Chapter 6: Discounted Cash Flows and Valuation
I. Multiple Cash Flows
1. Draw a timeline to determine the number of periods for which each cash
flow will earn the rate of return.
2. Calculate the future value of each cash flow using the equation:
FVn= PV x (1+i)^n
Where:
FVn = future value of the investment at end of period n
PV = original principle (P0) or present value
i = the rate of interest per period
n = the number of periods, often in years
3. Add the future values
II. Level Cash Flows: Annuities and Perpetuities
- Annuity: A series of equally-spaced and level cash flows extending
over a finite number of periods.
- Perpetuity: A series of equally-spaced and level cash flows that
continue forever.
- Ordinary Annuity: cash flows occur at the end of a period.
Example: mortgage payment, interest payment to bondholder.
- Annuity Due: cash flows occur at the beginning of a period
Example: lease
III. Calculate the present value of an annuity
- To calculate a future value or a present value is to calculate an
equivalent amount
- The amount reflects an adjustment to account for the effect of
compounding
Present value of an annuity
1. amount needed to produce the annuity
2. current fair value or market price of the annuity
3. amount of a loan that can be repaid with the annuity
Level Cash Flows: Annuities and Perpetuities
Loan Amortization: (khấu hao khoản vay)
- Each payment includes less interest and more principal; the loan is paid
off with the last payment
- Amortization schedule shows interest and principal in each payment,
and amount of principal still owed after each payment
Mỗi khoản thanh toán bao gồm ít tiền lãi hơn và nhiều tiền gốc hơn;
khoản vay được trả hết với lần thanh toán cuối cùng
Lịch khấu hao thể hiện tiền lãi và tiền gốc trong mỗi lần thanh toán và
số tiền gốc còn nợ sau mỗi lần thanh toán
Tìm lãi suất:
Finding the Interest Rate:
- The present value of an annuity equation can be used to find the
interest rate or discount rate for an annuity
- To determine the rate-of-return for an annuity, solve the equation for i
- Using a calculator is easier than a trial-and-error approach
- Giá trị hiện tại của một phương trình niên kim có thể được sử dụng để tìm lãi
suất hoặc tỷ lệ chiết khấu cho một niên kim
- Để xác định tỷ lệ hoàn vốn cho một niên kim, hãy giải phương trình cho i
- Sử dụng máy tính dễ hơn phương pháp thử và sai
Future Value of an Annuity (FVA)
Perpetuity
- A stream of equal cash flows that goes on forever
- Preferred stock and some bonds are perpetuities
- Equation for the present value of a perpetuity can be derived from the
present value of an annuity equation
- Dòng tiền đều nhau kéo dài mãi mãi
- Cổ phiếu ưu đãi và một số trái phiếu là vĩnh viễn
- Phương trình giá trị hiện tại của một khoản vĩnh viễn có thể được suy
ra từ giá trị hiện tại của một phương trình niên kim
Present Value of a perpetuity (PVP) o
Ordinary Annuity versus Annuity Due
- Present Value of Annuity Due
Cash flows are discounted for one period less than in an ordinary
annuity
- Future Value of Annuity Due
Cash flows earn compound interest for one period more than in an
ordinary annuity.
Ordinary Annuity versus Annuity Due
- The present value or future value of an annuity due is always higher
than that of an ordinary annuity that is otherwise identical.
Chapter 8:Bond Valuation and the Structure of
Interest Rates Learning Objectives
I. Bond Valuation
PB = PVCoupon Payments + PVPar Value
-General equation for the price of a bond:
C:Annual Coupon Payment
F: Bond’s Face Value
I:interest rate
C = iC x F
iC: coupon rate
oSemiannual Compounding
oZero Coupon Bonds
F: Face Value
I:interest rate
n: number of years until maturity
M:number of coupon payments in a year
III. Bond Yields
oYield to Maturity (YTM)
•YTM
the rate that makes the present
value of the bond’s cash flows
equal the price of bond
the rate a bondholder earns if
the bond is held to maturity
and all coupon and principal
payments are made as
promised
–changes daily as interest rates change
oEffective Annual Yield
