Answer:
Price of share today = $9.74
Explanation:
The price of a share can be calculated using the dividend valuation model
According to this model the value of share is equal to the sum of the present values of its future cash dividends discounted at the required rate of return.
If dividend is expected to grow at a given rate , the value of a share is calculated using the formula below:
Price=Do (1+g)/(k-g)
Do - dividend in the following year, K- requited rate of return , g- growth rate
Step 1 : PV of dividend from year 1 to 3
PV = D × (1+r)^(-n)
D- dividend receivable in a particular year, r- required rate of return, n- year
Year PV of Dividend
1 0.50 × 1.07^1 ×1.08^(-1) = 0.495
2 0.50 × 1.07^2 ×1.08^(-2) = 0.491
3 0.50× 1.07^3× 1.08^(-3) = 0.486
Step 2 : PV of dividend from year 4 to infinity
PV (in year 3 terms) of dividend= 0.50× 1.07^3 ×1.02/(0.08-0.02) = 10.41
PV in year 0 terms = 10.41 × 1.08^(-3) = 8.27
Total Present Value = 0.495 + 0.491 + 0.486 + 8.27 = 9.738
Price of share today = $9.74
