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)
Company wants to raise money by selling shares to pay dividends for investors - How many shares has to sell?
raising amount in $ / share price = needed amount of shares to sell
Note: the overall dividend is higher, but the number of shares is also higher, but does not affect the shareholders.
the new div. per share
PV(firm v) / new # of shares
Instead of dividends, repurchases on the open market: how many shares will repurchase & effect on shares outstanding and dividends?
- cash for repurchasing ÷ price per share = amount of shares
- original share amount - repurchase amount + share left outstanding
The net effect is that the share price remains unchanged, however future dividend changes
How to calculate pre-tax and post-tax profits on dividends?
𝜋 𝑃𝑟𝑒−𝑡𝑎𝑥 = (𝑃 𝑒𝑥−𝑃 𝑐𝑢𝑚) + 𝐷 — pre-tax profit
𝜋 𝑎𝑓𝑡𝑒𝑟−𝑡𝑎𝑥 = (𝑃 𝑒𝑥−𝑃 𝑐𝑢𝑚) (1−𝜏 𝐶𝐺) + 𝐷 (1− 𝜏 𝐷) — after tax profit with equity capital gain and dividend taxes
What is the optimal payout policy?
Almost same as a bond payment
(1 - tax on dividends) * all dividend payments, discounted with return on equity + price ex-div, discounted with return on equity
div and Pex - n+1, while discount with n
equity in the firm has two effects — how do we quantify the two aspects separately? pre, post, ownership change
- Pre-Money Valuation: valuation of outstanding shares at the time
- Post-Money Valuation: valuation of shares at the price which new equity is sold
What is the pre-money valuation of your firm?
pre-money valuation = # shares (1.75mill) × price of funding ($1)
What is the post-money valuation of your firm?
new # of shares (all combined 1.75mill) × price of funding ($1)
How does your ownership change if you accept the round of financing?
******precentage of ownership calculated = (the money YOU contributed) / (the whole amount invested)******
- typical methods of setting the IPO price
- Compute the present value of the estimated future cash flows — as usual
- Estimate the value by examining comparable IPOs.price (post share amount x price of shares) / earnings = value of comparable firm
the 4 IPO puzzles
- Under-pricing : The Winner’s curse
- Issuance is cyclical
- Costs of IPO are high, not usual for companies to make
- Long-run performance of newly public company usually bad
B (risk) for unlevered firm
WCC w/o tax with beta on both
B for equity
Bu + D/E (Bu - Bd)
same as return on equity
In case of permanent debt - Firm value with leverage
V(L) = V(U) + t*D
