Every finance student has been exposed to the concept of the time value of money. They learn how to calculate the net present value (NPV) of even and uneven cash flows and the importance of the discount rate. This rate is synonymous with your required yield and is often tied to a market rate of a comparable asset plus or minus some risk spread. This is normally further adjusted to ensure that minimum corporate profitability goals are achieved. Often this rate is referred to as the “hurdle rate”.  What is rarely discussed, however, is how to derive the appropriate discount rate on negative cash flows. 

This issue comes up when valuing portfolios of distressed mortgage loans that are expected to throw off significant losses. It is easy to construct such a portfolio where the NPV of the expected negative cash flows actually increases as the hurdle rate goes up. This is counter-intuitive and does not reflect market reality.

A simple illustration may make my point:

1. I have a contract to receive $100,000 one year from now (positive cash flow). I want to sell this receivable to you today.  You will pay me $91,000 if you want to earn 10% on your money (the hurdle rate). If I were to tell you, however, that it is uncertain if you will receive the entire $100,000 a year from now, you will probably conclude that such uncertainty will demand a higher return - say 20%. Accordingly, you will only pay only $83,000 for the receivable.
2. Alternatively, I have a contract to pay $100,000 one year from now (negative cash flow). I want to sell this payable to you today (i.e. give you cash to take over the liability). Would you accept $91,000 from me if your hurdle rate is 10%?  If I were to tell you that the $100,000 it is uncertain if you will have to pay the $100,000 a year from now (it could be more), would you discount it at 20% and then accept only $83,000 for the payable?

Needless to say, #2 does not make any sense. You would not discount the payable to this extent unless you were sure you could reinvest these dollars at 10% or 20%. Not only is this implausible, but why would you want to share this upside with the seller! You would probably use a risk-free rate such as the 1 month Treasury (+/-4.5% today).  If the payable amount is uncertain, and could be higher, you would certainly NOT discount the amount you want from the seller of this negative cash flow. You would want an amount closer to, or equal to, the payable. On negative cash flows, you should not use your hurdle rate, but rather your marginal reinvestment rate, adjusted for volatility.

The difference is huge. The net present value of a constant negative cash flow of $10,000 per month for 15 years is $1.2MM at a 6% discount rate. At a zero % discount rate it equals $1.8MM. If $1.8MM reflects par (100), the $1.2 equals 66. The latter is more reasonable theoretically, and certainly more in line with the way the market looks at negative cash flows.

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