Asonia Co. will pay a dividend of $3.90, $8.05, $10.90, and $12.65 per share for each of the next four years, respectively. The company will then close its doors. If investors require a return of 11 percent on the company's stock, what is the stock price

Stock price today $26.34

Explanation:

The stock price today is the sum of the present value of the future cash flows(dividends) payable by the stock to investors using the 11% reuired rate of return as the discount rate:

Years           Cash flows       Discount factor                      Present values

1                       $3.90                1/(1+11%)^1=0.900900901        $3.51

2                      $8.05                1/(1+11%)^2=0.811622433          $6.53

3                       $10.90                1/(1+11%)^3=0.731191381           $7.97

4                       $12.65                  1/(1+11%)^4=0.658730974      $8.33

Total present values =$3.51+$6.53+$7.97+$8.33=$26.34

Price of stock = $57.26

Explanation:

According to the dividend valuation model , the current price of a stock is the present value of the expected future dividends discounted at the required rate of return.

So we will discount the steams of dividend using the required rate of 11% as follows:

Year Present Value(PV)

1 $3.90 × 1.11^(-1) = 1.486  

2 $8.05× 1.11^(-2) = 1.322

3 $10.90× 1.11^(-3) = 1.2064

Year 4 and beyond

This is annuity of 12.65 for four years. So the steams of constant amount would be discounted as follows:

PV = A × (1- (1+r)^(-n) )/r

  A- 12.65, r - 0.11, n - 4

PV = 12.65 × (1- 1.11^(-4))/0.11 =  39.24593797

Total PV=  1.486 + 1.322 + 1.2064 + 39.24=  $57.26

Price of stock =  $57.26

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