I'm having a little problem trying to select which rates to use when discounting a liability cash flow under different interest rate scenarios. In my little example below I'm trying to find the present value of a 5yr zero coupon bond. Here are the possble interest rates that I could use to calculate the present value:1. Use the current yield curve only (1%, 1.5, 2, 2.5 and 3.0%).2. Use the short rates from each yield curve (1%, 1.1, 1.2, 1.3 and 1.4%).3. Use the appropriate forward rate from each yield curve (1%, 1.6%, 2.2%, 2.8% and 3.4%).So which one should I use? Is there another option that I'm not considering?The example here is for a 5yr zero coupon bond.Scenario #2 (1yr Forward Rates) 1yr 2yr 3yr 4yr 5yr = Yield Curvet=0 1% 1.5% 2% 2.5% 3.0% (5 years to maturity) Current yield curve.t=1 1.1% 1.6% 2.1% 2.6% 3.1% (4 years to maturity) This is what actually occurs in 1 year.t=2 1.2% 1.7% 2.2% 2.7% 3.2% (3 years to maturity) This is what actually occurs in 2 years.t=3 1.3% 1.8% 2.3% 2.8% 3.3% (2 years to maturity) This is what actually occurs in 3 years.t=4 1.4% 1.9% 2.4% 2.9% 3.4% (1 year to maturity) This is what actually occurs in 4 years.t=5 1.5% 2.0% 2.5% 3.0% 3.5%

I'm no finance professor, but it seems to me your present value is approximately the lowest price you would sell this cashflow for right now. So how much money would someone have to bid before you would sell one more such bond? What would you pay to buy this bond back?So suppose I owe $1,000 on my credit card, due in one year grace period. What is the most money I would be willing to pay right now to give up this grace period? How much more money would I spend right now, knowing my cost would be an extra $1,000 a year out?Perhaps I would spend $900 more dollars, but not $899 more to owe another thousand. Perhaps I would pay $898 to get out of owing the current $1,000.Did I get this right?One more thing: You might also assume that you have already sold bonds down to where the interest rate where you are willing to sell the next one is lower than the interest rate demanded by the market for your resultant credit rating for selling one more bond. But you have not specified this is the case. Absent this theoretical ideal - which I can imagine there are plenty of reasons would not take place in real life - your appropriate discount would seem to be purely subjective, as suggested. In other words, there may be theoretical profits to your borrowing more money, which would make any "market" rate irrelevant to your own tradeoff or utility. You might theoretically prefer to call your bonds, or buy them in the open market and be unable to. In any case, the decision to buy back your zeros would take place after you had computed your own utility. So you would have to perform your calculation - and determine if it would be profitable to go to market - before your rate came in line with the market rate. Your going to market would be a result of your calculating a discrepancy between your own rate and the market rate.Course, you're saying you think under one probable scenario, you will be able to spend $899 more on your credit card now to owe a thousand in five years, but then get out of it by paying perhaps only $897 in just one year. In this situation, you might both 1) borrow at the 1-year rate, and B) short the 1-year forward for the future 4-year, by just borrowing at the 5-year rate? In this case, you are gambling on different "profit" opportunities possibly appearing at different time horizons (which will also involve your probable belief changes coincident with those rate changes), so you have to understand you are speculating and borrowing at the same time. Speculating involves predicting the utility of others, borrowing involves arbitraging your own utilities against theirs. I would separate the two.Or, you can theoretically claim you are "borrowing with a 1-year duration at a negative interest rate," while what you are really doing is borrowing for five years and entering synthetic futures positions without adjusting your discount rate for the subtle risk and volatility changes, or without comparing your rate to the rates for those risks.Just ignore me...MP

From your question, it sounds like you are working with a much simpler situation then the one MP describes, (i.e. there is no such thing as risk-free rate, and you have to worry about risk premia and utility curves just to discount cash flows.)If you are willing to assume that the time value of money is determined by the risk free interest rate, which is the standard finance assumption, then the term structure of interest rates is all you need to properly discount your cash flows. If your bond were a coupon bond, then you would need to discount each payment by the appropriate rate for a zero of equivalent maturity, and then reinvest it at the appropriate forward rate. However, since you are dealing with a zero, your problem is actually quite simple. Discount the par value of the bond by the rate of interest for the five-year term, 3% in your example. par*exp(-.03*5) will give you the present value of the bond under continuous compounding.

Put simply, "their present value for the 5-year coupon, is the rate implied in the price discount they are presently paying for it, that being 3%."MP

Thanks for all of your responses. The question was: How do you discount using interest rate scenario yield curves? Typical discounting using interest rate scenarios uses only the short rate. But I have entire yield curves for my scenarios. The solution is just use the current yield curve and ignore future yield curves in the discounting process. The problem is actually a lot more complex than the solution would indicate. The correct solution involves the looking at every possible investment scenario to find the lowest present value. Here are some: 1. Use t=0 yield curve only.2. Invest for one year (t=0 yield curve), then use the yield curve at t = 1 to invest for the next four years.3. Invest for two years (t=0 yield curve), then use the yield curve at t = 2 to invest for the next three years.4. Invest for three years (t=0 yield curve), then use the yield curve at t = 3 to invest for the next two years.5. Invest for four years (t=0 yield curve), then use the yield curve at t = 4 to invest for the next year.6. There are other combinations as well.The path that gives the lowest present value is the one to use. Unfortunately, I have 50 interest rate scenarios with 50 different cash flows that last for 30 years or more. So it is not possible for me to search out the most optimal solution. Using the current yield curve is probably to best way to go because that's how our investment department would actually make its investments.Thanks for all the help.

----------The path that gives the lowest present value is the one to use. Unfortunately, I have 50 interest rate scenarios with 50 different cash flows that last for 30 years or more. So it is not possible for me to search out the most optimal solution. Using the current yield curve is probably to best way to go because that's how our investment department would actually make its investments.-------------As Myers book on Corporate Finance points, you have to either simulate various cash flows scenaria at the risk free rate or simulate various discount rates for a steady stream of cash flow. You cant do both at the same time.The first approach is a risk neutral valuation. Furthermore, at the first approach employing palisade decision tools you can assess project's critical success factors usually through a tornado graph. Perhaps that the most interesting information refarding project's risks.