THE TIME VALUE OF MONEY On The Calculator The BAII Plus Texas Instrument calculator, one of two financial calculators that the CFA Institute allow in the exam hall, has five keys on it for calculating time-value of money questions. The keys and their meanings are … -
[N] [I/Y] [PV] [PMT] [FV]
= number of years = interest rate = present value = payment = future value
When the calculator is in “END” mode which means cash flows are netted and received or paid at the end of the given period, the following formulae apply…
And for a perpetual cash flow, the present value is equal to the payment divided by the interest rate…
Net Present Value (NPV) The NPV of a potential financial project is the present value of its future cash flows. Internal Rate of Return (IRR) The IRR is the discount rate that makes the NPV = 0. Holding Period Yield (HPR) The HPR, often used interchangeably with the Holding Period Return (HPY), is the percentage profit received from holding an asset over a period of time…
…where P0 is the starting value of the portfolio or asset, P1 is the ending value and D1 is the cash flow during the period. Time Weighted Rate of Return (TWRoR) The TWRoR eliminates the effects of cash flows by taking the geometric mean of individual period IRRs.
Money Weighted Rate of Return (MWRoR) The MWRoR is the rate of returm that equates the present value of the cash inflows and the terminal value to the present value of the cash outflows, including the initial investment. Bank Yields - Bank Discount Yield (BDY)…
- Holding Period Yield (HPR)…
- Money Market Yield (MMY)… - Effective Annual Yield (EAY)… - Holding Period Yield (HPY) [a second formula]…
- Bond Equivalent Yield (BEY)… [Tip: remember the “x 2” at the end of the BEY formula is to establish an annual yield on the bond given its two semi-annual coupons]. Continuous Compounding To find the interest rate on a continuously compounded basis we use the natural logarithmic function ln. Example 1: $20,000 to $43,689 over 7 years =>
ln(43,689 /20,000) =11.2 % per annum. 7
Example 2: $500 continuously compounded at 15% for 3 years =>
500.e(15%)3 = $784.16
Roy’s Safety First Ratio When choosing between two or more portfolios, Roy’s Safety First Ratio is a formula that takes the portfolio which has the least chance of falling below a required return, RR. It is the portfolio that produces the largest value from the formula…
Roy’s Safety First Criterion Minimises the probability that the expected return of the portfolio, E(R), is below the threshold or required return, RR…
Effective Annual Rate (EAR) If x is of a normal distribution then ex is lognormal. It is helpful for modelling asset prices because it has a lower bound of zero and thus the EAR is based on a lognormal distribution. It is the interest rate on a loan restated annually when originally its compounding occurs more often than once a year. If we take m as the number of compounding periods per year then…
Example: if compounding occurs every two months then there are 12/2 = 6 compounding periods per year, so compounding 3.2% every two months… EAR = (1+0.032/6) 6 – 1 = 32.4%.
Furthermore if rcc is the continuously compounded annual rate then the following formula applies…
…where the continuously compounded annual rate is given as;