Chapter 3: Time value of money
Annuity Examples
-Mortgage payment - 1,200 monthly payment paid over 30 years -Lottery - win 1,000,000 jackpot and get paid in 20 annual payments -Retirement annuity - pension payment of 800 received on the first of every month, beginning at age 65 and continuing for the lifetime of the retiree -Defined contribution plan pg 3.31
Applications to Total Rewards Problem Solving -Growth rate of base salary or benefit plan costs
Formulas can be applied to determine growth rate (e.g., sales, population, participation, salaries, costs, earnings per share, stock price appreciation).
Calculation of Interest rate- pg. 3.24
If you retirement fund grows from 10,000 to 20,000 in 6 years compounded monthly, what annual interest are you earning? -Computer using percent change/compound interest worksheet --compound monthly PV=10,000 FV=20,000 N=6 yrs x 12 periods=72 %I=?
Calculation of Future Value
PV = Present value %i = Interest rate per period N = Number of periods FV = Future value --Suppose you have 1,000 that you invest in a savings account earning 4% annually over two years. -year one, interest is earned only on the principal amount. In year two, interest is again earned on the principal amount (the original 1,000) but also on the interest earned in year one (40). -the notion of "compounding" interest is born. In other words, interest is earned on interest. -The amount earned in year two on the interest made in year one is 40.00 times 4%, or 1.60. Thus, the second year's interest is 41.60. --We will utilize the "Δ%" worksheet mode to make these calculations
Applications to Total Rewards Problem Solving -Alternative work-life programs -
TVM can be used to anticipate return on an investment in an on-site child- and elder-care center, or to compare the cost of adding an additional paid holiday vs. increasing the vacation schedule.
Calculation of Present Value
The future value equation consists of four terms: PV, FV, i and N. Given any three ofthese terms, we can use algebra to solve for the fourth term. 1. Future value process in reverse -Present value is the future value process in reverse. -It's the inverse of compounding and involves removing or unraveling compound interest. -How do you determine the amount of money you need to invest today in order to realize a specific future value? 2.PV = FV / (1 + i )N -Present value calculations reflect the economic trade-off between money received today versus a future date, based on a length of time involved and the available earnings opportunity. -The greater the i, the smaller the PV needs to be. -The greater the N (i.e., the further in the future a sum is to be received), the less you have to invest at the current time.
Calculation of Present Value ...cont'd
pg 3.17-3.18
Time Value of Money
1. Money in the past / money today / money in the future - Money in hand today is worth more than money promised at some future time, because it can be invested with interest and grow over time. 2. Opportunity costs and lost earnings potential - Opportunity costs and lost earnings potential should influence decisions. --Opportunity costs refers to what is given up when a decision is made (the "trade-off"). --The lost earnings potential is the opportunity cost. 3. Applications of TVM in business / HR decisions - The application of TVM principles to business/HR decisions is now commonplace. 4.Calculations easier now - Present-value tables, calculators, spreadsheets and Internet "calculators" have made calculations easy.
Using the Rule of 72 to Determine Time to Double
1. Note that by using the TVM feature of your calculator, you can determine that the actual number years for Peter's salary to double is 5.89830503, given a compound salary growth rate (CSGR) of 12.47. Thus, 5.77 years is a reasonably good approximation to the actual value of 5.90 (rounded). 2.The rule can be tested by selecting a value for OLD (such as 25,000) and a value for NEW that is double the value for OLD (such as 50,000), and letting %CH equal 12.47. The resulting value will be #PD = 5.90 (rounded).
Compound Salary Growth Rate
A special case of compound interest that helps determine the rate at which a salary has grown. -A special case of compound interest FV>ending base salary PV>starting base salary N># of increase periods %I>CSGR
Calculation of Compound Salary Growth Rate
FV --> Ending Base Salary --> 56,900 PV --> Starting Base Salary --> 32,000 N --> # of Increase Periods --> 5 %I --> Interest Rate per Period --> ? (pg. 3.21)
Future Value Formula
FV= principal+(principal x %i) FV=PV(1+i)N 1. This equation represents the future value of: -money invested today -for N periods of time -at compounding interest rate of %i 2. variations of the equation can be used to determining FV, PV, %i or N.
Compound Interest
-Compounding -The process of finding future values (of a payment or a series of payments) is called compounding.
Time Value of Money (TVM)
The concept of time value of money is relatively simple. -Present value (PV) will increase to a future value (FV) with the inclusion of time (# PD) and interest (Δ%).
Applications to Total Rewards Problem Solving -Executive compensation payments
-Assess value of current vs. future compensation and benefits to negotiate an employment offer. --sign on bonus --long term cash bonus --termination payout --deferred comp. plans
Percent Change/Compound Interest Worksheet (Δ%)
-Calculator -Old=Present Value(PV) -New=Future Value(FV) -%CH Present change (interest rate per period) -#PD-Number of periods(N) -Given any three of these values, we can always determine the fourth value. This is the essence of algebra.
The Rule of 72
-a commonly used concept in finance, allowing quick calculations of compound interest. -an approximation. As the interest rate (or growth rate) increases, the rule becomes less accurate. For practical purposes, it usually provides a reasonable approximation until the interest rate begins to approach or exceed 20%. For lower interest rates, it is generally very accurate.
Annuity
-an investment that pays on a scheduled basis over a fixed amount of time --A series of regular periodic payments comprising principal and interest that lead to a predetermined amount in the future --A stream of equal cash flows delivered over some finite period of time (a perpetuity* that ends)* Perpetuity is a cash flow without a fixed end point or time period. --A series of future cash flows (i.e., payments, receipts, deposits or withdrawals)
The Rule of 72 applications
-provides a good approximation of how long it will take to double something, given a specified constant interest rate. -It is a valuable tool for understanding investments in retirement programs, supplemental income planning, and other financial planning processes.
Future Value Definition
-provides a means of seeing the future value (FV) of an investment (PV) that receives compound interest (%i) over a period of time (N). -Utilizing this formula to calculate future value, given that you have any three of the four variables (FV, PV,%i, N), you can solve for the missing fourth variable.
Why the Value of Money Over Time Is of Interest
1. Savings account planning (Wedding fund,College savings fund, Home purchase fund, Retirement savings fund) 2. Alternative purchase and investment decisions (Home ownership, Personal computer, Automobile) --automobile-cash, loan, lease, balloon pmt. 3. Equities vs. fixed income investing -Equities (stocks) vs. fixed income (bonds) --Capital gains --Dividend streams --Yield to maturity --Par value and coupon interest
Compound vs. simple interest
1. Simple interest - Interest is applied at the end of the period and only on the beginning balance or principal. 2. Compound interest - Interest is applied during the period, which results in a return not only on the principal amount but also on the interest (thus, interest on interest, or "compounding"). The interest is applied at certain intervals or frequencies (i.e., monthly, quarterly) during the total time interval being studied.
Constant Midpoint Progression
1. Use percent change worksheet - When constructing salary ranges, we can use the percent change worksheet to calculate a constant midpoint progression. 2. Use salary grade and survey midpoints - Use the four salary grades provided along with survey average salary. 3. Calculate between lowest and highest midpoints - Calculate a constant midpoint progression between the lowest and the highest midpoints. -#PD --> Number of intervals --> (always the number of grades minus one) -NEW --> Highest Midpoint --> 1,119 OLD --> Lowest Midpoint --> 834 This is a useful tool for helping with broad banding. For example, it can be useful when transitioning from 12 grades to 3 or 4 grades.
Applications to Total Rewards Problem Solving -Retirement plan payments
Determine contributions and fund performance necessary to deliver future benefits. --Final average pay benefit --Lump sum vs. annuity --Actuarial equivalent
Constant Midpoint Progression ...cont'd
In the example above (pg. 3.27), the Δ% (midpoint progression) is not an equal distribution. In a typical salary structure, if a uniform midpoint progression is not used, lower grades have a lower midpoint progression (and, conversely, higher grades have a greater percent difference). In the example above, the Δ% appears to be very random.
Calculation of Future Value ...cont'd
It is important to always set up the calculator with the three known variables. Then it is a simple matter to find the fourth variable. *pg. 3.15
Calculation of Future Value example
Now let's go back to our original example. PV = 1,000 %i = 4% per year N = 2 years FV = ? Let's set up the problem for the TI BAII Plus calculator. We know three of the four variables, so we can solve for the unknown variable "FV." *Pg. 3.12
Constant Midpoint Progression-applying the constant percentages
When constructing salary ranges we can use the percent change worksheet to calculate a constant midpoint progression. Use the four salary grades provided along with survey average salary. -Calculate a constant midpoint progression between the lowest and the highest midpoints. -#PD>Number of intervals >3 (always the number of grades minus one) NEW>Highest Midpoint >1,119 OLD>Lowest Midpoint> 834