1.3 TVM Flashcards
(10 cards)
An annuity that pays at the beginning of a period
Annuity Due (AD)
An annuity that pays at the end of a period
Ordinary annuity (OA)
Rule of 72.
This rule says that the number of years it takes for a sum of money to double in value (the “doubling time”) is approximately equal to the number 72 divided by the interest rate expressed in percent per year:
Doubling Time = 72/interest
So at an interest rate of 10% per year, it should take approximately 7.2 years to double your money. If you start with $1,000, you will have $2,000 after 7.2 years, $4,000 after 14.4 years, $8,000 after 21.6 years, and so on.
Using a variation of the same equation, you can determine the rate of return required to double your money. Assume you have $5,000 and you want to determine what rate of return you need to have $10,000 in 6 years. You would use the following formula:
Rate to Double = 72/years
So for your money to double from $5,000 to $10,000 in 6 years, you would need to earn 12% on your money. 12% = 72/6 years.
If Joe invested $3,250 for 5 years at a rate of 6%, and his marginal tax bracket is 35%, how much would he accumulate after taxes?
Using the calculator keystrokes:
n = 5
i = 3.9 [(6% x (1 – 35%)]
PV = ($3,250) Note: Use the CHS key to show a cash outflow.
Solve for FV = $3,935.15
Effective rate
To compute the effective rate, take the future value as the numerator and divide by the beginning present value of $100 as the denominator
Forumula for real rate of return
(nominal rate - inflation rate) / (1 + inflation rate) OR ((1.nomial / 1.inflation) - 1) * 100
Justin and Diane were recently divorced. Beginning at the end of the month, Justin must pay Diane $1,000 per month for the next 5 years. These payments must be indexed to inflation, which is expected to average 3.0% over the next 5 years. Justin would like to set aside an amount today in a money market yielding 4.5% that will be sufficient to fund his 5-year obligation. What amount should Justin deposit into the money market?
Justin should set aside $57,833.78 to fund his obligation. The annual real rate of return is (4.5 − 3.00) ÷ 1.03 = 1.456311%. This must be divided by 12 to accommodate the frequency of the monthly payment.
Enter the keystrokes:
f REG f FIN g END 1000 CHS PMT 5 g 12x 1.5 ENTER 1.03 ÷ g 12 ÷ PV
The calculator returns: 57,833.78
Serial Payment
A payment that increases over time (usually to account for inflation)
Sue wants to start a sole proprietorship in five years. She needs to have $200,000 (in today’s dollars) to begin the business. Inflation is expected to average 3.5% over the next five years and Sue’s investment projections show that she can earn 9% on her investments over this time horizon. What serial payment should Sue make at the end of the first and second years?
Solution:
These payments, since they will not be equal, must be calculated one year at a time. What serial payment should Sue invest at the end of the first year?
Keystrokes
f REG f FIN 200000 FV 5 n 5.5 ENTER 1.035 / i g END PMT
The calculator returns: -35,968.65
Then you must increase by the inflation rate to compensate for purchasing power parity one year from today: $35,968.65 × 1.035 = $37,227.55. This is the amount of the first payment that must be deposited one year from today in an account generating a rate of return of 9%. It is extremely important to observe that when we calculate serial payments, we use today’s dollars as the future value and the real rate of return as the interest rate.
What would be Sue’s required payment at the end of the second year?
Second Year = $37,227.55 × 1.035 =$38,530.52
1) Serial Payment
2) Level Payment
3) Loan amortization
1) Payment increases over time - eg: calculate first and second payment. i=real rate; amount = FV
2) Payment is the same over time - i=real rate; amount = FV; calcualte PV then calculate payment using i=nominal rate
3) Calculate amount paid in interest/ principal; calculate payment then AMORT on number of payments (AMORT cumulative)
Assume that your child is going to college next year for 4 years and that the current cost of college is $40,000, the return on your investment portfolio is 7.5%, the increase in college costs are 6%, and the CPI is 3% over the 4-year period. What is the present value of college costs needed today to fund this goal?
The annual spending can be adjusted for college inflation at 6% (Step 1) and these nominal expected values can be discounted at the nominal investment rate of 7.5% (Step 2) to obtain a $154,497 present value.
To use this method, calculate the risk-adjusted rate which is [(1 + Nominal Rate) / (1 + College Inflation Rate) − 1] × 100 and obtain 1.4151% (calculated as: (1.075 / 1.06 − 1) x 100). Next, schedule the payments in today’s dollars to obtain the same present value of $154,497:
Year Annual College Cost in Today's Dollars PV Of College Costs 1 $40,000 ÷ (1.01415)1 = $39,442 2 $40,000 ÷ (1.01415)2 = $38,892 3 $40,000 ÷ (1.01415)3 = $38,349 4 $40,000 ÷ (1.01415)4 = $37,814 Present Value Needed Today $154,497
