Finance Formulas Flashcards
MM I proposition
The value of the un-leveraged firm is equal to the value of the leveraged firm, perfect capital market assumption
A = U = E + D :
PV (assets) = unlevered equity = equity + debt
MM proposition II
The cost of capital (the required rate of return on a portfolio company’s existing securities) of levered equity increases with the firm’s market value debt-equity ratio (D+ / E)
Cost of capital of levered equity (return for investors)
based on MM II, r e = r u + D/E (ru - rd)
Cost of capital of unlevered equity
rWACC =rU = rA without tax
debt to value ratio - risk, cost of equity and debt
D/(E+D)
If the debt-to-equity ratio goes up,the perceived risk goes up - more debt
high considered risky, suggests thatthe company is financing a significant amount of its potential growth through borrowing.
If you don’t make your interest payments, the bank or lender can force you into bankruptcy.
cost of equity vs. debt
- cost of equity higher: tax advantages, higher rate of return - wants to take risk since perfect capital market: costly
- return on debt higher if risk higher: debt holders don’t want to loose money, compensation needed
Total value of the firm — with and without leverage, since interest expense and taxes included
EBIT ( - interest expense) - taxes = net income
- Might be present value of debt and equity (perpetuity)
after tax WACC
Interest tax shield — meaning, formula, present value, perpetual
The gain to investors from the tax deduct of interest expense on debt is called the interest tax shield
Interest tax shield = Corporate tax rate x Interest payments (risk-free rate * Debt)
For perpetual debt:
PV(ITS) = interest tax shield / risk-free rate = ITS
Total value of levered firm with tax shield
V(L) = V(U) + PV(tax shield) tax shield discounted with risk-free rate
The effective borrowing rate - effective return on debt
r(d) = r(d) (1-tc)
personal taxes to debt & equity holders: effects
Debt holders (1-tc) - since only pay one type of tax
Equity (1-tc)(1-te) - since also pay dividend taxes on equity
Value of equity according to MM
Equity = Value of Cashflows − Value of Debt (project price)
Value of cash flows:
1. cash flow = initial investment outcomes
2. debt repayment = cash flow - initial investment future value
3. total from both scenarios
Initial market value of unlevered equity —> PV of equity, expected cash flow is the value that can be gathered from investors now
Trade-off theory - how to calculate distress costs
When securities fairly priced the original shareholders of a firm pay the present value of the costs associated with bankruptcy and financial distress.
total value of a levered firm = firm without leverage + PV(interest tax shield: tax * shield rate) - PV(financial distress cost)
V(L) = V(U) + PV(tax shield) - PV(distress costs)
Value of a levered firm with agency costs: meaning and problem defenition
When a firm faces financial distress, shareholders can gain from decisions that increase the risk of the firm sufficiently, even if they have a negative NPV, so they’re gambling with debt holders money (risky investments that might or may not be profitable) — asset substitution problem
V(L) = V(U) + PV(tax shield) - PV(distress costs) - PV(agency costs of debt) - PV(agency benefits of debt)
Tax for dividends or capital gains
(1-t(c)) — only corporate tax rate
Tax on equity Income
(1-t(c))*(1-t(e)) — corporate tax with tax on equity income = double taxation
Effective tax advantage on debt - How high must the marginal corporate tax rate be to offer a tax advantage?
1- (equity income taxes, double)/(debt taxes)
- every dollar debt holders get from interest payments costs equity holders (1-t*) dollars on after-tax basis
- to increase debt by 1, you cut the dividends by (1-t*) dollars
- in case of no personal taxes, t* = t(c)
If asked for a specific tax rate: change the formula.
Debt Overhang Problem
Positive NPV investments are not made since all the benefits are appropriated by debt holders, equity holders do not gain from the investments since for them it’s a negative NPV investment
Signaling theory of debt
- firm can use leverage to convince investors that it has information that the firm will grow, even if it cannot provide verifiable details about the sources of growth.
- investors know that firm would be at risk of defaulting without growth opportunities, so they will interpret the additional leverage as a credible signal of the firm’s confidence
the dividend-capture theory
states that, absent transaction costs, investors can trade shares at the time of the dividend so that non-taxed investors receive the dividend.
Unlevered firm — what is the price of each share?
P = PV(value of firm or cash flows) / # of shares
- might be perpetuity
Unlevered firm — has cash reserves, what is the price of each equity share?
P = PV(value of firm) / # shares + cash / # shares
Unlevered firm — dividend prices (cum/ex)?
P cum = div + PV(future div. - perpetuity)
P ex = PV(future div. - perpetuity)