Yale School of Management 1 Emerging Market Finance Lecture 14: Valuation of Corporate Bonds

Yale School of Management 2 Corporate Bond B T = X if V T > X or = V T if V T < X where V T is the value of the firm at bond maturity T, and X the face value of a zero- coupon bond.

Yale School of Management 3 Example Company ABC:  Vt = $1 billion ，  ROA = 10% ，  Volatility(ROA) = 30% 。 Consider a 5-yr zero-coupon bond with $500 million face value 。 Then, the probability of bankruptcy in yr. 5 = 21.32% 。

Yale School of Management 4 Relationship between Bond Maturity and Probability of Bankruptcy Years to Maturity

Yale School of Management 5 Standard Textbook Calculation According to standard textbook, Bt = {500*p + E(V T ) * (1-p) }/(1+r)^(T-t) where p = prob of No bankruptcy in yr 5 and E(V T ) = the expected value of the firm if bankruptcy occurs If r=2% ， then Bt = $450.6 million and 5-yr corporate bond yield =3.53%

Yale School of Management 6 If no recovery of value at bankruptcy, then the picture differs Bt = 500*p /(1+r)^(T-t) Bt = $407.6 million And the 5-yr bond yield = 7.05% 。

Yale School of Management 7 No recovery vs. full recovery Based on Textbook Actual corp. bond yields in China (2002) No recovery assumed BondYieldBondYield Years to Maturity

Yale School of Management 8 Spread between Corporate and Government Bond Yields Actual Spread (2002) No recovery assumedYieldSpreadYieldSpread Years to Maturity