Question is already solved , just explain the calculations (STEP BY STEP )

QUESTION:

ABC Inc in considering a right offer . The company has considered that the Ex-right price would be the $52 . The current price is $55 per share & there are 5 Million shares outstanding .The right offer would raise a total of $60 Million .What is the subscription price?

SOLUTION:

The number of new shares is the amount raised divided by the subscription price, so: Number of new shares = $60,000,000/$Ps And the ex-rights number of shares (N) is equal to: N = Old shares outstanding/New shares outstanding N = 5,000,000/($60,000,000/SPs) N = 0.0833PS We know the equation for the ex-rights stock price is: Px = [NPRO + Ps]/(N + 1) We can substitute in the numbers we are given, and then substitute the two previous results. Doing so, and solving for the subscription price, we get: Px = $52 = [N($60) + $Ps]/(N + 1) $52 = [55(0.0833Ps) + Ps]/(0.0833Ps + 1) $52 = 4.58P/(1 + 0.0833Ps) Ps = $41.60