David,
Yes, agreed, this is a vital operation…thank you for surfacing to remind folks
What is rf? riskless rate
What is c=convineince yield? it is the intangible equivalent of a dividend/income: non-financial benefit of ownership which reduces cost of carry; since it is difficult to directly observe, whereas futures prices are not, often is it the solved for “plug variable”
F = S*e^((r-c)*T) = S*EXP[(r-c)T); both are exponential function, I note this only b/c we tend to use EXP() here and I like EXP() a little better if the formula gets hairy
divide both sides by S
F/S = EXP[(r-c)T]
so here is the key: LN() and EXP() are inverse functions
e.g., EXP(LN(x)) = x and LN(EXP(x)) = x
we have F/S = EXP[(r-c)T] and we need to “liberate” (r) from the exponent
so take LN() of both sides
LN(F/S) = (r-c)*T
...now you can get to the riskless rate
Okay, so now let me connect this to another similar formula, and ask you a question:
under continuos compounding, the price of a zero-coupon bond is given by:
D = F*EXP(-y*T), D = price, F = Face, y = yield
but yield is riskless rate + spread, so y = r + s, so:
D = F*EXP(-(r+s)*T)
now, Stulz gives the formula for the spread as a function of debt price (D), face value (F), riskless rate (r), and term to maturity (T). Can you show the derivation of (s)?
David
How do you solve for risk free rate/or any superscript variable? 
