Time Value of Money Flashcards
What are the 3 dimensions of Time Value Money?
Time, rate of interest, interaction between time and interest rate
______ is the price that one pays (receives) for borrowing (lending) sums of money.
interest rate = i
_____ allows one to advance forward through time
compounding = n
_____ allows one to start at a point in the future, and go backward in time to the present.
discounting
What a sum of money to be received sometime in the future is worth in today’s
dollars, based on a specific discount rate.
Present Value =PV
The future amount to which $1 today will increase, based on a defined interest
rate and period of time.
Future Value
A systematic payment occurring at the beginning of each compounding period is ____
an annuity due =PMT
____ when the annuity occurs at the end of each compounding period.
an ordinary annuity =PMT
Used for cash outflows for college funding, retirement funding, gifting, and insurance premium payments. o Used for cash inflows received from Social Security benefits, pensions, retirement planning, and disability payments
an annuity due
g BEG
example of an ordinary annuity
mortgage
g END
____ is used to evaluate the cash flows associated with capital projects and capital expenditures.
NPV- Net present value
what are the keystrokes used to find NPV?
Use the g CFo, g CFj, and g Nj keys - to multiple CFj
The Method of NPV?
The method discounts the future cash flows at an appropriate discount rate and allows the present value of the inflows to be compounded to the present values of outflows.
what does the NPV result tell us?
If the answer is positive, then undertake the investment. The actual “i” > the required “i.”
If the answer is negative, do not undertake the investment. The actual “i” < the required “i.”
If the answer is zero, then undertake the investment. The actual “i” = required “i.”
NPV vs IRR
The NPV is considered a superior model to IRR when comparing investment projects of unequal lives. Why? Because investing at the required rate of return is more reasonable than at the IRR.
With changes of more than two inflows/outflows in an investment project, there is only one NPV, but multiple IRRs.
__ Allows the financial planner to compare computed rate to required rate of return.
IRR- Internal rate of return
The Method of IRR?
The method discounts the future cash flows at an appropriate method used to determine the exact discount rate to equalize cash inflows and outflows of a specific investment or project.
what are the keystrokes to calculate IRR
Use CHS – used to input cash flows received as a positive number and cash flows paid as negative
g CFo – represents a cash flow at time zero
g CFj – represents a cash flow after time zero
F IRR
when you are discounting future amounts to present value terms, larger interest rates will lead to ____ present values, while smaller interest rates will lead to ____ present values. This is the exact opposite of compounding.
smaller
larger
Calculating a future value will always involve ______ , while calculating a present value will always involve _____.
compounding
discounting
An ____ is a series of equal payments
annuity
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:
CHS is the “change sign” key
must be used in order to respect cash flow convention. Your financial calculator is designed to treat cash inflows going into an investment as a negative number and cash outflows (or funds available) from an investment as a positive number. This is particularly important when you are making a calculation that involves both a lump sum and periodic payments (such as a bond). The context of a problem could require these “payments” to be either additional deposits into an account, or funds that will be withdrawn from an account. Just remember, any money that is going into an investment is negative, and money coming out (or is avail
If there are no periodic payments involved, you may solve for any of the following four variables, given the other three:
n i PV FV
If there are periodic equal payments involved, you may solve for any of the following five variables, given the other four:
n i PV PMT FV
what is the keystroke to enter a discount rate?
CHS i
real rate of return
nominal rate adjusted for inflation
Real rate return formula
n = (Nominal Rate - Inflation Rate)/ (1 + Inflation Rate)
____ is a payment that increases incrementally over time. The increase from one year to the next is usually to compensate for the inflation rate. Therefore, even though the payments are increasing through time, the purchasing power is consistent.
A serial payment
The present value method -
calculates the lump sum that would be required today to fund some future event.
The nominal rate is 7% and the inflation rate is 3%. What is the real rate of return?
nominal rate – inflation rate) ÷ (1 + inflation rate). 7 – 3 = 4 and 4 ÷ 1.03 = 3.88
On June 1st, Donna lent a friend $25,000. The term of the loan is for 6.5 years, and carries an annual interest rate of 8.25%. The first monthly payment payable to Donna is due on July 1st, and the will be due the first of each month thereafter. How much are the monthly payments Donna will receive?
[HP 12C] f REG f FIN 25000 CHS PV 6.5 g 12 × 8.25 g 12 ÷ g END PMT
The Calculator returns: 415.17
Marcia wants to begin a business in seven years. She needs to have $75,000 (in today’s dollars) to begin the business. Inflation is expected to average 3.0% over the next seven years and Marcia’s investment projections show that she can earn 6% on her investments over this time horizon. What serial payment should Marcia make at the end of the first and second years?
[HP 12C] f REG f FIN 75000 FV 7 n 3 ENTER 1.03 ÷ i g END PMT
The Calculator returns: -9,813.90
The first year is $9,813.90 X 1.03 = $10,108.32
The second year is $10,108.32 X 1.03 = $10,411.57
Andre has just learned that in 22 months he is being transferred overseas. He purchased his house exactly 5 years ago and borrowed an initial mortgage amount of $333,700. The term of the loan was 30 years, and carried a fixed rate of 5.75%. How much is André’s current remaining loan balance (after 60 months) and how much will Andre’s remaining balance on his mortgage be in 22 months when he is transferred? (Round your answer to the dollar).
[HP 12C] f REG f FIN 333700 PV 5.75 g 12÷ 30 g 12× g END PMT
The Calculator returns: -1,947.38 60 f AMORT The Calculator returns: -92,690.34 RCL PV The Calculator returns: 309,547.54 22 f AMORT The Calculator returns: -32,100.94 RCL PV The Calculator returns: 298,806.12
Dan is considering buying an apartment building for $3.2 million. The building will generate the following after-tax cash flows:
Year 1 $26,000
Year 2 $20,000
Years 3-6 $31,000
Year 7 $35,000
Furthermore, it is anticipated that Dan can sell this building for $4.3 million in 7 years, net of taxes and transaction costs. Dan has an after-tax opportunity rate of 5%. Calculate the IRR and NPV of this investment opportunity.
HP 12C] f REG f FIN 3200 CHS g CF0 26 g CFj 20 g CFj 31 g CFj 4 g Nj 4335 g CFj f IRR
The Calculator returns: 5.11
5 i f NPV
The Calculator returns: 23.41
1000 ×
The Calculator returns: 23,410.79
Jason is 20 years old and has just been offered an opportunity to invest in his employer’s 401(k) plan. Jason has determined that he can contribute $500 per month starting next month. Jason is reviewing three different mutual funds. Fund A is an income fund with a historical rate of return of 6%. Fund B is a balanced fund with a historical rate of return of 9%. Fund C is an aggressive growth fund that has historically generated a 12% return. Projecting these historical rates of return into the future for each fund, what will be the value of Jason’s 401(k) in 47 years, when Jason is 67 years old? (Round all calculations to the dollar).
[HP 12C] f REG f FIN g END 500 CHS PMT 47 g 12 × 6 g 12 ÷ FV
The Calculator returns: 1,565,937.99
9 g 12 ÷ FV
The Calculator returns: 4,442,742.63
12 g 12 ÷ FV
The Calculator returns: 13,634,370.30
How to calculate Serial Payments:
- Calculate the future value using the inflation rate
PV = given
n = given
i = given
FV = SOLVE - Calculate the serial payments:
FV = Solved
n = given
i = [(1.interest rate / 1.inflation) – 1] x 100
PMT = (Solve**) (annuity due) - When you schedule the future value of payments, All payments are as follows: Example 5 year payments
Solve** x 1.interestrate = ___ x (1.inflation)^4 = payment year 1
Payment year 1 x 1.interestrate = __ x (1.inflation)^3 = payment year 2
Payment year 2 x 1.interestrate = ___ x (1.inflation)^2 = Payment year 3
Payment year 3 x 1.interestrate = ___ x (1.inflation)^1 = Payment year 4
Payment year 4 x 1.interestrate = ___ x (1.inflation)^0 = Payment Year 5
What is Amortization?
is an accounting technique used to periodically lower the book value of a loan or an intangible asset over a set period of time.
How to solve a Loan Amoritzation Question
number of payments(12) f n (to use amort function)
What is the monthly mortgage payment?
Solve for PMT in end mode
How much interest will be paid in the first year?
n= given year
How much loan principal is paid in the first year?
After finding the interest paid click on the x<>y key to get the principal amount
