Week 2 : Time Value of Money Flashcards
Why does money have a time value?
- Suppose you have a choice of receiving Rs100 today or in 1 year’s time.
- Assuming that there is no inflation and no uncertainty as to the receipt of Rs100 in 1 year’s time, what would you do?
- As a rational person, you will choose to take the money today.
- This means that Rs100 today is more valuable than what it would be in 1 year’s time.
- In fact, the further in time cash is to be received, the higher is its value now.
- This is why investors require some kind of compensation (called interest) to forego current consumption and to increase future consumption.
Factors Influencing TVM
- The nominal risk-free rate of return
- This is a return to the investor for giving up current consumption/liquidity in order to increase future consumption, assuming there is no future inflation and no uncertainty as to the receipt of the increased cash flows in the future. - Inflation
-If prices rise, value of money in terms of purchasing power declines overtime.
-Investors will, therefore, require further compensation in the form of an inflation premium.
-Real risk-free rate of return = Nominal risk
free return + Inflation premium
= 5% + 5% =10% - Risk
-If promised future cash flows are uncertain, then the investor will require a risk premium.
-The amount of the risk premium will depend on the level of risk and uncertainty which the investment is
subject to.
Real risk-adjusted return = Real risk free
return +Risk premium
10%+6% =16%
Timeline
- A timeline is a linear representation of the timing of potential cash flows.
- It helps to visualize a financial problem.
- It is important to differentiate between 2 types of cash flows:
- Inflows
- Outflows
Inflows and Outflows
-Cash outflows: amount of capital used for buying financial products today, i.e. for investing.
E.g. when buying shares of common stock
-Cash inflows: amount of capital obtained in the future, i.e. the returns from actual investments.
E.g. Dividend payments from shares of common stock.
Timeline
3 rules apply for the timeline:
- Only values at the same point in time can be compared or combined.
- To move a cash flow forward in time, it must be compounded (Future Value)
- To move a cash flow backward in time, it must be discounted (Present Value)
Future Value (FV)
- If a capital amount is invested today, it will offer interest in future periods.
- To calculate the interest the following can be used:
(i) Simple interest
(ii) Compound interest
Simple interest
-Interest earned is not added back to the principal amount invested in order to calculate subsequent interest amounts.
Example 1:
-Suppose you invest Rs1,000 for 2 years at 10% simple interest per annum. Calculate the future value at the end of 2 years.
FV = PV + Int yr 1 + Int yr 2
= 1000 + (0.1x1000) + (0.1x1000)
=1000 +100+100
=1200
FV = PV(1+Rn) where R = interest rate, n = years
= 1000(1+0.2) = 1200
(ii) Compound interest
-Interest earned is added back to the principal amount (i.e initial amount invested) to calculate subsequent interest payments.
Example 2:
-Suppose you invest Rs1,000 for 2 years at 10% compound interest. What is the future value at the end of 2 years?
FV = PV + Int yr 1 + Int yr 2
= 1000 +(0.1x1000) + (0.1x[1000+100])
=1210
FV = PV (1+R)ª where a = n = number of years
= 1000 (1+0.1)² = 1210
Present Value (PV)
-When the future value and interest rates are known, the present value of investment may be determined through discounting. Example 3: -You have investment that will produce Rs1,331 at end of year 3. Calculate the present value, given a rate of return of 10%. FV = PV (1 + R )ª PV = FV / (1 + R )ª (Dividing) PV = 1331 /(1+0.1)³ = 1000 PV = FV / (1+Rn) (Dividing)
Example: Effective Annual Rate
-An investment of Rs1000 is made at a 6-monthly interest rate of 5%.
-The interests are compounded on a 6 monthly basis over 3 years.
-Calculate the effective annual rate (interest rate paid over 1 year)
Method 1: (calculate future value)
-Investment over 3 years (i.e. 6 periods of 6
months):
Future value = 1000(1.05) 6 = 1340.095
Assume effective annual rate = R
1000*(1 + R) 3 = 1340.095
R = 10.25%
Interest compounded monthly. How many
periods do we have in 1 year? 12 periods
Interest compounded quarterly? 4 periods
Method 2: (using formula) Formula: Effective annual rate = [(1+r) N – 1] Where r = periodic interest rate; N = number of periods in 1 year EAR = (1 + 0.05) 2 – 1 = 0.1025 = 10.25% Monthly compounded, N = 12 Quarterly compounded , N = 4
Annuity:
-Fixed payments made at uniform
time intervals.
E.g. Annuity (A) being paid over 5 years:
0 1 2 3 4 5
Ordinary Annuity
Due Annuity
Future Value (ordinary annuity)
= A (1 + r) 4 + A (1 + r) 3 + A (1 + r) 2 +
A (1 + r) + A
Future Value (due annuity)
= A (1 + r) 5 + A (1 + r) 4 + A (1 + r) 3 +
A (1 + r) 2 + A (1 + r)
Present Value (ordinary annuity)
= A/ (1 + r) + A/ (1 + r) 2 + A/ (1 + r) 3 +
A/ (1 + r) 4 + A/ (1 + r) 5
Present Value (due annuity)
= A + A/ (1 + r) + A/ (1 + r) 2 + A/ (1 + r)
3 + A/ (1 + r) 4
