These questions relate to mergers and acquisitions and stock valuation, but they are not directly related to financial accounting principles or standards. However, I can provide you with the calculations based on the information given:

a. To find the stock price of Harrods after the acquisition, we need to determine the total value of the combined company first. The combined firm's post-synergy value is given as £181 million. If Harrods acquires Selfridge for a premium of £10 million, the total cost of the acquisition would be £44 million (Selfridge's market value plus the premium). Since Harrods is exchanging 1.5 million shares for 3 million shares of Selfridge, the new total number of Harrods shares outstanding will be 6.5 million (original 5 million + 1.5 million for Selfridge). The new market capitalization of Harrods would be the sum of its original market value and the cost of the acquisition, which equals £132 million (£132 million = £132 million + £10 million). To find the new stock price, we divide the new market capitalization by the new number of shares outstanding:

Stock Price = New Market Capitalization / New Number of Shares Outstanding Stock Price = £132,000,000 / 6,500,000 Stock Price = 20.31 (rounded to 2 decimal places)

b. To find the exchange ratio, we need to equate the value of the stock offer to the cash offer of £44 million. Each Selfridge share is exchanged for the equivalent of £44 million / 3 million Selfridge shares = £14.67 per share. The exchange ratio (Harrods shares / Selfridge shares) that makes this equivalent to the cash offer is:

Exchange Ratio = Value per Selfridge Share / Stock Price of Harrods Exchange Ratio = £14.67 / Stock Price Exchange Ratio = £14.67 / £20.31 Exchange Ratio ≈ 0.7218 (rounded to 4 decimal places)

So, the answers are: a. Harrods' stock price after the acquisition would be approximately £20.31 per share. b. The exchange ratio between the two stocks to equal a cash offer of £44 million is approximately 0.7218.