of its future cash flows discounted at the required rate of return

The dividend for three years is an annuity. Hence we discount using the present value of annuity.

PV of annuity = A× 1- (1+r)^(-n)/r

r- discount rate, n- number of years, A- annual dividend

PV of annual dividend= 1.20 × (1- 1.09^(-3)/0.09)=3.037

The expected selling price of the stock in year three is a lump sum.

The PV of a single sum is given as

PV of a single sum = F× (1+r)^(-n)

FV- Future value , n- number of years, r- discount rate

PV of sales value in three years = 42.60 × 1.09^(-3)=32.8

Price of the stock today = 3.037 + 32.895  =35.9

Price of the stock today=$35.9

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