Question

Bill owns 449 shares of ABC Corp. They are currently 5,427 shares outstanding, with a share price of $64. They have an EBIT of $48,779, which is expected to remain constant forever. The cost of debt for both Bill and ABC is 4.2%. ABC is currently 21% debt, but Bill would prefer that they were 66% debt. If Bill wishes to adjust his portfolio to make it behave as if ABC had his preferred capital structure, how much money would Bill have to borrow to buy additional shares with?

Answer 1

Let B be the amount Bill would have to borrow to buy additional shares with. Also, let's say the value of the firm is V.

Current capital structure = 21% Debt

Hence, debt currently = 21% of V = 0.21V

Hence, equity value = V - 0.21V = 0.79V

Also equity value = P x N = 64 x 5,427 =  347,328

Hence, 0.79V =  347,328

Hence, V =  347,328 / 0.79 =  439,656

Desired capital structure = 66%

Hence, debt portion = 0.66V = 0.66 x 439,656 =  290,173  

Also, there is no informatation on tax rate, hence we assume the taxes to be zero.

Hence, net income for ABC = EBIT - interest = 48,779 - 4.2% x 290,173 =   36,592

Hence, net income that belongs to Bill by virtue of being a shareholder = Proportionate net income = Net income x number of shares held by Bill / total number of shares outstanding = 36,592 x 449 / 5,427 =  3,027

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Additional Borrowing by Bill + 21% debt structure

Also, since Bill has borrowed an amount B, he will now buy additional shares = B / P = B / 64

Debt in the firm ABC = 0.21V =  92,328

Net income of the firm = EBIT - interest = 48,779 - 4.2% x 92,328 =  44,901

Hence, net income that belongs to Bill by virtue of being a shareholder = Proportionate net income = Net income x number of shares held by Bill / total number of shares outstanding = 44,901 x 449 / 5,427 =  3,714.88  

Since Bill has borrwed an amount B, he will have to pay an interest of B x 4.2% = 0.042B.

Hence, his net cash flows in this case = 3,714.88 - 0.042B

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Net cash flows in either case should be same, hence

3,714.88 - 0.042B = 3,027

Hence, B = (3,714.88 - 3,027) / 0.042 =  16,368.61

Bill have to borrow = B = 16,368.61