Midterm Analysis – Eiling
Topic 1: Time Value of Money (TVM)
TVM is a fundamental concept in finance: money can be invested to earn interest or returns, therefore
the value changes over time. You are entitled to some reward when you invest your money because
you are selling the ability to use that money to someone else. It is also assumed that any cash can be
invested in some way because investing is as easy as putting the money in a bank.
Future Value (FV): the lump-sum value of an amount of cash or a series of cash flows at some
time in the future
Present Value (PV): the lump-sum value of an amount of cash or a series of cash flows as of now.
Simple Interest: when interest is not re-invested to the original principal to generate extra
interest on top of interest earned. Example: coupon bond.
Compound Interest: when all interest is re-invested to the original principal so that it helps
generate extra interest in the future. Example: bank savings account.
Annuity: a series of periodic cash flows of the same amount. Can be ordinary annuity or annuity
due. Ordinary annuity means cash payments are made at the end of each period. Annuity due
means cash payments are made in the beginning of each period. For simplicity, you can use the
same formula for both. Just bring the lump-sum value of the annuity due 1 year forward to find
the correct PV (this is a magic trick that will save you a lot of hassle. You don’t need a separate
annuity due formula).
Growing annuity: a series of periodic cash flows that grow at a fixed rate
Perpetuity: a series of infinite cash flows of the same amount
Growing perpetuity: a series of infinite cash flows that grow at fixed rate
Compounding Frequency: compounding frequency refers to how many times a principal earns interest
in a given period (usually in a year).
Quoted Rate (QR): period rate times the number of periods per year – not a very significant
concept in Finance by still good to know
Effective Annual Rate (EAR): an investment’s conceptual annual rate of interest when
compounding occurs more than once per year. Of course, when compounding only occurs once
a year, the EAR is the same as the stated rate.
Continuous compounding: compounding occurs continuously (infinitely many times)
throughout a period (year). Use formula: A = Pe^(rt); A = Amount after growth. P = initial
Principal investment. e = constant. r = interest rate (7% would be 0.07). t = number of periods.
In any formula plugging, be careful to match the correct interest rate with the correct number of periods.
If the interest rate you plug in is a yearly interest rate, then use number of years as t. If you plug in
monthly interest rate, then use number of months as t. Questions: the mortgage questions
Question: mortgage question
Topic 2: Bond Valuation
The idea of bond valuation is to find a theoretical intrinsic value of a bond. This is technically
not a new topic but merely an extension of the time value of money chapter. Just remember
this core concept: the value of a bond right now is the present value of all the future cash flows
this bond will give you, discounted at the current market rate of the interest.
What is a Bond: a bond is a debt contract between a lender and a borrower. Selling a bond
means borrowing money from someone else. Similarly, buying a bond means lending out
money (get this concept straight or you will stumble in your senior year classes)
Face Value (F): the value printed/stated on a bond contract (in practice, usually $1000). At the
end of the bond contract, the borrower will return to the lender an amount equivalent to the