Reading 1: Time Value Of Money

Question 1

Interpret interest rates as required rates of returns, discount rates, or opportunity cost

Answer 1

Interest Rates: Denoted as “r” and reflects the rate of return that depicts the relationship between differently dated cash flows

Discount Rates: reduce FV by its value based on how much time passes before the money is paid

Required Rate of Return: is the minimum rate of return an investor must receive in order to accept the investment

Opportunity Cost: The value investors forgot by choosing a particular course of action.

Question 2

Explain an interest rate as the sum of a real risk free rate + premium that compensate investors for bearing distinct type of risk

Answer 2

• Economist view interest rates as being set in the market place by the forces of supply and demand, where investors are the suppliers of funds and the borrowers are demanders of funds.
• Interest rate = Real risk free rate + inflation premium + Default Risk premium + liquidity premium + Maturity premium

Real risk free rate: single period of interest for a completely risk free security with absent inflation

Inflation premium: Compensates investors for inflation and reflects the average inflation rate expected over the maturity of the debt. (Real risk free rate + inflation premium = Nominal Risk Free Rate)

Default risk premium: Compensates investors for the possibility of failure to make a promised payment on time in the contracted amount.

Liquidity Premium: Risk of loss relative to an investment FCF if the investment needs to be converted to cash quickly

Maturity Premium: increased sensitivity of the market value of debt to a change in market interest rates as maturity is extended, holding all else equal.

Question 3

Calculate and interpret the effective annual rate, given the stated annual interest rate and the frequency of compounding

Answer 3

The effective annual rate represents the true effective rate on an annual basis accounting for compounding.

Formula: EAR = (1 + Periodic Interest rate) ^ m - 1

Formula (continuous): EAR = e^rs - 1

Question 4

Calculate the solution for TVM problems with different frequencies of compounding

Answer 4

Time value of money - is a popular topic in investment mathematics which deals with equivalence relationships between cash flows with different dates

Formulas:
PV = FV (1+r/m)^-nm
FV = PV (1+r/m)^nm 
FV Continuous Compounding = PVe^(rs x N) 
N = LN(FVn/PV) / LN(1+r)
I/Y = (FVn / PV)^ (1/N) - 1
PMT = PV/PV Annuity Factor

Question 5

Calculate and interpret the FV and PV of a single sum of money, an ordinary annuity, an annuity due, perpetuity, and a series of unequal cash flows (cash flow additivity).

Answer 5

Annuity: A finite set of level of sequential cash flows

Ordinary Annuity: Has the first cash flow occurs one period from now (indexed at T=1)

Annuity Due: Has the first cash flow occur immediately (indexed at T=0)

Perpetuity: is a perpetual annuity, meaning a set of level never ending sequential cash flows with the first cash flow occurring one period from now (indexed at T=1)

Note: you can move between an ordinary annuity and an annuity due by multiplying an ordinary annuity by (1+r)

CF Additivity: when dealing with uneven cash flow, we take maximum advantage of the principle that dollars amounts indexed at the same point in time are additive to one another.

Formulas:

FV = A [((1+r)^N - 1) / r]
PV = A [ (1-(1+r)^-N) / r]
PV Perpetuity = A/r