Discounted Cash Flow Valuation

• All financial assets are priced (valued) based on their expected cashflows

• An asset's size, timing, and risk are factored in

• Financial assets are priced using the discounted cash flow model

• Interest rate equates earlier and later money

• Discount rate is also called the required rate of return, or the cost of capital

• Opportunity cost indicates the return from the next best alternative investment

• Compound interest describes earning interest on the initial principal and prior reinvested interest

• Rule of 72 estimates how long it takes to double money based on prevailing interest rates (72/interest rate)

Discounted Cash Flow Valuation

• Annuity describes consistent cash flows over a fixed time frame

Ordinary annuity

• Payments occur at the period's conclusion

Annuity Due

• Payments transpire at the start of the period
• Future value of an annuity due can be calculated with the formula FV = CF (1 + r)³ + CF (1 + r)² + CF (1 + r)

Growing Annuity

• It is a growing stream of cash flows with a fixed maturity
• PVGA = C * [1 - ((1 + g)/(1 + r))^t] / (r - g)
• C represents the initial future cash payment
• g represents the annual growth rate
• r represents the discount rate

Perpetuity

• It is an annuity where cash flows last indefinitely
• PV = C/r

Preferred Stock

• It gives a fixed cash dividend every period(quarter usually).
• It must be paid before regular shareholder dividends giving it the name preferred

Growing Perpetuity

• It represents growing cash flows that endure indefinitely
• PV=C/(r-g)
• Can be computed as PV = 1.30 / (.10 - .05) = $26

Uneven Cashflow

• Analysis of non-constant cash flows is typically required over fixed payments
• Can be computed with PV = CF1/(1+r) + CF2/(1+r)² ... CFn/(1+r)
• Alternatively, use the Excel function npv (rate, value 1,..., value n)

Time Shifting Problems

• Solves problems like finding the value of an annuity at t=0

• Presumes an interest rate of 9%

• PV = 70/1.09^4 + 70/1.09^5 + 70/1.09^6 + 70/1.09^7 = 175.12

• All rates are not created equally

• Semiannual, quarterly, and compounding periods more frequent than on an annual basis are often

• Compounding on a non annual basis requires adjustments to compounding and discounting procedures

Effective Annual Rate (EAR)

• It measures the real return after compounding has been factored in to a rate
• It utilizes effective annual rate
• EAR = (1 + (APR / m))^m - 1
• Period rate = stated rate = quoted interest rate = APR/# compounding periods

Annual Percentage Rate (APR)

• It shows the yearly cost of a loan, without factoring compounding
• Can solve formula for EAR/APR using Excel functions

Types of Loans

Pure Discount Loan

• Future Value = Present Value (1 + rate of return)^time

Interest-Only Loan

• Only interest is paid each period, the principal is paid at the end

Amortized Loans

Amortized with Fixed Principal:

• The Original balance is simply the # of years

Amortized with Fixed Payment:

• Fixed payments
• The PMT will always include interest paid + principal paid

Retirement Problem

• This is an application of time shifting problems

Chapter 6 Quiz

• Ordinary annuity signifies equal payments overtime
• Perpetuity reflects unending equal payments at a single constant rate
• Stated interest rate = period rate
• Effective annual rate : It is the rate on the annual basis that reflects compounding effects
• The annual percentage rate : rate before considering any compounding effect
• Only cash is received today and repays a single lump sum at some time called a pure discount loan
• Loans in which interest is paid and a lump sum principal is paid can only be interest
• A loan with equal payments and with interest and principal amounts is called an amortized payment
• A loan wherein the regular payments are insufficient to retire the loan after both interest is paid and principal payments
• This is also referred to as a balloon loan

Chapter 7: Interest Rates and Bond Valuation

• Bond means a legal agreement between two parties where one is the investor(you) and the other is a company, government, municipalities, or schools

Bonds contain 3 Key or Fixed features:

• Time to maturity (nper, t)
• Par value or principal/maturity/ future value (FV)
• Coupon rate(%), which is not the discount rate. It is used to calculate the coupon payment (PMT)

Bonds contain 1 Variable feature:

• Discount rate (%) (rate, r)

• A Bond's discount rate(r) is called Yield to maturity

Example

• Bonds issued by Stainless Tubs bear an 8 present coupon, payable semiannually
• The bond matures in 11 and have $1,000 value face
• Currently the bonds sell at $952
• Meaning, the rate and the Excel rate are both 4.34 * 2 which is 8.68%

Interest Rate Risk

• Also called the "duration"
• Denotes risk to fluctuations

All Things Equal

• The greater the bond time to maturity

• The greater the interest rate risk

• When interest rate increases<