As in Example 11, you are reviewing the pricing of a speculative-grade, one-year-maturity, zero-coupon bond. Your goal is to estimate an appropriate default risk premium for this bond. The default risk premium is defined as the extra return above the risk-free return that will compensate investors for default risk. If R is the promised return (yield-to-maturity) on the debt instrument and RF is the risk-free rate, the default risk premium is R − RF. You assess that the probability that the bond defaults is 0.06: P(the bond defaults) = 0.06. One-year US T-bills are offering a return of 5.8 percent, an estimate of RF. In contrast to your approach in Example 11, you no longer make the simplifying assumption that bondholders will recover nothing in the event of a default. Rather, you now assume that recovery will be $0.35 on the dollar, given default.
A. Denote the fraction of principal and interest recovered in default as θ. Following the model of Example 11, develop a general expression for the promised return R on this bond.
B. Given your expression for R and the estimate of RF, state the minimum default risk premium you should require for this instrument.