Question

Firm A and firm B have the same expected returns, but different methods of financing. Firm A has taken on debt in t = 0 and has to pay back 18735158.0864 in t = 5. Firm A has also issued 100000 shares in t = 0. Firm B has no debt, but has issued 120000 shares. Each share of firm B cost $250 when issued in t = 0. The annual interest rate is 6%. How much did one share of firm A cost when it was issued?

Answer 1

Objective - To determine cost of one share at t=0 for firm A

Solution -

Total capital/financing for firm A is composed of debt and equity. and for firm B its only equity

Step 1: Total financing of firm B at time T=0 is, Number of shares * cost per share,

equating numbers Total capital of Firm B = 120,000 * 250 = 30,000,000 (consider this as label 1)

Step 2: For firm A, lets calculate value of debt at time t = 0 this time value of money problem

Value of Debt = Payback/(1+ interest rate)^maturity

Equating value, = 18,735,158/(1+6%)^5 = 14,000,000

Step 3: Very important, as first row of problem statement says firm A and firm B have same expected returns- the amount of financing raised by 2 firms should be same.

Hence, total financing for firm A = Value of debt + Value of Equity = 30,000,000 --->based on label 1

Equating value of debt, we get value of equity = Total financing - Value of debt

Value of equity = 30,000,000 - 14,000,000 = 16,000,000

Step 4 : Cost per share = Value of equity/number of shares

Equating values, Cost per share = 16,000,000/100,000 = 160

This gives the final answer one share of firm A costs $160 at time 0.