(^290) Financial Management
Unlevered Co. Levered Co.
Rs Rs
Net operating income, X 60,000 60,000
Total cost of debt, kdD 0 12,000
Net earnings, NI 60,000 48,000
Equity capitalisation rate, ke 0.100 0.111
Market value of shares, S 6,00,000 4,32,000
Market value of debt, D 0 2,00,000
Total value of the firm, V 6,00,000 6,32,000
Mr X holds Rs 2,000 worth of the Levered Companyís shares. Is it possible for Mr
X to reduce his outlay to earn same return through the use of arbitrage? Illustrate.
Solution
Through arbitrage it is possible for Mr X to reduce his outlay and earn the same return.
- Mr X would sell his shares in the Levered Company for Rs 2,000.
- He would create a personal leverage equal to his share of debt in the Levered
Company by borrowing Rs 926 (= Rs 2,000 x Rs 2,00,000/Rs 4,32,000). - He would buy Rs 2,778 (= Rs 6,00,000 x Rs 2,000/Rs 4.32,0001 of the Unlevered
Companyís shares His return is:
Return on the Unlevered Co.ís shares: Rs 2,778 ◊ 10% Rs 2,77.80
Less: Interest, Rs 926 ◊ 6% 55.56
Net return Rs 2,22,24
His return from the Levered Co. is Rs 2,000 x 11.1% = Rs 222.22, same as in the
Unlevered Co. However, the funds involved in the Unlevered Co are Rs 2,778 - Rs
926 = Rs 1,852 which is less than Rs 2,000 cash outlay involved in the Levered
Company.
Problem 3: Firms A and B are similar except that A is unlevered, while B has Rs
2,00,000 of 5 per cent debentures outstanding. Assume that the tax rate is 40 per cent;
NOI is Rs 40,OM) and the cost of equity is 10 per cent. (i) Calculate the value of the
firms, if the M - M assumptions are met. (in Suppose VB = Rs 3,60,000. According
to M-M. do these represent equilibrium values? How will equilibrium be set? Explain.
Solution
(i) The value of the unlevered firm is:
VA =
- (^) = - =
The value of the levered firm is:
VB = VA + TD = Rs 2,40,000 + 0.4 of Rs 2,00,000
= Rs 2,40,000 + Rs 80,000 = Rs 3,20,000