Gladrock Corporation is about to launch a new product. Depending on the success of the new product, Gladrock might have actually one of four worths following year: $150m, $135m, $95m or $80m. These outcomes are all equally most likely, and also this threat is diversifiable. Gladstone will not make any payouts to investors in the time of the year. Suppose the risk-free interest rate is 5% and also assume perfect funding sectors.
(a) What is the initial value of Gladstone's equity without leverage?
solution 0.25*(150+135+95+80)/1.05 = 109.52m
(b) Now intend Gladstone has zero-coupon debt through a $100 million face value due next year. What is the initial worth of Gladstone's debt?
solution (0.25)(100+100+95+80)/1.05 = 89.28m
My question for component (b), why is the initial value of debt calculated through 100,100,95, and 80? I thought because the FV of debt at time 1 is 100, you can ssuggest discount it earlier by 1.05 such that Debt at time 0 is 100/1.05? Can someone define this to me? Thanks
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The worths (100, 100, 95, 80) are the payoffs to debtholders given a certain realization of the equity worth next period. I.e. If equity = 150 or 135, then debtholders are completely repassist, however if equity = 95 or 85, then the firm defaults and also debtholders only get 95 or 85 (the worth of the firm). Given that this danger is diversifiable (as assumed in the question), then the worth of debt is the expected value of these payoffs, discounted at the risk-cost-free rate.
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