The pricing of risky corporate debt to be issued at par value. (includes appendix)

I. INTRODUCTION

Building on the rational option pricing theories of Black and Scholes (1973) and Merton (1973) suggesting that the option pricing model can be used to price elements of corporate capital structure, Merton (1974) presents the systematic development of a theory for pricing discount bonds when there is a significant probability of default at maturity. In addition, Merton shows that one can derive a risk-structure of interest rates as a function of the debt-to-equity ratio, a measure of the riskiness of the assets of the firm, and the riskless debt rates.

Merton (1974,p. 454) shows that the value of risky discount bond debt can be written:

D(d) = B exp(-rt) {P(d)}

where d = B exp (-rt) / V (a quasi debt-to-asset ratio where the promised payment on debt is valued at the riskless rate of return, r, and P (d) is the per dollar price of risky debt. B exp (-rt) is the present value of the promised payment, B; b is the par value of the bond.

Merton noted that the function P (d) decreases from 1 to 0 as d increases from 0 to [infinity] (its derivative is always negative). Hence if the proceeds at maturity. B were accumulated at the riskless rate of return r, i.e. B = b exp (-rt), then the market value

D(d) = b exp(rt) exp(-rt) P(d) = bP(d) < b

This just states the financially plausible fact that the market value of a risky discount bond is less than par if it promised the investor only the riskless rate of return. In order to obtain market value equal to par value Merton showed that the yield to maturity on risky debt R is given by:.

R = r-(1/t)1n(P(d)

with risk premium

R …