Question

In: Finance

a) Two firms, ABC Ltd and XYZ Ltd, are identical in every respect apart from their...

a) Two firms, ABC Ltd and XYZ Ltd, are identical in every respect apart from their capital structure. Both will earn $284 million if the market swings upwards and $100 million in a downward swing. There is an even chance of the market swinging upwards or downwards. ABC Ltd has no debt. XYZ Ltd has issued $800 million of its debt at an interest rate of 10% and hence, $80 million of its income is paid out as interest. Assume that investors can borrow and lend at the same rate as the corporation. The WACC of both firms is 16%.

I) Suppose that you have $40 million to invest in XYZ Ltd shares. Is there an alternative investment in ABC Ltd that would generate the same payoff?

Solutions

Expert Solution

All financials below are in $ million.

Value of the firm ABC or XYZ, VF = Operating income / WACC

Hence, in case of upswing, probability of upswing = PUpswing = 50%; VF, Upswing = Operating incomeUpswing / WACC

= 284 / 16% = 1,775

in case of downswing, probability of downswing = PDownswing = 50%; VF, Downswing = Operating incomeDownswing / WACC

= 100 / 16% = 625

Hence, expected value of firm, VF = PUpswing x VF, Upswing + PDownswing x VF, Downswing = 50% x 1,775 + 50% x 625 = 1,200

In case of ABC, Value of equity, VE, ABC = VF = 1,200 as it's unlevered

In case of XYZ, Value of equity, VE, XYZ = VF - Debt = 1,200 - 800 = 400

If you invest $40 million in XYZ Ltd shares, your ownership = Investment amount / VE, XYZ = 40 / 400 = 10%

Net income of XYZ = Operating income - interest

Net income in case of upswing = 284 - 10% x 800 = 204

Net income in case of downswing = 100 - 10% x 800 = 20

Expected net income = 50% x 204 + 50% x 20 = 112

Hence, expected payoff to you from XYZ = Ownership x expected net income = 10% x 112 = 11.2

Let's say the equivalent position in ABC be:

  • Borrow an amount B
  • Invest B + $ 40 mn in ABC

Expected Net income of ABC = 50% x 284 + 50% x 100 = 192

Proportion ownership in ABC = Investment in ABC / VE, ABC = (B + 40) / 1,200

Equity income = Proportion owned in ABC x Expected net income of ABC = (B + 40) / 1,200 x 192

Interest to be paid on borrowing = B x 10%

Hence, total payoff on this position = Equity income - interest to be paid = (B + 40) / 12,00 x 192 - B x 10%

If we force the payoff from position in ABC to be same as that from position in XYZ then,

(B + 40) / 1,200 x 192 - B x 10% = 11.2

Hence, 0.16B + 6.40 - 0.1B = 11.2

Hence, B = (11.2 - 6.40) / (0.16 - 0.1) = 80

Hence, the alternative investment in ABC Ltd that would generate the same payoff will be:

  • Borrow an amount of $ 80 million and
  • Invest B + $ 40 mn = $ 120 mn in ABC

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