FIN.5:4.5 - Use discount factors and financing effects on compatible grounds

A single annual rate is a useful compression only when the valued cash and financing model support it. For deterministic annual forward discount rates r1 through rt, the discount factor to time t is 1/[(1+r1)×…×(1+rt)]. A time-t spot rate zt instead gives 1/(1+zt)^t. Do not treat a quoted spot rate as a one-year forward rate and compound both adjustments. For risky cash, use the corresponding supported pricing factors or model; the risk-free term structure alone does not supply them.

When risk changes over time, identify which remaining claim is exposed to which conditions before selecting its pricing model. A fixed contractual payment, an uncertain operating receipt and an exercisable option can have different risks even when they occur on the same date. Value materially different components on their matched grounds and combine their present values. FIN.8 supplies the changing contingent payoff of an option.

For a certainty-equivalent approach, obtain the amount certain at each date that has the same value as the risky claim, then discount that amount using the matching risk-free factors. The risk adjustment needs a supported model; a discretionary haircut is not enough. For an expected-cash approach, use the required expected-return model that prices those cash flows. Keep the two representations distinct through the calculation.

Do not apply an increasing “risk rate” indiscriminately to unavoidable future costs. A higher positive discount rate reduces the present magnitude of a negative payment and can make an adverse obligation appear cheaper. Establish the payment’s own risk and timing. Similarly, a bond yield computed from promised payments includes a different relationship between price, default losses and receipts from a required return computed on expected payments. When losses matter, obtain the expected payment/recovery account and its matching pricing basis rather than transferring the promised yield unchanged.

APV is especially useful when the financing schedule must remain visible. It separates operating value from the usable deductions, subsidies, issue costs and other financing effects that change value. Value each effect once with its own timing and risk. Adding a distress estimate already included through lost customers or recovery flows would count that consequence twice. Omitting such effects merely because a tax-shield calculation is precise would overstate the benefit of borrowing.

Finally propagate a defensible range into the receiving decision. In the worked case below, a tiny rate difference changes the NPV sign. More displayed decimals cannot settle uncertain debt policy or business comparability. Return the rate’s grounds and the condition that would change the choice; FIN.11 decides the financing mix and FIN.12 determines what can actually be obtained.