Lecture 10 - Final exam practice problems - solutions.pdf -...

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Final exam practice problem solutionsManagement 430, Winter 2018William MannProblem 14.1- note that all chapter 14 problems assume perfect capital markets.a)-$100,000 +12×$130,000+12×$180,0001+20%= $29,167b)12×$130,000+12×$180,0001+20%= $129,167c) Debt investors will receive $100,000×(1 + 10%) = $110,000 no matter what.This means leveredequity investors will receive the remaining amount, which is $70,000 in the good outcome, $20,000 inthe bad outcome.Without needing to discount these cash flows, we know from MM that the total market value of debtand equity today remains at $129,167, so the levered equity is worth $129,167 - $100,000 = $29,167.Problem 14.2a) $4 million. This is simply because investors value 50% of the firm at $2 million.b) MM says that total firm value must remain at $4 million. If you borrow $1 million (that is, use $1million of debt financing), then the remaining value of equity is $4m-$1m= $3 million. To raise theremaining $1 million, you would need to sell one-third of this remaining equity value, or 33.3%.c) $2 million in either case.Problem 14.10There may be no risk of default, but there is still risk in the sense that there is a spreadbetween the good and bad outcomes.In fact, risk-free debt has the biggest effect on the equity cost ofcapital, precisely because the debtholders aren’t bearing any risk. They leave all the risk in the hands ofequity holders.Problem 14.13Recognize that, when Visa has no debt, its equity cost of capital is equal to its unleveredcost of capital, sorU= 9.2%. Then we use the formula from MM part II to see how the equity cost of capitalwill change when we increase leverage (be careful aboutD/EversusD/V):rE=rU+DE×(rU-rD) = 9.2% +0.131-0.13×(9.2%-6%) = 9.68%
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Problem 14.17a) $75. Because we are in perfect capital markets, no value is created or destroyed by the transactions,and Mercer’s share price does not change.b) $50. Mercer will pay $250 million in dividends, so the dividend per share is $25, so on the ex-dividenddate (not the announcement date) the share price will fall by this amount.The textbook hint suggests a different way to get the same answer: Equity value is enterprise valueminus net debt. In perfect capital markets, enterprise value is only affected by the firm’s operations,not its financial decisions, so it is the same after the transaction as before.Before the transaction,enterprise value was $750m+ $100m= $850m, so it will still be this much afterward. Then the equityvalue afterward is $850m-$350m= $500m.Divided by 100m shareholders (since the company ispaying dividends, not repurchasing shares), this gives us a share price of $50.c) We will use the formularE=rU+DE(rU-rD). To use this formula, we first need to getrU. Use theinformation on Mercer before the transaction:rU=DD+E×rD+ED+E×rErU=100850×4.25% +750850×8.5% = 8%Now recognize thatrUdoes not change as a result of the transaction, and plug it into the formula forrEusing the numbers from after the transaction. Note that we use the newrDstated in part (c), andwe use equity valueE= $50×10m= $500mbased on the new share price we calculated in part (b).rE=rU+DE(rU-rD)rE= 8% +$350$500(8%-5%) = 10.1%Problem 17.5

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