The Time Value of Money Flashcards
What is opportunity cost?
The next best alternative foregone return in decision making
What is the saying about the time value of money?
Explain
A dollar today is worth more than a dollar tomorrow.
One reason for this is the opportunity costs of holding cash instead of investing in higher-return projects. Also, inflation.
What does the time value of money concern?
Both present value (PV) and future value (FV)
What is the measure of time value of money?
Interest rate (r):
- Expected rate of return
- Discount rate
- Opportunity cost of money
Is travelling from the future the expected rate of return?
No, that is the discount rate.
Travelling to the future is the expected rate of return.
What is the equation showing the FV of a single cash flow?
FV = C x (1 + r)^t
C= Cash flow
r = Periodic interest rate
t= No. of period interest is calculated
What happens when funds are invested for a long time in terms of interest?
The longer the funds are invested, the greater the advantage with compound interest
Define annuity
A stream of equal cash flows that occurs yearly over a given period
Example of future value of annuities:
Your education account – an annuity of £2,000 for 15 years. The FV of the account at the end of year 15 is the sum of the FV of the 15 individual CFs, given r = 3%:
FV1st CF = £2,000 x 1.0314 = £3,025.18
FV14th CF = £2,000 x 1.031 = £2,060.00
FV annuity = FV1st CF + FV2nd CF + … + FV15th CF = £37,197.83
> £30,000 so your educational cost is safely covered
What is the equation for the FV of an annuity?
FV annuity = C / r x [(1 + r+)^t - 1]
What is the equation for the PV of a future single cash flow?
PV = C / (1+r)^t = C x 1 / (1 + r)^t
What is 1 / (1 + r)^/t known as?
The discount factor
How can you calculate the discount factor?
PV / C
What is the equation for the present value of multiple cash flows happening at different periods (Discounted cash flow formula (DCF) ?
PV0 = [C1 / (1+r)^1] + [C2 / (1+r)^2 + …
In the discounted cash flow formula, if t is a finite or infinite number, what is it the PV of?
Annuity if t is a finite number.
A perpetuity if t is an infinite number.
In the discounted cash flow formula, if t is a finite or infinite number, what is it the PV of?
Annuity if t is a finite number.
A perpetuity if t is an infinite number.
Your education will increase your annual salary (without the degree) by £1,800 for the next 30 years. Given a discount rate of 5%, the PV of salary increase is?
PV = (1800 / 0.05) X [1 - (1 / (1 + 0.05)^30 )] = £27,670.41
What is the equation for the PV of annuities?
PVannuity= [C / r] x [1 - (1 / (1 + r)^t]
What is the net present value (NPV) of a project or investment?
It is the difference between the present value of its benefits and the required investment
What is the NPV formula?
NPVo= Co + PVo = Co + Sigma[Ct / (1 +r)^t]
Co = initial investment for the project. Cash outflow so has a negative sign
r = opportunity cost of capital
What is the NPV rule?
Accept investments with positive NPVs
What is meant by perpetuity?
Like annuity but the cash flow goes on forever
What is the formula for the PV of perpetuities?
PV perpetuity= C / r
What is the formula for the PV of growing annuities?
PV of growing annuities = [C1 / (r - g)] x [1 - [(1 + g) / (1 + r)]^t]
g= the annual growth rate of cash flow
What is the equation of the PV of a growing perpetuity?
PV of a growing perpetuity = C1 / (r - g)
What is the effective annual rate (EAR)?
The annual rate of return actually earned after adjustments have been made for different compounding periods
What is the annual percentage rate (APR)?
Annualised interest rate without compounding (the quoted rate)
How do you calculate EAR?
EAR = (1 + periodic rate)^m - 1
Periodic rate = stated annual rate /m
m = the number of compounding periods per year
Compute EAR if the stated annual rate (this is the annual percentage rate, APR) is 12%, compounded semi-annually
Here m = 2 , so the periodic rate is 12/2= 6%.
Thus, EAR= (1 + 0.06)2 - 1 = 1.1236- 1 = 0.1236 = 12.36%
