Private Equity Transforming Public Stock To Create Value 1st Edition Harold Bierman - Solutions

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Consider a one-period economy and an individual with a time-additive but state-dependent expected utility so that the objective is maxθ u(c0, X0) + e−δ E[u(c, X)].The decisions of the individual do not affect X0 or X. For example, X0 and X could be the aggregate consumption in the economy at
Use Eq. (5.7) to compute approximate relative risk premia for the consumption gamble underlying Table 5.5 and compare with the exact numbers given in the table.
Consider an individual with log-utility, u(c) = lnc. What is her certainty equivalent and consumption risk premium for the consumption plan which with probability 0.5 gives her (1 − α)c¯ and with probability 0.5 gives her(1 + α)c¯? Confirm that your results are consistent with the numbers for
Provide a proof of Theorem 5.5.
Consider an atemporal setting in which an individual has a utility function u of consumption. His current consumption isc. As always, the absolute risk aversion is ARA(c) = −u(c)/u(c) and the relative risk aversion is RRA(c) = −cu(c)/u(c).Let ε ∈ [0,c] and consider an additive gamble
Consider a one-period choice problem with four equally likely states of the world at the end of the period. The consumer maximizes expected utility of end-of-period wealth. The current wealth must be invested in a single financial asset today. The consumer has three assets to choose between. All
(Adapted from Chapter 3 in Kreps (1990).) Imagine a greedy, risk-averse, expected utility maximizing consumer whose end-of-period income level is subject to some uncertainty. The income will be Y with probability p¯ and Y < Y with probability 1 − p¯.Think of = Y − Y as some loss the
(Adapted from Problem 3.3 in Kreps (1990).) Consider the following two probability distributions of consumption. π1 gives 5, 15, and 30 (dollars) with probabilities 1/3, 5/9, and 1/9, respectively. π2 gives 10 and 20 with probabilities 2/3 and 1/3, respectively.(a) Show that we can think of π1
Give a proof of Theorem 5.3.
Consider a two-period arbitrage-free economy where the resolution of uncertainty is illustrated in the following binomial tree.t = 0 t = 1 t = 2 10.9 0.95 0.95(2; 8)(8; 2)(6; 10)(10; 4) (10; 6)(4; 10) 0.85 0.9 Each branch in the tree has a conditional probability of 1 2 . Assets in the economy are
In a one-period framework show that if x is a pricing factor and k1, k2 are constants with k2 = 0, then y = k1 + k2x is also a pricing factor.
Show that ζ ∗t = V∗0 /V∗t , whereV∗ and ζ ∗ are given by Eqs. (4.42) and (4.41).
Consider a continuous-time economy in which the state-price deflator follows a geometric Brownian motion:dζt = −ζtrf dt + λ dzt, where rf and λ are constant.(a) What is the price Bs t of a zero-coupon bond maturing at time s with a face value of 1?Define the continuously compounded yield ys
Consider a two-period economy where the resolution of uncertainty can be represented by the tree in Fig. 2.2 in Chapter 2. Assume that three assets are traded. Their dividend processes are illustrated in Fig. 4.1, where a triple (D1, D2, D3) near a node means that asset i = 1, 2, 3 pays a dividend
Consider a one-period economy where two basic financial assets are traded without portfolio constraints or transaction costs. There are three equally likely end-ofperiod states of the economy and the prices and state-contingent dividends of the two assets are given in the following
Consider a one-period economy where the assets are correctly priced by a state-price deflator M. A nutty professor believes that the assets are priced according to a model in which Y is a state-price deflator, where Y is a random variable with E[Y] = E[M].Refer to this model as the Y-model.(a) Show
Assume a one-period framework with no redundant assets. Show that ζ ∗ can be rewritten as in (4.47).
Show Lemma 4.1.
Give a proof of Theorem 4.7 both for the one-period framework and the continuous-time framework.
Consider a one-period, three-state economy with two assets traded. Asset 1 has a price of 0.9 and pays a dividend of 1 no matter what state is realized. Asset 2 has a price of 2 and pays 1, 2, and 4 in state 1, 2, and 3, respectively. The real-world probabilities of the states are 0.2, 0.6, and
Imagine a one-period economy where the state-price deflator ζ is lognormally distributed with E[ln ζ ] = μζ and Var[ln ζ ] = σ 2ζ . What is the maximal Sharpe ratio of a risky asset? (Look at Eq. (4.8).) What determines the sign of an asset’s Sharpe ratio?
In a one-period two-state economy the risk-free interest rate over the period is 25%. An asset that pays out 100 in state 1 and 200 in state 2 trades at a price of 110.(a) What is the no-arbitrage price of a second risky asset that pays out 200 in state 1 and 100 in state 2?(b) If this second risky
Verify Eq. (3.5).
Imagine a one-period economy with two possible end-of-period states that are equally likely. Two assets are traded. Asset 1 has an initial price of 1 and pays off 1 in state 1 and 2 in state 2. Asset 2 has an initial price of 3 and gives a payoff of 2 in state 1 and a payoff k in state 2, where k
Consider a one-period model with only two possible end-of-period states.Three assets are traded in an arbitrage-free market. Asset 1 is a risk-free asset with a price of 1 and an end-of-period dividend of Rf , the risk-free gross rate of return. Asset 2 has a price of S and offers a dividend of uS
The dynamics of the continuous-time stochastic processes X = (Xt) and Y =(Yt) are given by dXt = Xt [μX dt + σX dz1t], dYt = μY dt + ρσY dz1t +'1 − ρ2σY dz2t, where z1 and z2 are independent standard Brownian motions, and μX, σX,μY, ρ, σY are constants with σX, σY ≥ 0 and ρ ∈
(Adapted from Björk (2009)) Define the process y = (yt) by yt = eazt , where a is a constant and z = (zt) is a standard Brownian motion. Find the dynamics of y. Show that yt = 1 +1 2a2 t0 ys ds + a t0 ys dzs.Define m(t) = E[yt]. Show that m satisfies the ordinary differential equation m(t) = 1
(Adapted from Björk (2009)) Define the process y = (yt) by yt = z4 t , where z = (zt) is a standard Brownian motion. Find the dynamics of y. Show that yt = 6 t0 z2 s ds + 4 t0 z3 s dzs.Show that E[yt] ≡ E[z4 t ] = 3t 2.
Suppose that the continuous-time stochastic process X = (Xt) is defined as Xt = 1 2t 0λ2 s ds +t 0λs dzs, where z = (zt) is a one-dimensional standard Brownian motion and λ = (λt) is some ‘nice’stochastic process.(a) Argue that dXt = 1 2 λ2 t dt + λt dzt.(b) Suppose that the
Suppose X = (Xt)is a geometric Brownian motion, dXt = μXt dt + σXt dzt.What is the dynamics of the process y = (yt) defined by yt = (Xt)n?What can you say about the distribution of future values of the y process?
Let X = (Xt) and Y = (Yt) be the price processes of two assets with no intermediate dividends and assume that dXt = Xt [0.05 dt + 0.1 dz1t + 0.2 dz2t], dYt = Yt [0.07 dt + 0.3 dz1t − 0.1 dz2t].(a) What is the expected rate of return of each of the two assets?(b) What is the return variance and
What are the advantages of a firm with publicly traded stock?
a. A firm's equity has a value of $604.Investors are taxed on ordinary income at .396 and on capital gains at .20. Assume that the firm's equity is purchased for $604. Instead of a $100 dividend the corporation will retain $125 per year and will earn .15 on reinvested funds. The reinvested earnings
A corporation has a market capitalization of $400,000,000 and annual cash flow of $100,000,000. There are 20,000,000 shares outstanding. Maintenance Cap-Ex is $10,000,000. The stock price is $20.If cash flow in excess of maintenance Cap-Ex is used to repurchase shares, how many shares can be
How much debt did Metromedia issue on November 30, 1984?
Was the total outlay of $1,183,000,000 to the shareholders too high? Assume the stock was selling no higher than $35.75 before the offer. What value do you place on Metromedia's equity?
As a stockbroker would you tender your stock for an offer price of $40?
How was value added?
If you were structuring the bank debt or the replacement debt, what would you (the lender) change?
What was the value of Kluge's equity immediately before the LBO? Assume a stock value of $20.38 per share.
Assume a firm value of $1,228,000,000 after the LBO (before any sale of pieces). What was the value of Kluge's equity?
What is the maximum value KKR should bid assuming the $50 stock price accurately reflects the firm's value before the LBO competition starts?
What is the maximum amount of .12 debt (incremental) that RJR can support? What would be the effect of a higher interest rate?
How much did KKR pay for the common stock of RJR?
Did KKR overpay for RJR? Did KKR win or lose?
Using just the balance sheet, determine the value of the Marietta Corporation as of September 30, 1995. Assume Marietta debt yields .10 contractually and the current rate for equivalent risk debt is .06.
As a stockholder, would you accept the $10.25 offer? Assume there are 3,621,000 shares outstanding and that the calculations are based on the information from the quarter ending December 30, 1995.
If you acquired Marietta, what would be your capital structure?What would be the value per share?
What should the management and Board of Directors have done, given the $11 offer?
What is happening to U.S. Can?
Who and what are the rollover stockholders?
What are the tax consequences of the transaction to the selling stockholders?
There is a one-time cash bonus of $1,182,700 for management.What do you think?
What percentage of equity will management own? What per centage of common equity?
If the total equity is $160 million after the recap, what is the value of management's investment? What was the value before the recap if management owned .54% of the equity?
How much were the total fees associated with the recapitaliza tion?
What was the stock price on the last trading day before the re cap announcement? What premium is being paid?
See the buying history. What do you think?
Assuming a market value of $15 per share and 13,442,000 shares what was the common stock's total value? With the earnings of $21,156,000 for 1999, what was P/E? What was the EPS?
The EBITDA for June 30, 2000 is $106.4 million. The ratio of market cap to EBITDA is what?
Which of the facts given in the case are relevant in determining your preference of offers? How is value created?
Assuming an initial $40 stock price, what was the value of the stock equity before the restructuring?
Estimate the stock price per share after the second offer is accepted, and after the buyout of Mesa and after the three-for-one split.
The answers to (2) and (3) implicitly make what assumptions?
How much value per share does a shareholder receive from the second offer?
Carl Icahn demanded:■ More preferred stock■ Larger common stock dividend■ A three for one stock split Of what economic significance are these changes?
If the first offer was worth $51.83 per share and the second offer was worth $52.39, what is the total value difference in the two offers?
Icahn and Pickens each received $25,000,000 to cover expenses.Is this ethical? Strategically sound?
Who won? Who lost?
Should Mr. Boeschenstein accept the Wickes offer?
What is the value of the $35 debenture (assume a .15 discount rate)?
Assume the initial stock price is $50 and there are 29,695,000 shares outstanding initially. There are 347,000 shares in the ESOP that will not be exchanged (they will receive a number of new shares). There will be 29,348,000 shares exchanged and re ceiving $52 cash, a debenture (see 2), and a new
What is the value of the distribution to a shareholder if the in vestment banker's plan is accepted? Use the information from questions (2) and (3).
If the investment banker's plan is accepted what real things should OCF management then do?
How can management turn this negative event (a raid by Wickes)into a positive event?
If the firm guarantees that the ESOP will receive as much value as the shareholders receive who exchange, what will be the new stock price if the new stock equity value is $141,000,000 after the exchange?
Why are insurance companies more likely to buy preferred stock than individuals?
a. Assume the market capitalization of a firm's stock is $6,500,000 and there is $10,000,000 of debt outstanding. How much additional debt can be issued if the $6,500,000 is accepted as being reasonable? There is a .35 corporate tax rate.b. If a bid of $7,000,000 is made for the $6,500,000 of
If equity investors contribute $1,000,000 and want a .30 return at time 4, how much do they require at time 4?
a. Assume an investor can earn .12 before investor tax and .07248 after investor tax. The tax rate on ordinary income is .396. If the corporation pays a $100 dividend, after 20 years the investor will have how much?b. If the corporation retains the $100 and earns .12 per year for 20 years, the
What IRR does the investor earn with retention compared to an immediate cash dividend?
a. What is the value of a firm paying $100 dividend taxed at .396, with zero growth and a .07248 discount rate?b. Assume the $100 per year is reinvested for 20 years and the basic firm value of $833.33 is present at time 20.The firm's value at time 20 is $8,038.57.Assume the $7,205.24 is sold at
Assume a $800 investment returns $1,000 at time 1 (a .25 return).What is the IRR on $100 of equity if $700 of .08 debt is used as well as equity?
a. Assume the value of a firm's equity is $1,000 and $800 of .10 debt is substituted for equity. The corporate tax rate is .35.What is the new value of the equity?What total wealth do the stockholders have?b. If the debt rate is used as the discount rate, what is the present value of the interest
a. Assume a firm with a value of $10,000 earns $1,000 EBIT. The tax rate is .35. An investor owning 100 percent of the equity earns how much?b. If the firm earning $1,000 EBIT is financed with .90 debt($9,000) that pays .08 and .10 equity, the investor (who owns 100% of the equity) buys .65 of the
Change the cost of debt of problem 3b. to .10. Recompute the investor's return if the firm earns $2,000 EBIT.
A firm with a value of $1,000 and zero debt has a cost of capital of .12. Assume $900 of .08 debt is substituted for stock. The tax rate is .35. Estimate the new cost of capital.
Assume the value of an unlevered firm is $10,000,000. The tax rate is .35.What is the maximum amount of debt that can be issued in substitution for equity if the $10,000,000 is an accurate measure?How much value can be added?
a. Assume a one year investment of $10,000 returns $10,900 at time 1.What is the return on $1,000 of equity if $9,000 of .05 debt is used? Assume zero taxes.b. What is the IRR (after tax) on $1,000 of equity if the firm earns$12,000 before tax? The tax rate is .35.With no debt, what is the IRR on
a. The market capitalization of a firm with 100 percent stock equity is $10,000,000. Assume $8,000,000 of .10 debt is substituted for stock (the debt is given to the shareholders). The tax rate is .35.There are no costs of financial distress. What is the value of the firm after the debt is issued?
a. A firm is paying $8 per year dividend (the next dividend is in one year). There is zero growth. The tax rate on ordinary income is .396. The investor's after tax opportunity cost on comparable risk investments is .12.What is the stock price?b. What is the stock price if the horizon being
A firm is earning $8 per year. It can earn .20 (after corporate tax) on reinvested funds. Based on a constant dividend the firm's value is $40.27. If the funds are reinvested the firm's value after five years is estimated atThe investor has a .20 capital gains tax rate and a .07248 after tax
What are the advantages of private equity?
Of the eight factors listed by DeAngelo and DeAngelo, which one do you consider most important?
a. Assume the LBO management firm is paid 2 percent on Company B's total assets and 20 percent of the gross profits (before capital charges and after taxes). The capital structure for Company B is:Company B has a .35 tax rate. It earned $90 before interest before taxes before management
Which is a more reliable estimate of value, market capitalization or the present value of the firm's future cash flows?
The price-earnings multiplier for comparable firms is a popular method of valuation. When would this valuation method not be reliable?
In the chapter we have:If the firm has a low retention rate and a large growth rate what does this imply? Would you expect a high or low P/E ratio? P/E = (1-b) k-g
One can multiply a constant (multiplier) times a firm's EBITDA. Explain what one gets from the product.
Assume the value of a firm is: The firm uses zero debt. The retention rate is .60. What is the earnings return on new investment? What is the value of the firm's PVGO? D 50 P = == $2,500 k-g .12-.10

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