Question

If it is managed​ efficiently, Remel,​ Inc., will have assets with a market value of $ 50.4 ​million, $ 100.9 ​million, or $ 150.8 million next​ year, with each outcome being equally likely.​ However, managers may engage in wasteful empire​ building, which will reduce the market value by $ 5.1 million in all cases. Managers may also increase the risk of the​ firm, changing the probability of each outcome to 47 %​, 12 %​, and 41 %​, respectively. a. What is the expected value of​ Remel's assets if it is run​ efficiently? Suppose managers will engage in empire building unless that behavior increases the likelihood of bankruptcy. They will choose the risk of the firm to maximize the expected payoff to equity holders. b. Suppose Remel has debt due in one year as shown below. For each​ case, indicate whether managers will engage in empire-building, and whether they will increase risk. What is the expected value of​ Remel's assets in each​ case? i.​ $40.1 ​million, ii.​ $47.4 ​million, iii.​ $88.8 ​million, iv.​ $96.2 million. c. Suppose the tax savings from the​ debt, after including investor​ taxes, is equal to 11 % of the expected payoff of the debt. The proceeds from the​ debt, as well as the value of any tax​ savings, will be paid out to shareholders immediately as a dividend when the debt is issued. What is the expected value of​ Remel's assets, including the tax​ savings, for each debt level in part ​(b​)? Which debt level in part ​(b​) is optimal for​ Remel?

Answer 1

ANSWER (A)

EXPECTED PAY OFF 1/3(50.4)+1/3(100.9)+1/3(150.8)=100.7

ANSWER (B)

EXPECTED PAYOFF IF MANGERS WILL MAKE EMPIRE BUIDING

EXPECTED VALUE OF ASSETS : 1/3(50.4-5.1)+ 1/3(100.9-5.1) +1/3(150.8-5.1) = 1/3(186.8)=95.6

EXPECTED VALUE OF NET ASSETS IN CASE (i) WHEN DEBT IS 40.1

=95.6-40.1=45.5

EXPECTED VALUE OF NET ASSETS IN CASE (ii) WHEN DEBT IS 47.4

=95.6-47.4=58.2

EXPECTED VALUE OF NET ASSETS IN CASE (iii) WHEN DEBT IS 88.8

=95.6-88.8=6.8

EXPECTED VALUE OF NET ASSETS IN CASE (iv) WHEN DEBT IS 40.1

=95.6-96.2=-0.6

CONCLUSION : IN CASE (iv) MANAGER WILL NOT ENGAGE IN EMPIRE BUILDING SINCE THERE WILL BE A CHANCE OF BANKRUT

EXPECTED PAYOFF IF MANGERS WILL CHOOSE THE RISKF

EXPECTED VALUE OF ASSETS : 47%(50.4)+ 12%(100.9) +41%(150.8) = 97.624

EXPECTED VALUE OF NET ASSETS IN CASE (i) WHEN DEBT IS 40.1

=97.624-40.1=57.524

EXPECTED VALUE OF NET ASSETS IN CASE (ii) WHEN DEBT IS 47.4

=97.624-47.4=50.224

EXPECTED VALUE OF NET ASSETS IN CASE (iii) WHEN DEBT IS 88.8

=97.624-88.8=8.824

EXPECTED VALUE OF NET ASSETS IN CASE (iv) WHEN DEBT IS 40.1

=97.624-96.2=1.424

SO ANSWERS ARE 57.524,50.224,8.824,1.424

ANSWER (C)

EXPECTED VALUE OF NET ASSETS AFTER TAX SAVING ON DEBTS

IF MANGERS WILL MAKE EMPIRE BUIDING

CASE (i)

45.5+11%(40.1)=45.5+4.411=49.911

CASE (ii)

58.2+11%(47.4)=58.2+5.214=63.414

CASE (iii)

6.8+11%(88.8)=6.8+9.768=16.568

CASE (iv)

-0.6+11%(96.2)=-0.6+10.582=4.582

SO ANSWERS ARE 49.911,63.414,16.568,4.582

IF MANGERS WILL CHOOSE RISK

CASE (i)

57.524+11%(40.1)= 57.524+4.411=61.935

CASE (ii)

50.224+11%(47.4)= 50.224+5.214=55.438

CASE (iii)

8.824+11%(88.8)= 8.824+9.768=18.592

CASE (iv)

1.424+11%(96.2)= 1.424+10.582=12.006

SO ANSWERS ARE 61.935,55.438,18.592,12.006