Corp Fin - Midterm

You want your (wealthy) friend to invest in your new company that provides actual financial training to Wall Street traders. He argues that given the volatility of future cash-flows (20%) and his low tolerance for risk, he'd be willing to pay only a low price for each stock of your firm. What can you tell him?

"Total risk (volatility) is not relevant for you. In particular, if you are well diversified, you should care only about the exposure of my firm's cash-flows to systematic risk. If the β of my firm is low, you might actually be willing to pay a higher price than you think for each stock".

Stock Beta formula - on formula sheet

(Covariance of stock and market) / (Variance of market)

Return Volatility

(Probability ** return^2 + Probability ** return^2 .. - average^2)

True / False (c) Two firms with identical assets have the same expected return on equity.

(c) Incorrect, they need to have identical leverage as well.

CAPM Assumptions - which is the most unrealistic

*Homogeneous expectations regarding volatility, correlations, and returns* - No transaction costs - Investors only hold efficient portfolios - * Market portfolio is the tangency portfolio *

Dutch bid auction -- which google used

- Firm announces # of shares to be issued - each investor posts a bid specifying a number of shares and a price - Underwriter goes from the highest price to the lowest one untill reaching the number of shares - The price everyone pays is the lowest bid accepted - if the number of remaining shares is insufficient, shares are allocated on a pro-rata basis

F has 2 categories of bonds: senior secured bonds (A) and unsecured debt (B). Bonds A are secured on real estate owned by F. Following the subprime crisis, the value of those assets plummeted. How does that information impact your valuation of each class of debt?

- It affects negatively the value of A-bonds: the value of the security decreases therefore the expected loss given default is likely to increase. - It affects negatively the value of B-bonds as well, even though they are not secured on those assets: in case of liquidation, holders of A-bonds will get less out of secured assets and therefore demand more out of unsecured assets. As A-bondholders are senior, this will come at the expense of B-bondholders who get proceeds from the liquidation of unsecured assets only if senior bondholders are fully repaid.

Advantages of auction

- less discretion to the underwriter on price setting - market-clearing price - less room for manipulation

Advantages of book building

- price discovery (reduces information assymetries hence winner curse) - post ipo-performance

Whats the beta of a risk free security

0

Whats the β of risk free debt

0

Fu is (still) unlevered, ₋ Fl (still) has outstanding perpetual debt, with face value D =$500,000, annual interest rate 5%. State of the Economy Earnings bf interests equal probability of each Recession $30,000 Normal $80,000 Boom $120,000 Risk-free rate (rf) is 4% expected return on Fu or Fl assets (rA) is 8% Compute expected return on equity rS of Fl

1) Compute market value of equity for Fl (1/3) * $30,000 + (1/3) * $80,000 + (1/3) * $120,000 / .08 = 958.33 2) compute market value of debt (500,000 * .05) / .04 = 625 - have to discount using the rf rate Then 958.33 - 625 = to get the value of equity 3) Write your expected CF = 30k - 25k (cost of debt) then (1/3) * $5,000 + (1/3) * $55,000 + (1/3) * $95,000 / 333.33 = 15.5%

Rights Offering

an option given to existing shareholders to purchase new issue shares at a given price w/in a time frame with seasoned equity offering ex right date: before this date when you buy a stock you also get a rights offering

. F's has assets worth $1,000,000, 20,000 common stocks outstanding at a market price of $20 and risk-free debt. Expected return on equity is 15%, risk-free rate is 3%. F plans to buy new assets that generate an additional expected EBIT (= operating cash-flow) of $50,000 per year (perpetuity), and require an investment of $600,000. New assets do not affect the fundamental risk of the firm. The acquisition is financed through the issuance of new common stocks and does not affect the risk of existing debt. ∗ [email protected] 1 (a) What is the issue price and the number of stocks to be issued? (b) What is the expected return on equity after the operation?

1) Find the unlevered cost of equity using MM2 The unlevered cost of equity is r0 = 400, 000 1, 000, 000 × 15% + 600, 000 1, 000, 000 × 3% = 7.80%. 2) Find the NPV of the project using unlevered cost of equity: The NPV of the project is 50, 000/7.80% − 600, 000 =$41,026 3) Find value of equity and stock value after the announcement of the 400,000 + 41,026 = $441,026 value of stock 441, 026/20, 000 =$22.05 4) find how many Stocks are issued at $22.05 600, 000/22.05 =27,209. Total equity value = 41,026 +600,000=$1,041,026. 5) Find equity return using MM2 Debt is still risk-free so its value is not affected rS = r0 + B S (r0 − rB) rS = 7.80% + 600, 000 1, 041, 026 (7.80% − 3%) = 10.57%

Hedging vs. diversification

1) Hedging = limit risk in one state of the world (the downside usually) 2) Diversification = reduce risk in all states of the world

F has existing unsecured debt with face value $2 million, maturity 3 years, in fine. It raises additional debt to finance a new plant (P). ₋ F contracts a mortgage, face value $8 million, maturity 10 years, in fine, secured on P. ₋ Two years later F goes bankrupt and is liquidated: ₋ liquidation value of P is $5 million, ₋ liquidation value of other assets is $3 million. ₋ How much does each category of debtholders recover? (neglect due interests)

1) Pay off secured debt holders with the value of the secured amount - secure gets 5 mm 2) Deduct the the amount payed off to the secured debt holders and repay the secured and unsecured debt holders pro-rata - secure gets (3 / 5) * 3 = 1.8 mm - unsecured gets (2 / 5) * 3 = 1.2 mm

Capital Structure with taxes Application 1: Tax Shield and Risk-free debt ₋ F has risk-free debt and the following characteristics: EBIT = 400,000 Face value of Debt = 3,000,000 Corporate tax rate = 30% Risk-free rate = .035 ₋ Compute the annual corporate taxes paid by F. ₋ Compare with the annual corporate taxes F would pay if it had no debt. ₋ What is the appropriate discount rate for tax savings here? Compute TS

1) Taxes levered =(400,000 - .035 (3,000,000) ) ** .3 = 88,500 2) Taxes unlevered = (400,000) .3 = 120,000 3) tax savings = 120,000 - 88,500 = 31,5000 4) tax shield = 31,5000 / .035 = 900,000

Capital Structure without frictions Application 2: Dividend Recap F has 200,000 stocks outstanding at a market price of $50, and no debt. ₋ F plans to issue 3,000 bonds at par value (i.e. market value of one bond is $1,000). ₋ The proceeds from the issuance will be immediately paid to stockholders as a special dividend. 1. Compute the value of one stock after the operation 2. Does the operation create value for stockholders?

1) The value of the assets is 10m since that is the equity. When you raise the debt of 3m assets increase by 3 m but then decrease immediately by 3m bc pay out in cash, then debt remains the same so value of equity must decrease by 3 m, so equity decreases to 7 m / 200,000 = 35 2) Shareholders recieved 15 (3m /200k) but the value of their stock went down to 35 so no value was created

F firm value in one year is $6 million or $3.5 million with equal probability. ₋ F has existing debt, face value $2 million, zero-coupon, maturity one year. ₋ F cost of equity is rS=10% and the risk-free rate is 3%. ₋ F raises additional debt, face value $2 million, zero-coupon, maturity 1 year, same seniority as existing debt. The proceeds from the issuance are immediately distributed to stockholders 1. After the operation, the cost of debt is 4%. Does the operation create value for stockholders? Explain. 2. Debt Covenants restrict the issuance of new debt. Given this possibility, is this type of operation likely to happen?

1) Value of equity = (.5 (6-2) + .5 (3.5-2)) / 1.1 2) Value of bond = 2 / 1.03 = 1.94 Value of the firm = 1.94 + 2.5 = 4.44 3) Value of bond post new debt issuance = (.5(2) + .5(3.5) (2/4)) / (1.04) = 1.80 m 4) stock value post = 4.44 - 3.6 = .84 5) Wealth of the shareholders pre = 2.5 6) Wealth of the shareholders post = 1.8 + .84 = 2.64 - Shareholder wealth increases because the required return on the bond increases so the bond value decreases, which is made up by the stock value increase

Fu and Fl have identical assets, with value V1 in 1 year. Recession: V1 = 5 Normal: V1 = 10 same probability ₋ Fu is unlevered, cost of equity *r0* = 10% (*r0 = unlevered firm*) ₋ Fl has debt with face value $6 million, interest rate 5%, maturity one year, cost of debt rB = 5.5%. 1. Compute equity and debt value for both firms. 2. Compute Fl expected return on equity without using MM2. Check that MM2 applies

1) Value of stock for unlevered = (.5**5 + .5**10) / 1.1 = 6.82 value of bond = .5 (5) + .5 (6**1.05) / 1.055 = 5.36 *take value of stock for unlevered and subtract value of bond* to get value of stock for levered: MM1 -- dont calc because you don't know the required rate of return for the levered firm (rs) = 1.46 -- How do we check that MM2 applies? Calculate the expected returns by hand and compare with the MM2 formula: rS = r0 + B/ S (r0 − rB) .5(10-6(1.05)) / 1.46 - 1 = .26 - return on equity (only .5 because in the other state you make no money) MM2 = .1 + 5.36 / 1.46 (.1 - .055) = .26 Yes it holds

Modigliani-Miller I (MM1)

1) What ultimately matters is operational performance (size of the pie). 2) Capital Structure only affects the repartition (division) of cash-flows (slices of the pie).

(e) As leverage increases, it can be that β of equity (βS) and β of debt (βB)increase while β of firm's assets (βA) remains constant

Correct, the risk of assets βA remains constant from MM, but the risks of both debt and equity are affected by leverage. In particular, they might both increase when leverage increases (see slide 29).

Expected return of portfolio formula

E(rPF ) = xE(rA ) + (1− x)E(rB )

If a firm is flow-based insolvent but not stock based insolvent and files for bankruptcy, what does that say about its assets?

Yes, if you're company has a lot of fixed assets it can not readily sell or the value of the assets are valuable when combined but not seperate

F start-up cost is still $500 000 (beginning of year 0), but this covers only phase 1 of the development (2 years). ₋ If phase 1 is successful, more extensive testing (phase 2) is needed for cost of $1 million to be invested upfront (beginning of year 2). Phase 2 lasts 2 years, and an additional year is needed to get FDA approval ₋ The estimated probability of successfully completing phase 1 is 20%. Once phase 1 is completed, the estimated probability of successfully completing phase 2 and getting FDA approval is 50%. ₋ Estimated value of F if the product gets FDA approval is $40 millions. ₋ VCs expected return for biotech companies is 12%. - Find the phase 2 investors stake and phase 1 investors' stake - Find Sharholder composition after phase 2 - how many new shares do you have to issue at phase 2 -- say you start with 1 million

1st do the phase two post money then deduct the 1 million to get to pre money post-money valuation = 14.23 phase 2 stake = .0702 then take the pre-money valuation and set equal to PostMV*(share)=(amt of financing) phase 1 stake = .2370 = 2.11 Phase 2 shareholder composition: - phase 1 investors: .2370 * (1 - .0702) = .2202 (it's okay they knew they were going to be diluted) - phase 2 investors: .0702 Creating shares - S1 / (1,000,000 + s1) = .2370 = 310,615.99 - S2 / (1,310,615.99 + S2) = .07025 = 98,951.65

F has 1 million shares outstanding. ₋ F needs to raise money, and Bcom Partners invests $4 millions in F in exchange for a new issue of 600 000 shares - Find the premoney valuation

6.67 million

α - formula

= (r PF − rf ) − βPF (r M − rf )

Tax shield formula

= B * tax rate = bond must be perpetual

underwriting

An IB buys shares from the firm and sells them, - firms don't go public directly - IB two roles: advising and placing stocks

F generates an annual expected CF of $5 million (perpetuity) ₋ F is unlevered (10 million shares), cost of equity r0 = 10%. ₋ F considers investing in a new plant that generates an additional expected $1 million per year, and costs $4 million (upfront). This investment does not modify the risk of F's assets. 1. The investment is financed with new equity. Write the BS of F a) right after the investment announcement b) right after the equity issue (before the investment) c) after the investment. 2. Same question if investment is financed with debt Capital Structure without frictions Application

Assets: 5/.1 = 50 Liab/OE: 50 Announcement Assets: exisiting assets: 50 NPV of plant: 1/.1 -4 = 6 Liab/OE: 50 +6 of the equity Issue Equity Assets: exisiting assets: 50 NPV of plant: 1/.1 -4 = 6 Cash = 4 Liab/OE: Old equity = 56 New equity = 4 After investment Assets: Existing assets: 50 Plant: 10 Liab/OE: Equity: 60 after an investment plant is just worth the 10 Issue *Debt* Assets: exisiting assets: 50 NPV of plant: 1/.1 -4 = 6 Cash = 4 Liab/OE: equity = 56 LT Debt = 4 After investment Assets: Existing assets: 50 Plant: 10 Liab/OE: equity = 56 LT Debt = 4

What does a beta of 1.2 mean

Beta is a correlation of returns to the market That means when a market goes up by 1%, the stock is expected to go down by 1.2%, and when the market goes down by 1%, the stock goes down by 1.2%

Public debt

Bonds traded over the counter

Limits to diversification

Cannot have negative correlation when (Pij)^(1/2) - impossible to find an infinite # of variables that are negatively correlated Consider N securities indexed by i = 1,2..., N. ₋ Assume that ₋ All securities have the same variance ₋ All pairs of securities have the same correlation ₋ Consider a portfolio equally weighted in each security. ₋ Volatility? ₋ What happens as N becomes larger? σpf = ((1/N)σ^2 + (1- 1/N)σ^2Pij) ^ (1/2) - Pij = correlation σpf -----> σ(pij)^(1/2)

MM2

Concerns WACC of company Without Tax- cost of equity increases as company takes on more debt because now riskier. Therefore proportion does not matter because it is offset With Tax- WACC is minimized with 100% debt r0 = S / (S + B ** rS) + B / (S + B) ** rB = 1 / (1+ L) * rS + L / (1+ L) rB

Debt Security

asset pledged by the firm to (certain classes of) debtholders. Considered collateral when the pledged asset is tangible

Who is an underpriced IPO especially bad for?

Existing shareholders cause they get diluted even more - their shares are based on a premoney valuation in the IPO which was supposed to be higher --> so they got a smaller stake and are dilluted more because the new shareholders need a bigger pecentage of the company now that the ipo premoney valuations is lower

F is an all-equity firm with assets worth $1,000,000. Current expected return on F equity is 9%. F buys new assets at market value for $500,000 (same risk as existing assets). The acquisition is financed by debt. Following the operation, the expected return on equity increases to 12%. What is F's cost of debt?

F's firm value after the operation is $1,500,000. Debt value is B = $500, 000, equity value is S = $1, 000, 000. From MM2 rS = r0 + B S (r0 − rB) ⇔ rB = r0 − S B (rs − r0) = 9% − 1 0.5 (12% − 9%) = 3%

(b) Two firms with identical assets have the same equity β.

False, may have different B's if their leverage differs

"higher capital requirements would increase the cost of capital for banks and reduce banks' willingness to lend" Comment given MM2

Higher equity reduces the amount of debt, which reduces the cost of debt, so raising more equity decreases the cost of capital

F is an all-equity firm, with equity β of 0.8. F decides to issue new debt and pay out the proceeds from the issuance to investors. Following the operation, F's leverage increases to 0.6, and the equity β to 1.2. Is F's debt risk-free?

I guess that beta can replace the returns in the MM2 formula βS = β0 + L(β0 − βB) 1.2 = .8 + .6 (.8 - βB) = .13

₋ Seniority defines priority in case of default.

If debt A is senior to debt B and the firm defaults, holders of A debt must be paid off (face value + due interests) from the proceeds of the liquidation before B-debt holders may be compensated. ₋ This equivalent to saying that B-Debt is subordinated or junior to A-Debt. ₋ Debt cannot be subordinated to equity. Pledged assets: senior secured debt has priority over junior secured debt, which has priority over unsecured debt. 2. Unpledged asset: senior secured debt has priority over junior secured debt and unsecured debt, junior secured debt and unsecured debt share proceeds from remaining assets (pro-rata).

When does a company care about the secondary market?

If the stock price decreases, maybe the market knows something that the company doesn't

(d) The cost of debt does not change with leverage.

Incorrect

Capital expenditures create value for shareholders only if they are financed by debt

Incorrect, capital expenditures create value for stockholders if their NPV is positive.

True False: (b) Two firms with identical leverage have the same expected return on equity.

Incorrect, they need to have identical assets as well

(d) The β of a firm's assets (βA) increases with leverage.

Incorrect. From MM, leverage does not affect asset returns, therefore it does not affect βA = β0 either.

(c) The β of debt is always 0.

Incorrect. It is 0 if debt is risk-free, or if debt is risky but has no systematic risk, but not in general if debt is risky.

. Stock A has a 10% volatility and stock B a 18% volatility. According to the CAPM, what can you say about the expected return on A relative to the expected return on B?

Nothing, the CAPM yields a relation between systematic risk (i.e. β) and expected returns. Total risk (i.e. volatility σ) is not the relevant measure of risk

F has: ₋ Tranche A: Senior secured debt with face value 200. ₋ Tranche B: Junior secured debt with face value 200 (same securities as tranche A). ₋ Tranche C: Unsecured debt with face value 300 (same seniority as B). ₋ Tranche D: Subordinated debt with face value 200. ₋ F goes bankrupt and is liquidated: ₋ Scenario 1: value of pledged assets is 300, value of unpledged asset is 200. ₋ Scenario 2: value of pledged asset is 100, value of unpledged asset is 300. How much does each category of debtholders recover in each scenario?

Pledged: - A get 200 - B gets 100 Unpledged: - B gets (100/ (100+300)) (200) = 50 - C gets (300/ (100+300)) (200) = 150 - F gets nuthin since its is subordinated Pledged: - A get 100 Unpledged: - A gets 100 -- because they are the most senior - B gets (200/ (200+300)) (200) = 80 - C gets (300/ (200+300)) (200) = 120 - F gets nuthin since its is subordinated

Post money valuation formula - share

PostMV*(share)=(amt of financing)

Expected loss on default

Probability of default x loss given default

Which of these two firms has the highest Beta: Gap or Ralph Lauren?

Ralph Lauren -- more cyclical and more risky

in fine debt

Repayment is at maturity only

2) Does capital structure operation (e.g. raising debt) create value for stockholders?

Reshuffling the capital structure does not affect firm value, ₋ therefore it cannot create value for stockholders. ₋ Shareholder value creation comes only from the operational side: investing in NPV-positive projects

return of the stock of the levered firm

Rs =r0 + B/S (r0 − rB )

MM1 with taxes

S + B = S0 + TS

₋ F has 200,000 stocks outstanding at a market price of $50, and no debt. ₋ F plans to issue 3,000 bonds at par value ($1,000). ₋ The proceeds from the issuance will be used to pay a special dividend to shareholders. ₋ The corporate Tax rate is 30% 1. Compute the value of one stock after the operation. 2. Does the operation create value for stockholders?

S + B = S0 + TS 1) value of unlevered stock S0 = 200,000 ** 50 = 10 mm 2) TS = 3mm * .3 = .9 4) value together = 10.9 - value of bond (3 mm) = 7.9 mm 5) per share value = 7.9 mm / 200k = 39.5 6) Compare wealth Wbefore = 50 W after = 39.5 + 15 = 54.5 = difference is tax shield divided by number of shares 15 = 3mm / 200k

Firm F has a debt with maturity one year, face value 50 that pays an 8% annual interest rate. ₋ Value of F's assets in one year can be either 80 or 40 with equal probability. ₋ No taxes (to simplify). ₋ The β of F's equity is 0.8. rf=2% and E(rM)=8%. ₋ Compute the value of F equity.

Split Equity value into two with 50% chance of 80 - DEBT and 40 - Debt then discount back - the price = 12.17

CAPM predicts beta of 1.36, whereas the actual calculated beta is 1.3 Do you buy this stock?

Yes, stock delivers a return that corresponds to a risk β of 1.36, whereas its actual risk is 1.30 only. So you should buy this stock and your (expected) α over the next year will be 0.06 × (8.40% − 3.80%) = 0.276%

F is an all-equity firm with 500,000 common shares outstanding. Current market price of one stock is $20. F plans the following operation: issue 2,500 new bonds at par value and pay out the proceeds from the issuance to stockholders. How does the price of F's stock react to the announcement of the operation? *assume no tax*

The price of F's stock does not react to the announcement because the operation does not create or destroy any value for stockholders. Firm value before the operation is $10 million. The operation affects the capital structure only, so firm value after the operation is also $10 million. Equity value is therefore 10 − 2.5 =$7.5 million, so stock value is $15. Each stockholder receives a dividend of 2.5/0.5 =$5. So stockholder wealth after the operation is 15 + 5 = $20 just as before the operation. if there was tax then we should expect a change in the price based on the announcement to reflect the increase in the value of the firm due to the tax shield.

In the absence of frictions, unlevered cost of equity (r0) is equal to WACC

True

T/F (a) As long as debt is risk-free, the β of equity (βS) increases with leverage.

True

True or false: (a) As long as debt is risk-free, the expected return on equity increases with leverage.

True 1. (a) Correct: just look at MM2 formula with rB = rf . as long as debt is risk-free (rB=rf), rS increases with L. But, as L increases, rB might start to increase as well => impact of L on rS is unclear

Type of underwriting Bought deal -- Firm commitment underwriting

Underwriter guarentees he will sell the entire issue at a given price - most popular type of underwriting in the US and CA

Type of underwriting Best Effort Underwriting

Underwriter legally bound to use "best efforts" to sell the issue at the best price but does not gaurentee any amount of money to issuer

Fu and Fl have identical assets. V1 denotes the value of their assets in one year (random). ₋ Fu is unlevered: equity with market value S0. ₋ Fl is levered: ₋ Equity with market value S. ₋ Debt with market value B, face value D, maturity 1 year, coupon r. 1. Write the payoff of these two strategies as a function of V1: ₋ buy a fraction α of Fu equity, ₋ buy the same fraction α of Fl equity and debt. 2. What do you conclude about Fu and Fl firm value?

Value of Equity *(V1 - (1 +r)D)α* if V1 > (1 + r)D *0* if V1 < (1 + r)D Value of Debt *((1 +r)D)α* if V1 > (1 + r)D *αV1* if V1 < (1 + r)D Firm cannot pay its debt it liquidates ( αE , αD) (V1 - (1 +r)D)α + ((1 +r)D)α ---> if V1 > (1 + r)D 0 + αv1 if V1 < (1 + r)D in both cases S0 = αS + αB S0 = S + B - See the value of the stock and the bond of the levered firm = the value of the unlevered firm

When would having debt affect operational performance?

When covenants restrict the use of assets

Does failure to pay interest payments trigger default?

Yes - Interest payments are also tax deductable

Does failure to pay interest principal trigger default?

Yes - not tax deductible

Underpricing costs: You are the only stockholder of F. F has 1 million shares outstanding and needs to raise $2 millions for future investments ₋ Following book building, you and your underwriter set a price of $2 per share ⇒ F needs to issue 1 million new stocks. ₋ You want to use the IPO to cash out, but decide to sell only 50% of your stake (500 000 stocks) in the IPO. ₋ The final offer is therefore 1,500,000 stocks at $2 per stock. ₋ On the first day following the IPO, F's price goes up to $2.30 and then remain stable. After 1 month you sell your remaining 500,000 stocks at $2.30. What is an estimate of your loss on the shares sold in the IPO? How do you explain it? ₋ What is an estimate of your loss on the shares sold after the IPO? How do you explain it?

You must calculate the value of the firm after the month, i guess because of the underpriced IPO --> so the true vaue of the firm is $2.30 ** 2,000,000 = 4.6 mm and the pre money valuation is 4.6 mm - (2 ** 1,000,000 - the amont of the IPO) = 2.6 mm / 1 mm shares oustanding --> your shares should be worth 2.6 but instead you get 2.0 and 2.3 IPO lose = (2 - 2.6) ** 2,000,000 = - 300,000 (underpricing) 1 month later lose = (2.3 - 2.6) ** 2,000,000 = - 150,000 (dilution)

How much should you bid in a dutch auction and why?

Your actual value Bid = 11.75 Price > 11.75 - get nothing, but lose nothing Price = 11.75 - likely to get a share of n (11.75-11.75) = no real gain Price < 11.75 - get all the shares e.g 10(11.75 - p) = big gain So you are no worse by betting your value bet below - you may get a fraction when the price < 11.75 - but you'd lose compared to betting the amount Bet above - you lose when p > 11.75 since you may get 10 (11.76 - p) - say p = 11, you would end up with a negative number

Capital Structure with Taxes Application 3: Financing Investments F generates annual expected EBIT (=CF) of $5 million (perpetuity). ₋ F is unlevered (10 million shares), cost of equity r0 = 10%, Corporate Tax rate is 30% Existing Assets: 5(1-30%)/.1 = 35mm Equity = 35 mm New plant: additional expected $1 million per year, costs $3 million (net of PV of future tax deductions), does not modify the risk of F's assets. 1. The investment is financed with new equity. Write the BS of F a) right after the investment announcement, b) right after the equity issue (before the investment) c) after the investment. 2. Same question if investment is financed with debt

a) right after the investment announcement, assets: Old assets = 35 NPV = ((1 * (1 - T)) /.1 ) - 3 = 4 Liabilities / OE Equity = 39 b) right after the equity issue (before the investment) Old assets = NPV = Old assets = 35 NPV = 4 Cash = 3 Liabilities / OE Equity = 42 c) after the investment. Old assets = 35 plant = 7 Liabilities / OE Equity = 42 2. Same question if investment is financed with debt After announcement Tax shield = .3 **3 = .9 Equity = 39.9 3. After issuing debt --> assets = 35 After debt issuance Assets Liabilities Existing assets: $35 million Equity: $39.9 million (10,000,000 stocks) Investment NPV: $4 million Long-Term Debt: $3 million Cash: $3 million Tax Shield: $0.9 million After investment Assets Liabilities Existing assets: $35 million Equity: $39.9 million (10,000,000 stocks) New Assets: $7 million Long-Term Debt: $3 million Tax Shield: $0.9 million

Why are IPO's under priced? Application 6: The Winner Curse Suppose that (unlike reality), IPOs are fairly priced on average: abnormal return on first day is 15% (underpricing) or -15% (overpricing) with equal probability ₋ You can't distinguish between under- and overpriced issues, and you decide to buy 10 stocks in the next IPO ₋ Sophisticated investors only buy in underpriced IPOs ⇒ underpriced issues are oversubscribed and you only get 5 shares. You get 10 shares in other IPOs. assume price = $10 - compute the net profit from the strategy - what can you conclude about the opportunity to buy stocks? Suppose now that the return on underpriced issues is 40%. Are IPOs still fairly priced on average? ₋ Would you then be willing to buy stocks in the next IPO?

asymmetric information --> Less sophisticated investors are afraid of being disproportionately allocated in bad IPO's You have .5 (1.15 * 5 * 10) - 10* 5 = 7.5 and .5 ((1-.15) * 10 * 10) - 10* 10 = -15 = .5(7.5) + .5(-15) = -3.75 5 (1.40 * 5 * 10) - 10* 5 = 20 = .5(20) + .5(-15) = 2.5 -- yes in the second case you would invest

control rights

how and under which conditions the security holder can affect the firm's decisions - control of firm operational and financial decisions in "normal times".

cash flow rights

how much money the security holder can expect, and under which conditions - Dividends. ₋ Liquidation rights: remaining assets after all liabilities have been paid.

Risk that can be eliminated through diversification is called ______ risk.

idiosyncratic risk

Private debt

mostly bank debt

Stock Based Insolvency

net value assets < face value of debt

Flow-based Insolvency

operating cash-flow < debt service (i.e. interests payments + principal repayments)

Seasoned Equity Offering (SEO)

public company issues additional shares

• F generates 1mil net income per year. Valued at 10 million. - What is the required rate of return on F? • What is the yearly return on investment if you purchase F for 10 million (your own money)? • Suppose you can borrow 9 million in perpetual debt at 5% interest to finance a LBO. • Is the yearly return on investment the same now?

required rate of return on F: 10% the yearly return on investment if you purchase F for 10 million your own money = return / initial investment = 10% 1 - 9(.05) / 1 = 55% -- much more risky, since increased chance of default --> small fluactuations in the value of the firm transfers ownership of the company to debt holders

risk that cannot be eliminated through diversification

systematic

Same Companies, one is levered and the other isn't - What is the Price of levered firm + borrow 6,250 at risk free rate

t = 0 get 6,250 from borrowing t =1 CFfor all = sum of discounted stream of levered firms fcf * = pL* stock price of levered firm Value of *pL + 6250 = Pu *

Why have covenants?

to avoid increasing the interest rate on the debt

Everything else being equal, a firm with a higher leverage pays less corporate taxes

true

subordinated debt

unsecured debt that has the most junior claim on a company's assets

Post-money valuation:

value of the venture, given the terms of the equity issue, taking into account the cash raised in the issue.

Pre-money valuation:

value of the venture, given the terms of the equity issue, without taking into account the cash raised in the issue.

B

x

F develops a molecule with medical applications. ₋ F needs a seed investment of $500 000 (beginning of year 0). ₋ The estimated length of the development period is 3 years until F can apply for Federal Drug Agency (FDA) Approval. ₋ The estimated probability of successfully developing and obtain FDA approval is 10%. ₋ Estimated value of F if the product gets FDA approval and is $40 millions. ₋ You consider soliciting the VC Fund Bcom Partners. Expected return for biotech companies is 12%. ₋ What is the stake (% of equity) you need to offer Bcom Partners to get financed?

xV0 = .5 v0 = .1 * 40 / (1.12^3) x = 17.56%

Beta = linear

βPF = x1β1 + x2β2 + ...+ xN β

β is linear => MM2 relation translate easily

βS = β0 + L(β0 − βB ) β0 = 1 / (1+ L) βS + L / (1+ L) βB

Fu and Fl have the same fundamental risk. Fu is all equity and its stock has a β of 0.8. Fl has debt and its stock has a β of 1.1. Fl market capitalization is $1,000,000. Suppose that Fl 's debt carries no systematic risk, what is its market value?

βS = β0 + L(β0 − βB) - L = B / S - β of risk free debt = 0 1.1 = .8 + B / 1 (.8 - 0) B = .375 Total market cap = 1.375 mm

correlation of returns formula - on formula sheet

σAB / σAσB

Bankruptcy advantages

₋ (temporary) relief from obligations to creditors. ₋ Possibility to suspend payments/obligations from other contracts (union agreements, leases). ₋ Possibility to contract new loans by giving priority to new lenders (DIP)