Question

I- If it is managed​ efficiently, Remel,​ Inc., will have assets with a market value of $ 50.1​million,$ 99.2​million, or $ 148.9 million next​ year, with each outcome being equally likely.​ However, managers may engage in wasteful empire​ building,which will reduce the market value by $ 5.2 million in all cases. Managers may also increase the risk of the​ firm, changing the probability of each outcome to 48 %,10 %​,and 42 %​,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.​ $44.6 ​million, ii. $46.8 ​million, iii. $82.1 ​million, iv. $95.7million. c. Suppose the tax savings from the​ debt, after including investor​ taxes, is equal to 9 % 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

a)

If managed properly
Value	Probability	Expected value
A	B	C=A*B
50.1	33.33%	16.7
99.2	33.33%	33.06666667
149	33.33%	49.63333333
	Total	99.4

If there is no debt, manager will engage in wasteful empire nuilding and value of firm reduces by $5.2 million

Value of frim will = 99.4 - 5.2 = $ 94.2 million  

b)

i) If manager do increase the risk, then value of firm would be

Value	Probability	Expected value
A	B	C=A*B
50.1	48.00%	24.05
99.2	10.00%	9.92
148.9	42.00%	62.54
	Total	96.51

If debt due in 1 year is $ 44.6 mn, then there is no bankruptcy in any state. So managers would engage in empire building as that would not increase risk (Lowest value of 50.1 is greater than debt 44.6) by more than 5.2 mn (value of empire building). Expected value of firm will be 94.2 mn and mangers would engage in empire buidling but risk would not increase

ii)

If debt due in 1 year is $ 46.8 mn, then there is no bankruptcy in any state. But managers would not go for empire building as it would make firm bankrupt in first case (50.1- 46.8 - 5.2 would be negative). Thus value of firm will be $99.4 mn

iii)

If debt due in 1 year is $ 82.1 mn, then there is bankruptcy in first state. The expected value of equity will be

Value	Probability	Expected value
A	B	C=A*B
0	33.33%	0.00
(99.2-82.1)= 17.1	33.33%	5.70
(148.9-82.1) = 66.8	33.33%	22.27
	Total	27.97

However if they increase risk,

Value	Probability	Expected value
A	B	C=A*B
0	48.00%	0.00
(99.2-82.1)= 17.1	10.00%	1.71
(148.9-82.1) = 66.8	42.00%	28.06
	Total	29.77

Hence managers will take additional risk. Firm will go bank rupt in case 1 but not in case 2 and 3 even if they engage in empire building (99.2-82.1-5.3 >0) and (148.9-82.1-5.2>0)

Managers ould increase the risk and take empire building.

Value of firm is 96.51- 5.2 = 91.31

iv) If debt due in 1 year is $ 95.7 mn, then there is bankruptcy in first state and second state. The expected value of equity

Value	Probability	Expected value
A	B	C=A*B
0	33.33%	0.00
(99.2-95.7) = 3.5	33.33%	1.17
(148.9 - 95.7) = 53.2	33.33%	17.73
	Total	18.90

If they increase risk

Value	Probability	Expected value
A	B	C=A*B
0	48.00%	0.00
(99.2-95.7) = 3.5	10.00%	0.35
(148.9 - 95.7) = 53.2	42.00%	22.34
	Total	22.69

So they will increase the risk. But they would not take empire building as that will make them bankrupt in 2 states (99.2 - 95.7 -5.2 <0)

Value of firm will be $96.51 million

c)

Debt	Value of Firm	Debt Payoff	Reason for debt payoff	Cost of capital	Expected value of firm
44.6	94.2	44.6	No bankruptcy	9%	98.21
46.8	99.4	46.8	No bankruptcy	9%	103.61
82.1	91.31	64.244	Bankruptcy in case 1 and empirebuilding but not in 2 and 3)	9%	97.09
95.7	96.51	73.812	Bankruptcy in case 1 and without empirebuilding but not in 2 and 3)	9%	103.15

Thus optimum value of debt is $46.8 million