study session one - LOS 5a - 5f - Time Value of Money

mostly Time Value of Money. i read most of this in CFA Fundamentals (which i recommend - by Schweser).

• Constructing a timeline does actually help you work this out
• If you know all but one of PV, FV, Number of compounding periods (N), Interest per year (I/Y) you can work out the rest using a financial calculator pretty easily
• Watch out for questions where the investment compounds several times per year; in this case, divide the interest rate by the number of compounding periods per year and use the result as the I/Y
• Maturity payments at the end of an investment (e.g. T-Bills) are calculated as the FV of that investment
• FV or PV must be negative or your calculator will throw an error
• To calculate growth, use start and end payments as PV and FV respectively
• I often transpose numbers or just make stupid mistakes when inputting - must double check that what i have inputted is the actual number
• perpetuities are present valued by dividing the payment by the interest rate
• PV
• FV
• Annuity Due
• Ordinary Annuities
• For finding the PV of a series of uneven cash flows it is the sum of the PV of each cash flow; i do this using the NPV function and entering the cash flows and the interest rate (but this assumes interest rate is constant)
• For things like saving up for retirement plans, you have to work out the PV of the future sum needed to support the required payments
• For finding the FV/PV of a lump sum which receives coupons or payments, add the payments as PMT when calculating the value
• NOTE: Questions involving annuity due do not tell you explicitly but often use phrases like "Bob invests $10 now" or "If Mary invests $10 today" to imply that the compounding starts from the beginning of the period
• NB Don't forget to set your calculator to BGN for the compounding period and to switch it back when you are done.

I don't know most of these formulas but i do know how to calculate them using a Texas Instruments BA II Plus calculator - YouTube has some good videos on how to do this.

One note on interest rates:

1. Real Risk-Free Rate - This assumes no risk or uncertainty, simply reflecting differences in timing: the preference to spend now/pay back later versus lend now/collect later.
2. Expected Inflation - The market expects aggregate prices to rise, and the currency's purchasing power is reduced by a rate known as the inflation rate. Inflation makes real dollars less valuable in the future and is factored into determining the nominal interest rate (from the economics material: nominal rate = real rate + inflation rate).
3. Default-Risk Premium - What is the chance that the borrower won't make payments on time, or will be unable to pay what is owed? This component will be high or low depending on the creditworthiness of the person or entity involved.
4. Liquidity Premium- Some investments are highly liquid, meaning they are easily exchanged for cash (U.S. Treasury debt, for example). Other securities are less liquid, and there may be a certain loss expected if it's an issue that trades infrequently. Holding other factors equal, a less liquid security must compensate the holder by offering a higher interest rate.
5. Maturity Premium - All else being equal, a bond obligation will be more sensitive to interest rate fluctuations the longer to maturity it is.