In: Finance
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?
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:
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: