Answer: 2.09
Explanation:
Given the following ;
Strike price (K) = $50
Price (c) = $6
Rate (r) = 6% = 0.06
Stock price (So) = $51
Time (T) = 1
Recall, relation for a put-call parity(p) is given by:
p + So = c + Ke^-(rT)
p = c + [Ke^-(rT)] - So
p = 6 + [50e^-(0.06 × 1)] - 51
p = 6 + [50×e^-0.06] - 51
p = 6 + (50 × 0.9417645) - 51
p = 6 + 47.0882267 - 51
p = 53.0882267 - 51
p = 2.0882267
p = 2.09
Answer:
Price of the stock today = $82.35
Explanation:
Note: See the attached file for the calculation of present values for year 1 to 8 dividends.
From the attached excel file, we have:
Previous year dividend in year 1 = Dividend just paid = $2.50
Total of dividends from year 1 to year 8 = $23.46345631521910
Year 8 dividend = 8.77863318950395
Therefore, we have:
Year 9 dividend = Year 8 dividend * (100% + Dividend growth rate in year 9) = 8.77863318950395 * (100% + 7%) = 9.39313751276923
Price at year 8 = Year 9 dividend / (Rate of return - Perpetual dividend growth rate) = 9.39313751276923 / (13% - 7%) = $156.552291879487
PV of price at year 8 = Price at year 8 / (100% + Required return)^Number of years = $156.552291879487 / (100% + 13%)^8 = $58.88868846568915
Price of the stock today = Total of dividends from year 1 to year 8 + PV of price at year 8 = $23.46345631521910 + $58.88868846568915 = $82.35
