Transcript
79927450Duke/Wal-Mart/Microso Portfolio
Variance
1. find xi for each stock
2. multiply xixj for every combination for each stock- table
3. multiply #2*Cov(xi,xj) Every combination -table
4. Add up all #’s in table= Var(RP)
00Duke/Wal-Mart/Microso Portfolio
Variance
1. find xi for each stock
2. multiply xixj for every combination for each stock- table
3. multiply #2*Cov(xi,xj) Every combination -table
4. Add up all #’s in table= Var(RP)
50914300Stock X/Y Table
Calculating Volatility for ind. stock
1a. Set Up Table- Find Avg. of returns columns for both
2a. (return in each period - #1) for both X/Y for every period
3a. Var(Ri)= SUM(#2)2 for each period- both X/Y
4a. ?i (volatility)= (#3)2 for both stocks
Correlation between X/Y
1b. Covariance= 1T-1*?(#2a Stock X each period)(#2a Stock Y each period)
2b. Correlation= #1b/(SDx)(SDY)
Variance of Weighted Portfolio
1c. Var(Rp)= (xx)(Var(Rx)) + (xy)(Var(Ry)) + 2(w1)(w2)(1b)
00Stock X/Y Table
Calculating Volatility for ind. stock
1a. Set Up Table- Find Avg. of returns columns for both
2a. (return in each period - #1) for both X/Y for every period
3a. Var(Ri)= SUM(#2)2 for each period- both X/Y
4a. ?i (volatility)= (#3)2 for both stocks
Correlation between X/Y
1b. Covariance= 1T-1*?(#2a Stock X each period)(#2a Stock Y each period)
2b. Correlation= #1b/(SDx)(SDY)
Variance of Weighted Portfolio
1c. Var(Rp)= (xx)(Var(Rx)) + (xy)(Var(Ry)) + 2(w1)(w2)(1b)
A) Modigliani and Miller's conclusion went against the common view that even with perfect capital markets, leverage would affect a firm's value.
B) We can evaluate the relationship between risk and return more formally by computing the sensitivity of each security's return to the systematic risk of the economy.
C) Investors in levered equity require a higher expected return to compensate for its increased risk.
D) Leverage increases the risk of equity even when there is no risk that the firm will default.
A) Leverage increases the risk of the equity of a firm.
B) Because the cash flows of the debt and equity sum to the cash flows of the project, by the Law of One Price the combined values of debt and equity must be equal to the cash flows of the project.
C) Franco Modigliani and Merton Miller argued that with perfect capital markets, the total value of a firm should not depend on its capital structure.
D) It is inappropriate to discount the cash flows of levered equity at the same discount rate that we use for unlevered equity.
A) With no debt, the WACC is equal to the unlevered equity cost of capital.
B) With perfect capital markets, a firm's WACC is independent of its capital structure and is equal to its equity cost of capital only the firm it is unlevered.
C) As the firm borrows at the low cost of capital for debt, its equity cost of capital rises, but the net effect is that the firm's WACC is unchanged.
D) Although debt has a lower cost of capital than equity, leverage does not lower a firm's WACC
A) The unlevered beta measures the market risk of the firm's business activities, ignoring any additional risk due to leverage.
B) If a firm holds $1 in cash and has $1 of risk-free debt, then the interest earned on the cash will equal the interest paid on the debt. The cash flows from each source cancel each other, just as if the firm held no cash and no..
C) The unlevered beta measures the market risk of the firm without leverage, which is equivalent to the beta of the firm's assets.
D) When a firm changes its capital structure without changing its investments, its unlevered beta will remain unaltered, however, its equity beta will change to reflect the effect of the capital structure change on its risk.
799274550800Expected Return on 2 stock Portfolio
1. ?port= sum of (xi)(?i) +(xj)( ?j)
2. rport= rf + #1(market r- rf)
00Expected Return on 2 stock Portfolio
1. ?port= sum of (xi)(?i) +(xj)( ?j)
2. rport= rf + #1(market r- rf)
A) FALSE- Firms adjust dividends relatively infrequently, and dividends are much less volatile than earnings. This practice of maintaining relatively constant dividends is called dividend signaling.
B) When a firm increases its dividend, it sends a positive signal to investors that management expects to be able to afford the higher dividend for the foreseeable future.
C) The average size of the stock price reaction increases with the magnitude of the dividend change, and is larger for dividend cuts.
D) When managers cut the dividend, it may signal that they have given up hope that earnings will rebound in the near term and need to reduce the dividend to save cash.
A) The Law of One Price implies that leverage will not affect the total value of the firm under perfect capital market conditions.
500282525400Table Problem given 3 stocks, weights, volatility (SD), corr
1A; Beta4Market = (V of market*1.0)/(v of market)
2A; Calculating Beta of individual stock
Beta A,B,C = (Volatility of stock*corr with M)/(Volatility of Market)
2B. Calculating Portfolio Beta = A(w)+B(w)+C(w) = X(beta)
3A. Expected Return on portfolio of 3 stocks
= risk-free rate + X(beta) * (market return – risk-free rate) = answer
4A. Sharpe Ratio Individual Stock for A, B or C ref 2A. (same work)
4B. (V of m – RF) / (Volatility of stock) A,b, or c.
00Table Problem given 3 stocks, weights, volatility (SD), corr
1A; Beta4Market = (V of market*1.0)/(v of market)
2A; Calculating Beta of individual stock
Beta A,B,C = (Volatility of stock*corr with M)/(Volatility of Market)
2B. Calculating Portfolio Beta = A(w)+B(w)+C(w) = X(beta)
3A. Expected Return on portfolio of 3 stocks
= risk-free rate + X(beta) * (market return – risk-free rate) = answer
4A. Sharpe Ratio Individual Stock for A, B or C ref 2A. (same work)
4B. (V of m – RF) / (Volatility of stock) A,b, or c.
B) In the absence of taxes or other transaction costs, the total cash flow paid out to all of a firm's security holders is equal to the total cash flow generated by the firm's assets.
C) With perfect capital markets, leverage merely changes the allocation of cash flows between debt and equity, without altering the total cash flows of the firm.
D) In a perfect capital market, the total value of a firm is equal to the market value of the total cash flows generated by its assets and is not affected by its choice of capital structure.
A) Vertically integrated companies are large, and as large corporations they are more difficult to run.
799401512700Growth/Value Stocks Portfolio
1. E[rx]= (w)(E[r]i) + (w)(E[r]j)
2. ?P2= (w1)2(v1)2 + (w2)2(v2)2 +
2(w1)(w2)(Corr)(v1)(v2)
3. Volatility Port. = sqrt. Of #2
4. Sharpe= (E[rx] - rf)/(volatility port)
00Growth/Value Stocks Portfolio
1. E[rx]= (w)(E[r]i) + (w)(E[r]j)
2. ?P2= (w1)2(v1)2 + (w2)2(v2)2 +
2(w1)(w2)(Corr)(v1)(v2)
3. Volatility Port. = sqrt. Of #2
4. Sharpe= (E[rx] - rf)/(volatility port)
B) A company might not be happy with how its products are being distributed, so it might decide to take control of its distribution channels.
C) A company might conclude that it can enhance its product if it has direct control of the inputs required to make the product.
D) The principal benefit of vertical integration is coordination. By putting two companies under central control, management can ensure that both companies work toward a common goal.
A) It is often argued that merging with or acquiring a major rival enables a firm to substantially reduce competition within the industry and thereby increase profits.
B) Financial researchers have found that the share prices of other firms in the same industry did not significantly increase following the announcement of a merger within the industry.
C) While all companies in an industry benefit when competition is reduced, only the merging company pays the associated costs.
D) Society as a whole bears the cost of monopoly strategies, so most countries have antitrust laws that limit such activity.
A) Once a tender offer is announced, the uncertainty about whether the takeover will succeed adds volatility to the stock price. This uncertainty creates an opportunity for investors to speculate on the outcome of the deal.
B) Traders known as risk-arbitrageurs, who believe that they can predict the outcome of a deal, take positions based on their beliefs.
C) A potential profit arises from the difference between the target's stock price and the implied offer price, and is referred to as the merger-arbitrage spread.
D) It is not true arbitrage because there is a risk that the deal will not go through. If the takeover did not ultimately succeed, the risk-arbitrageur would eventually have to unwind his position at whatever market prices .
A) Companies with poison pills are harder to take over, and when they are taken over, the premium that existing shareholders receive for their stock is higher.
B) Because a poison pill increases the cost of a takeover, all else equal, a target company must be in worse shape (there must be a greater opportunity for profit) to justify the expense of waging a takeover battle.
C) Poison pills also increase the bargaining power of the target firm when negotiating with the acquirer because poison pills make it difficult to complete the takeover without the cooperation of the target board.
D) By adopting a poison pill, a company effectively entrenches its management by making it much more difficult for shareholders to replace bad managers, thereby potentially destroying value.
A) A board is said to be captured when its monitoring duties have been compromised by connections or perceived loyalties to management.
B) Even the most active independent directors spend only one or two days per month on firm business, and many independent directors sit on multiple boards, further dividing their attention.
C) On a board composed of insider, gray, and independent directors, the role of the independent director is really that of a watchdog.
D) Because independent directors' personal wealth is likely to be less sensitive to performance than that of insider and gray directors, they have less incentive to closely monitor the firm.
23) If a stock pays dividends at the end of each quarter, with realized returns of R1, R2, R3, and R4 each quarter, then the annual realized return is calculated as:
585914582550Project- Weak/Strong Economy
NPV
1a. =[(prob. * weak FCF) + (prob. * strong FCF)]/(1 + cost of capital) – initial investment
MV of unlevered equity
2b. = #1a without subtracting initial investment
CF equity holders receive in weak economy, borrows at rf
3c. = Weak FCF – [Amount Borrowed*(1+rf)]
CF equity holders receive in strong economy, borrows at rf
4d. Strong FCF – [Amount Borrowed*(1+rf)]
MV of levered equity when firm borrows
5e. = #2b – Amount Borrowed
Cost of Capital if firm borrows at rf
6f. Write equation like below
#5e=prob. * #3c+(prob. * #1d)1+x
x=prob. * #1c+(prob. * #1d)#5e-1
00Project- Weak/Strong Economy
NPV
1a. =[(prob. * weak FCF) + (prob. * strong FCF)]/(1 + cost of capital) – initial investment
MV of unlevered equity
2b. = #1a without subtracting initial investment
CF equity holders receive in weak economy, borrows at rf
3c. = Weak FCF – [Amount Borrowed*(1+rf)]
CF equity holders receive in strong economy, borrows at rf
4d. Strong FCF – [Amount Borrowed*(1+rf)]
MV of levered equity when firm borrows
5e. = #2b – Amount Borrowed
Cost of Capital if firm borrows at rf
6f. Write equation like below
#5e=prob. * #3c+(prob. * #1d)1+x
x=prob. * #1c+(prob. * #1d)#5e-1
292544585090Value/Beta of New Project
Value of Project Division
1a. = rf + ?division*(market risk premium)
2b. = FCF(#1a-G)
Total Value of Company Projects
3c. Sum of #2b for every project division A, B, C
Overall Asset Beta of Company Projects
4d. = #2b/#3c- for every project = W a,b,c
Overall Cost of Capital
5e. Overall Beta = ?(Wa,b,c)( ?a,b,c) for every project A,B,C
00Value/Beta of New Project
Value of Project Division
1a. = rf + ?division*(market risk premium)
2b. = FCF(#1a-G)
Total Value of Company Projects
3c. Sum of #2b for every project division A, B, C
Overall Asset Beta of Company Projects
4d. = #2b/#3c- for every project = W a,b,c
Overall Cost of Capital
5e. Overall Beta = ?(Wa,b,c)( ?a,b,c) for every project A,B,C
A) Rannual =
B) Rannual = (1 + R1)(1 + R2)(1 + R3)(1 + R4)
C) Rannual = (1 + R1)(1 + R2)(1 + R3)(1 + R4) - 1
D) Rannual = R1 + R2 + R3 + R4
Answer: C
-825528575Stock Prices with Outstanding Data
1A. Market Cap = (share price * # shares outstanding) = *A,B,C
2A. total market cap= A+B+C
Value-Weight = (total market cap) / (*A,B, or C)
1b. find x of each stock = (#1a of ind. stock)/(#2a)
# of Shares to buy
1c. = (% of ind. Stock * total amount to invest)/price of stock
00Stock Prices with Outstanding Data
1A. Market Cap = (share price * # shares outstanding) = *A,B,C
2A. total market cap= A+B+C
Value-Weight = (total market cap) / (*A,B, or C)
1b. find x of each stock = (#1a of ind. stock)/(#2a)
# of Shares to buy
1c. = (% of ind. Stock * total amount to invest)/price of stock
2913380219710Price and Dividend Historical Data
Return Rate (Yield) For a period
= (Ps + D’s – Pp)/Pp
00Price and Dividend Historical Data
Return Rate (Yield) For a period
= (Ps + D’s – Pp)/Pp
2925445828675Realized Returns Index vs. Stock A problem
Standard Error on Stock A
1a. Find the average for stock A
2a. (R-R) = (year stock% - avg)
3a. (R-R) values all ^2
4a. Var(Stock A) = Sum of values in column (R-R)2 / (T-1)
5a. SD(Stock A)= sqrt. Of #4a
6a. Standard Error = #5a/sqrt. Of # of periods
If 10 years, divide by sqrt. Of 10
Forecast Expected future return on 95% confidence interval
1b. lower bound: #1a – (2 x #6a)
2b. Upper Bound: #1a + (2 x #6a)
2 = # of standard errors
00Realized Returns Index vs. Stock A problem
Standard Error on Stock A
1a. Find the average for stock A
2a. (R-R) = (year stock% - avg)
3a. (R-R) values all ^2
4a. Var(Stock A) = Sum of values in column (R-R)2 / (T-1)
5a. SD(Stock A)= sqrt. Of #4a
6a. Standard Error = #5a/sqrt. Of # of periods
If 10 years, divide by sqrt. Of 10
Forecast Expected future return on 95% confidence interval
1b. lower bound: #1a – (2 x #6a)
2b. Upper Bound: #1a + (2 x #6a)
2 = # of standard errors
-63502659380Cost of Capital of New Project
1. Find “E”= share price x # of shares
2. ?U = #1#1+D?E+D#1+D?D
3. ri = rf + #2*(market risk premium)
020000Cost of Capital of New Project
1. Find “E”= share price x # of shares
2. ?U = #1#1+D?E+D#1+D?D
3. ri = rf + #2*(market risk premium)
53975107950Historical Returns Problem
1a. Avg. wyatt oil Historical Return = (Wyo – RF) / (#Periods)
2b. Avg. wyatt Historical Excess Return = (Mr – Rf) / (#periods)
3c. Excess Return for both, beta is closest to = (1a. / 2b.)
4d. Beta for one year =( oil return% – [rf% + 3c.(Mr%-rf%)] )
020000Historical Returns Problem
1a. Avg. wyatt oil Historical Return = (Wyo – RF) / (#Periods)
2b. Avg. wyatt Historical Excess Return = (Mr – Rf) / (#periods)
3c. Excess Return for both, beta is closest to = (1a. / 2b.)
4d. Beta for one year =( oil return% – [rf% + 3c.(Mr%-rf%)] )
5861050260985Enterprise Value Questions
Enterprise Value
1a. EV= E + D – Cash
Asset Beta
1b. ?U = EE+D-C?E+DE+D-C?D-CE+D-C?C Beta of Cash=0
WACC
1c. rWACC= rf + #1b*(MRP)
00Enterprise Value Questions
Enterprise Value
1a. EV= E + D – Cash
Asset Beta
1b. ?U = EE+D-C?E+DE+D-C?D-CE+D-C?C Beta of Cash=0
WACC
1c. rWACC= rf + #1b*(MRP)
Variance of a portfolio =
Year End
Stock X Realized Return
Stock Y Realized Return
Stock X Deviation
(RL - RL)
Stock Y Deviation
(RH - RH)
(RL - RL)
×
(RH - RH)
2004
20.1%
-14.6%
-4.7%
-18.1%
0.00843889
2005
72.7%
4.3%
47.9%
0.8%
0.00391456
2006
-25.7%
-58.1%
-50.5%
-61.6%
0.31079056
2007
56.9%
71.1%
32.1%
67.6%
0.21727489
2008
6.7%
17.3%
-18.1%
13.8%
-0.02496211
2009
17.9%
0.9%
-6.9%
-2.6%
0.00177389
average =
24.8%
3.5%
Variance =
0.125447467
0.177795367
Stdev =
0.354185639
0.421657879
Covariance =
0.103446133
Correlation =
0.692664763
89007952620645X/Y
00X/Y
58654950IPO Problem
Amount Raised
1a. Amount Raised= (# shares issued*IPO price)*(1-UW fee)
Market Value after IPO
1b. Total # Shares Outstanding= # existing + # issued
2b. MV= #1b * Price After IPO
Suppose IPO value… raises same amount as in #1a…
1c. #2b= (# existing + N new shares) * new stock price P
= (E + N)P= #2b
2c. Amount Raised= N new shares * new stock Price P
= #1a= NP
= N= #1a/P
3c. Substitute #2c in for “N” in #1c to get
= [E + (#1a/P)]*P = #2b SOLVE FOR P
Total Cost to Firm’s original investors
1d. (P from #3c – Price after IPO)*(# of shares issued)
00IPO Problem
Amount Raised
1a. Amount Raised= (# shares issued*IPO price)*(1-UW fee)
Market Value after IPO
1b. Total # Shares Outstanding= # existing + # issued
2b. MV= #1b * Price After IPO
Suppose IPO value… raises same amount as in #1a…
1c. #2b= (# existing + N new shares) * new stock price P
= (E + N)P= #2b
2c. Amount Raised= N new shares * new stock Price P
= #1a= NP
= N= #1a/P
3c. Substitute #2c in for “N” in #1c to get
= [E + (#1a/P)]*P = #2b SOLVE FOR P
Total Cost to Firm’s original investors
1d. (P from #3c – Price after IPO)*(# of shares issued)
29317954157345Government Contracting and Manufacturing
Value of Plant if sales increase
1a. V= Revenue*1+sales increase-Other CostsCost of Capital
Value of Plant if Sales Decrease
1b. V= Revenue*1-sales decrease-Other CostsCost of Capital
*Note- plant can be sold or abandoned instead of taking a loss, choose option with highest value here- most likely sell price
Value with embedded option to sell plant
1c. V= (prob. Of increase * #1a) + (prob. of dec. * sell price)
Not able to sell plant, can shut down for $0
1d. V= (prob. of incr. * #1a) + (prob. of decr. * $0)
*Note- if the value of running the plant and taking a sales decrease is greater than 0, don’t abandon. Use the #1b value instead.
Value of Option to Abandon
1e. #1d – [(prob. of incr. * #1a) + (prob. of decr. * #1b if don’t sell or abandon)]
Value of Option to Sell Plant
1f. #1c – (#1d or #1b) depending on if can abandon or not and which one is higher
*When given multiple options, always choose the one with the highest possible value.
00Government Contracting and Manufacturing
Value of Plant if sales increase
1a. V= Revenue*1+sales increase-Other CostsCost of Capital
Value of Plant if Sales Decrease
1b. V= Revenue*1-sales decrease-Other CostsCost of Capital
*Note- plant can be sold or abandoned instead of taking a loss, choose option with highest value here- most likely sell price
Value with embedded option to sell plant
1c. V= (prob. Of increase * #1a) + (prob. of dec. * sell price)
Not able to sell plant, can shut down for $0
1d. V= (prob. of incr. * #1a) + (prob. of decr. * $0)
*Note- if the value of running the plant and taking a sales decrease is greater than 0, don’t abandon. Use the #1b value instead.
Value of Option to Abandon
1e. #1d – [(prob. of incr. * #1a) + (prob. of decr. * #1b if don’t sell or abandon)]
Value of Option to Sell Plant
1f. #1c – (#1d or #1b) depending on if can abandon or not and which one is higher
*When given multiple options, always choose the one with the highest possible value.
29317951947545Prototype Test Marketing and Plant Operations
Assuming company can sell prototype, NPV?
1a. NPV if successful= Successful CFCost of Capital-Initial Investment
2a. NPV if unsuccessful= Unsuccessful CFCost of Capital-Initial Investment
3a. Don’t Build (Sell Prototype) NPV= Sell Price. Sell prototype if sell NPV is higher than eating test costs
4a. NPV= prob. * #1a+(prob. * #3a)(1+cost of capital)-test marketing costs
Assuming can’t sell prototype, but can abandon, NPV?
1b. NPV if successful= #1a
2b. NPV if unsuccessful= #2a
3b. Don’t Build (Abandon) NPV= $0. If abandon NPV is greater than eating test costs, abandon.
4b. NPV= prob. * #1a+(prob. * 0)(1+cost of captial)-test marketing costs
*Note- if can’t sell and unsuccessful NPV is greater than 0, use unsuccessful NPV instead
00Prototype Test Marketing and Plant Operations
Assuming company can sell prototype, NPV?
1a. NPV if successful= Successful CFCost of Capital-Initial Investment
2a. NPV if unsuccessful= Unsuccessful CFCost of Capital-Initial Investment
3a. Don’t Build (Sell Prototype) NPV= Sell Price. Sell prototype if sell NPV is higher than eating test costs
4a. NPV= prob. * #1a+(prob. * #3a)(1+cost of capital)-test marketing costs
Assuming can’t sell prototype, but can abandon, NPV?
1b. NPV if successful= #1a
2b. NPV if unsuccessful= #2a
3b. Don’t Build (Abandon) NPV= $0. If abandon NPV is greater than eating test costs, abandon.
4b. NPV= prob. * #1a+(prob. * 0)(1+cost of captial)-test marketing costs
*Note- if can’t sell and unsuccessful NPV is greater than 0, use unsuccessful NPV instead
29317950Market Value Balance Sheet
WACC
1a. rWACC=EE+D-CrE+DE+D-CrD(1-?c)
NPV = CF1(#1c)1+CF2(#1c)2+CF3(#1c)3 - Year 0 cash flow
Unlevered Cost of Capital
1c. runlevered=EE+D-CrE+DE+D-CrD
Unlevered Value
1d. VU= CF1(#1c)1+CF2(#1c)2+CF3(#1c)3
Interest Tax Shield in year 1
1e. Levered V0= #1b + Initial Investment (add it back in)
2e. D0= (DE+D-C)*(#1e)
3e. Interest Tax Shield = #2e*rD*?c
00Market Value Balance Sheet
WACC
1a. rWACC=EE+D-CrE+DE+D-CrD(1-?c)
NPV = CF1(#1c)1+CF2(#1c)2+CF3(#1c)3 - Year 0 cash flow
Unlevered Cost of Capital
1c. runlevered=EE+D-CrE+DE+D-CrD
Unlevered Value
1d. VU= CF1(#1c)1+CF2(#1c)2+CF3(#1c)3
Interest Tax Shield in year 1
1e. Levered V0= #1b + Initial Investment (add it back in)
2e. D0= (DE+D-C)*(#1e)
3e. Interest Tax Shield = #2e*rD*?c
left4007485Repurchase Shares/Share Prices
Price Per Share if firm is able to repurchase shares prior to market becoming aware of new info regarding true value- price after repurchase
1a. # of shares repurchased= Cash Invested/Current Share Price
2a. # Shares outstanding after repurchase= # original outs. - #1a
3a.True Value before repurch.= True Price * # original shares outs.
4a. True V after repurch.= #3a – Cash Invested
5a. P = #4a/#2a
Price Per Share if firm is not able to repurchase shares prior to market becoming aware of new info regarding true value- price after repurchase
1b. # of share repurchased= Cash Invested/True Share Price
2b. # shares outstanding after repurch.= # original outs. - #1b
3b. True Value before repurch= #3a
4b. True Value after repurch= #4a
5b. P = #4b/#2b
00Repurchase Shares/Share Prices
Price Per Share if firm is able to repurchase shares prior to market becoming aware of new info regarding true value- price after repurchase
1a. # of shares repurchased= Cash Invested/Current Share Price
2a. # Shares outstanding after repurchase= # original outs. - #1a
3a.True Value before repurch.= True Price * # original shares outs.
4a. True V after repurch.= #3a – Cash Invested
5a. P = #4a/#2a
Price Per Share if firm is not able to repurchase shares prior to market becoming aware of new info regarding true value- price after repurchase
1b. # of share repurchased= Cash Invested/True Share Price
2b. # shares outstanding after repurch.= # original outs. - #1b
3b. True Value before repurch= #3a
4b. True Value after repurch= #4a
5b. P = #4b/#2b
left2582545Expansion Project/Share Prices
Price Per Share if expand using cash
1a. Value= FCF*(1+FCF%)Cost of Capital
2a. Price= #1a/(# of shares outstanding)
Price Per Share if not to expand using cash (hold)
1b. Value= FCFCost of Capital+Cash Value
2b. Price= #1b/(# of shares outstanding)
NPV of expansion project
1c. = =FCF*(FCF%)Cost of Capital-In Cash
00Expansion Project/Share Prices
Price Per Share if expand using cash
1a. Value= FCF*(1+FCF%)Cost of Capital
2a. Price= #1a/(# of shares outstanding)
Price Per Share if not to expand using cash (hold)
1b. Value= FCFCost of Capital+Cash Value
2b. Price= #1b/(# of shares outstanding)
NPV of expansion project
1c. = =FCF*(FCF%)Cost of Capital-In Cash
left0Project- Weak/Strong Economy
NPV
1a. =[(prob. * weak FCF) + (prob. * strong FCF)]/(1 + cost of capital) – initial investment
MV of unlevered equity
1b. PV(equity CF)= #1a without subtracting initial investment
CF equity holders receive in weak economy, borrows at rf
1c. = Weak FCF – [Amount Borrowed*(1+rf)]
CF equity holders receive in strong economy, borrows at rf
1d. Strong FCF – [Amount Borrowed*(1+rf)]
MV of levered equity when firm borrows
1e. = #1b – Amount Borrowed
Cost of Capital if firm borrows at rf
1f. Write equation like below
#1e=prob. * #1c+(prob. * #1d)1+x
x=prob. * #1c+(prob. * #1d)#1e-1
Separate Part same topic
Equity Cost of Capitalc
1g. = COC+[(Amount Borrowed#1b-Amount Borrowed)*(COC-rf)]
00Project- Weak/Strong Economy
NPV
1a. =[(prob. * weak FCF) + (prob. * strong FCF)]/(1 + cost of capital) – initial investment
MV of unlevered equity
1b. PV(equity CF)= #1a without subtracting initial investment
CF equity holders receive in weak economy, borrows at rf
1c. = Weak FCF – [Amount Borrowed*(1+rf)]
CF equity holders receive in strong economy, borrows at rf
1d. Strong FCF – [Amount Borrowed*(1+rf)]
MV of levered equity when firm borrows
1e. = #1b – Amount Borrowed
Cost of Capital if firm borrows at rf
1f. Write equation like below
#1e=prob. * #1c+(prob. * #1d)1+x
x=prob. * #1c+(prob. * #1d)#1e-1
Separate Part same topic
Equity Cost of Capitalc
1g. = COC+[(Amount Borrowed#1b-Amount Borrowed)*(COC-rf)]
XiXj
XDuke
XMicrosoft
XWal-Mart
XDuke
0.04
0.06
0.1
XMicrosoft
0.06
0.09
0.15
XWal-Mart
0.1
0.15
0.25
801179555880
XiXjCOV(I,j)
Duke
Microsoft
Wal-Mart
Duke
0.002272
-0.00116
0.000367
Microsoft
-0.00116
0.021776
0.019153
Wal-Mart
0.000367
0.019153
0.035318
Var(P) =
0.096086
8011795286385008208645133353 portfolio cov/var
003 portfolio cov/var
Year End
Stock X Realized Return
Stock Y Realized Return
Stock X Deviation
(RL - RL)
Stock Y Deviation
(RH - RH)
(RL - RL)
×
(RH - RH)
2004
20.1%
-14.6%
-4.7%
-18.1%
0.00843889
2005
72.7%
4.3%
47.9%
0.8%
0.00391456
2006
-25.7%
-58.1%
-50.5%
-61.6%
0.31079056
2007
56.9%
71.1%
32.1%
67.6%
0.21727489
2008
6.7%
17.3%
-18.1%
13.8%
-0.02496211
2009
17.9%
0.9%
-6.9%
-2.6%
0.00177389
average =
24.8%
3.5%
Variance =
0.125447467
0.177795367
Stdev =
0.354185639
0.421657879
Covariance =
0.103446133
Correlation =
0.692664763
89007952620645X/Y
00X/Y
58654950IPO Problem
Amount Raised
1a. Amount Raised= (# shares issued*IPO price)*(1-UW fee)
Market Value after IPO
1b. Total # Shares Outstanding= # existing + # issued
2b. MV= #1b * Price After IPO
Suppose IPO value… raises same amount as in #1a…
1c. #2b= (# existing + N new shares) * new stock price P
= (E + N)P= #2b
2c. Amount Raised= N new shares * new stock Price P
= #1a= NP
= N= #1a/P
3c. Substitute #2c in for “N” in #1c to get
= [E + (#1a/P)]*P = #2b SOLVE FOR P
Total Cost to Firm’s original investors
1d. (P from #3c – Price after IPO)*(# of shares issued)
00IPO Problem
Amount Raised
1a. Amount Raised= (# shares issued*IPO price)*(1-UW fee)
Market Value after IPO
1b. Total # Shares Outstanding= # existing + # issued
2b. MV= #1b * Price After IPO
Suppose IPO value… raises same amount as in #1a…
1c. #2b= (# existing + N new shares) * new stock price P
= (E + N)P= #2b
2c. Amount Raised= N new shares * new stock Price P
= #1a= NP
= N= #1a/P
3c. Substitute #2c in for “N” in #1c to get
= [E + (#1a/P)]*P = #2b SOLVE FOR P
Total Cost to Firm’s original investors
1d. (P from #3c – Price after IPO)*(# of shares issued)
29317954157345Government Contracting and Manufacturing
Value of Plant if sales increase
1a. V= Revenue*1+sales increase-Other CostsCost of Capital
Value of Plant if Sales Decrease
1b. V= Revenue*1-sales decrease-Other CostsCost of Capital
*Note- plant can be sold or abandoned instead of taking a loss, choose option with highest value here- most likely sell price
Value with embedded option to sell plant
1c. V= (prob. Of increase * #1a) + (prob. of dec. * sell price)
Not able to sell plant, can shut down for $0
1d. V= (prob. of incr. * #1a) + (prob. of decr. * $0)
*Note- if the value of running the plant and taking a sales decrease is greater than 0, don’t abandon. Use the #1b value instead.
Value of Option to Abandon
1e. #1d – [(prob. of incr. * #1a) + (prob. of decr. * #1b if don’t sell or abandon)]
Value of Option to Sell Plant
1f. #1c – (#1d or #1b) depending on if can abandon or not and which one is higher
*When given multiple options, always choose the one with the highest possible value.
00Government Contracting and Manufacturing
Value of Plant if sales increase
1a. V= Revenue*1+sales increase-Other CostsCost of Capital
Value of Plant if Sales Decrease
1b. V= Revenue*1-sales decrease-Other CostsCost of Capital
*Note- plant can be sold or abandoned instead of taking a loss, choose option with highest value here- most likely sell price
Value with embedded option to sell plant
1c. V= (prob. Of increase * #1a) + (prob. of dec. * sell price)
Not able to sell plant, can shut down for $0
1d. V= (prob. of incr. * #1a) + (prob. of decr. * $0)
*Note- if the value of running the plant and taking a sales decrease is greater than 0, don’t abandon. Use the #1b value instead.
Value of Option to Abandon
1e. #1d – [(prob. of incr. * #1a) + (prob. of decr. * #1b if don’t sell or abandon)]
Value of Option to Sell Plant
1f. #1c – (#1d or #1b) depending on if can abandon or not and which one is higher
*When given multiple options, always choose the one with the highest possible value.
29317951947545Prototype Test Marketing and Plant Operations
Assuming company can sell prototype, NPV?
1a. NPV if successful= Successful CFCost of Capital-Initial Investment
2a. NPV if unsuccessful= Unsuccessful CFCost of Capital-Initial Investment
3a. Don’t Build (Sell Prototype) NPV= Sell Price. Sell prototype if sell NPV is higher than eating test costs
4a. NPV= prob. * #1a+(prob. * #3a)(1+cost of capital)-test marketing costs
Assuming can’t sell prototype, but can abandon, NPV?
1b. NPV if successful= #1a
2b. NPV if unsuccessful= #2a
3b. Don’t Build (Abandon) NPV= $0. If abandon NPV is greater than eating test costs, abandon.
4b. NPV= prob. * #1a+(prob. * 0)(1+cost of captial)-test marketing costs
*Note- if can’t sell and unsuccessful NPV is greater than 0, use unsuccessful NPV instead
00Prototype Test Marketing and Plant Operations
Assuming company can sell prototype, NPV?
1a. NPV if successful= Successful CFCost of Capital-Initial Investment
2a. NPV if unsuccessful= Unsuccessful CFCost of Capital-Initial Investment
3a. Don’t Build (Sell Prototype) NPV= Sell Price. Sell prototype if sell NPV is higher than eating test costs
4a. NPV= prob. * #1a+(prob. * #3a)(1+cost of capital)-test marketing costs
Assuming can’t sell prototype, but can abandon, NPV?
1b. NPV if successful= #1a
2b. NPV if unsuccessful= #2a
3b. Don’t Build (Abandon) NPV= $0. If abandon NPV is greater than eating test costs, abandon.
4b. NPV= prob. * #1a+(prob. * 0)(1+cost of captial)-test marketing costs
*Note- if can’t sell and unsuccessful NPV is greater than 0, use unsuccessful NPV instead
29317950Market Value Balance Sheet
WACC
1a. rWACC=EE+D-CrE+DE+D-CrD(1-?c)
NPV = CF1(#1c)1+CF2(#1c)2+CF3(#1c)3 - Year 0 cash flow
Unlevered Cost of Capital
1c. runlevered=EE+D-CrE+DE+D-CrD
Unlevered Value
1d. VU= CF1(#1c)1+CF2(#1c)2+CF3(#1c)3
Interest Tax Shield in year 1
1e. Levered V0= #1b + Initial Investment (add it back in)
2e. D0= (DE+D-C)*(#1e)
3e. Interest Tax Shield = #2e*rD*?c
00Market Value Balance Sheet
WACC
1a. rWACC=EE+D-CrE+DE+D-CrD(1-?c)
NPV = CF1(#1c)1+CF2(#1c)2+CF3(#1c)3 - Year 0 cash flow
Unlevered Cost of Capital
1c. runlevered=EE+D-CrE+DE+D-CrD
Unlevered Value
1d. VU= CF1(#1c)1+CF2(#1c)2+CF3(#1c)3
Interest Tax Shield in year 1
1e. Levered V0= #1b + Initial Investment (add it back in)
2e. D0= (DE+D-C)*(#1e)
3e. Interest Tax Shield = #2e*rD*?c
left4007485Repurchase Shares/Share Prices
Price Per Share if firm is able to repurchase shares prior to market becoming aware of new info regarding true value- price after repurchase
1a. # of shares repurchased= Cash Invested/Current Share Price
2a. # Shares outstanding after repurchase= # original outs. - #1a
3a.True Value before repurch.= True Price * # original shares outs.
4a. True V after repurch.= #3a – Cash Invested
5a. P = #4a/#2a
Price Per Share if firm is not able to repurchase shares prior to market becoming aware of new info regarding true value- price after repurchase
1b. # of share repurchased= Cash Invested/True Share Price
2b. # shares outstanding after repurch.= # original outs. - #1b
3b. True Value before repurch= #3a
4b. True Value after repurch= #4a
5b. P = #4b/#2b
00Repurchase Shares/Share Prices
Price Per Share if firm is able to repurchase shares prior to market becoming aware of new info regarding true value- price after repurchase
1a. # of shares repurchased= Cash Invested/Current Share Price
2a. # Shares outstanding after repurchase= # original outs. - #1a
3a.True Value before repurch.= True Price * # original shares outs.
4a. True V after repurch.= #3a – Cash Invested
5a. P = #4a/#2a
Price Per Share if firm is not able to repurchase shares prior to market becoming aware of new info regarding true value- price after repurchase
1b. # of share repurchased= Cash Invested/True Share Price
2b. # shares outstanding after repurch.= # original outs. - #1b
3b. True Value before repurch= #3a
4b. True Value after repurch= #4a
5b. P = #4b/#2b
left2582545Expansion Project/Share Prices
Price Per Share if expand using cash
1a. Value= FCF*(1+FCF%)Cost of Capital
2a. Price= #1a/(# of shares outstanding)
Price Per Share if not to expand using cash (hold)
1b. Value= FCFCost of Capital+Cash Value
2b. Price= #1b/(# of shares outstanding)
NPV of expansion project
1c. = =FCF*(FCF%)Cost of Capital-In Cash
00Expansion Project/Share Prices
Price Per Share if expand using cash
1a. Value= FCF*(1+FCF%)Cost of Capital
2a. Price= #1a/(# of shares outstanding)
Price Per Share if not to expand using cash (hold)
1b. Value= FCFCost of Capital+Cash Value
2b. Price= #1b/(# of shares outstanding)
NPV of expansion project
1c. = =FCF*(FCF%)Cost of Capital-In Cash
left0Project- Weak/Strong Economy
NPV
1a. =[(prob. * weak FCF) + (prob. * strong FCF)]/(1 + cost of capital) – initial investment
MV of unlevered equity
1b. PV(equity CF)= #1a without subtracting initial investment
CF equity holders receive in weak economy, borrows at rf
1c. = Weak FCF – [Amount Borrowed*(1+rf)]
CF equity holders receive in strong economy, borrows at rf
1d. Strong FCF – [Amount Borrowed*(1+rf)]
MV of levered equity when firm borrows
1e. = #1b – Amount Borrowed
Cost of Capital if firm borrows at rf
1f. Write equation like below
#1e=prob. * #1c+(prob. * #1d)1+x
x=prob. * #1c+(prob. * #1d)#1e-1
Separate Part same topic
Equity Cost of Capitalc
1g. = COC+[(Amount Borrowed#1b-Amount Borrowed)*(COC-rf)]
00Project- Weak/Strong Economy
NPV
1a. =[(prob. * weak FCF) + (prob. * strong FCF)]/(1 + cost of capital) – initial investment
MV of unlevered equity
1b. PV(equity CF)= #1a without subtracting initial investment
CF equity holders receive in weak economy, borrows at rf
1c. = Weak FCF – [Amount Borrowed*(1+rf)]
CF equity holders receive in strong economy, borrows at rf
1d. Strong FCF – [Amount Borrowed*(1+rf)]
MV of levered equity when firm borrows
1e. = #1b – Amount Borrowed
Cost of Capital if firm borrows at rf
1f. Write equation like below
#1e=prob. * #1c+(prob. * #1d)1+x
x=prob. * #1c+(prob. * #1d)#1e-1
Separate Part same topic
Equity Cost of Capitalc
1g. = COC+[(Amount Borrowed#1b-Amount Borrowed)*(COC-rf)]
XiXj
XDuke
XMicrosoft
XWal-Mart
XDuke
0.04
0.06
0.1
XMicrosoft
0.06
0.09
0.15
XWal-Mart
0.1
0.15
0.25
801179555880
XiXjCOV(I,j)
Duke
Microsoft
Wal-Mart
Duke
0.002272
-0.00116
0.000367
Microsoft
-0.00116
0.021776
0.019153
Wal-Mart
0.000367
0.019153
0.035318
Var(P) =
0.096086
8011795286385008208645133353 portfolio cov/var
003 portfolio cov/var