Is Debt Matters in financing firms.

As we know, money in a firm comes from either debt or stock equity. So if we use B to represent market value of firm's debt, S for market value of firm's equity, and V for market value of firm's assets, then we can get an easy equation: V = B + S

From previous class in finance, we know what stockholders want is to increase the stock price which leads to a increase in value of S. But what is the relationship between increase in value of V and S, and does debt impact V.

Maximizing V is equal to maximizing S
We start with a easy model:
100 shares selling at $10 each --> S0= 1000
Initial unlevered --> there is no debt --> B0= 0
Firm value: since there is no debt, value of the firm equal to value of equity --> V0= S0 = 1000
Next we start to lever up the firm
Borrow $500 --> B1 = 500
Use $ 500 to pay special dividends of $5 per share --> the value of the firm right after dividends payment is still 1000
Then we consider the following situation
New firm value V1 will be either 1250, 1000, or 750

What is the value of debt and equity with the leverage

	V0=1000	V1=1250	V1=1000	V1=750
Debt value	0	500	500	500
Equity Value	1000	750	500	250

Since there is no bankcrupt in either case, so debt owner would get 500 in all case, and equity holder get rest of the value of firm

how much do shareholders profit/lose from increase in leverage

	V1=1250	V1=1000	V1=750
Capital Gain	-250	-500	-750
Dividends	500	500	500
Shareholder profit	250	0	-250

So, increase of the value of the firm leads to a increase in value of equity.
In this simple case, debt does not matters since there is no difference between shareholder profit in either levered or unlevered case.
But we did not consider impacts of tax, default risk, agency cost etc.