FM212 Revision MT
Michaelmas Term
Week 1
Discount Rates: interest rate used to compute the present value of future cash flows, also
known as the forgone opportunity cost of capital
Present Value: value today of future cash flows PV
rit
=
Future Value: amount an investment is willing to grow after earning interest FV ((1+r)T
=
Simple Interest ((1+ rn) Compound Interest C(1+r)
Stated Annual Rate: simple interest earned without compounding EAR= [1+ated] 1
-
Effective Annual Rate: interest that includes compounding (same as annual interest rate)
Net Present Value: computing each individual cash flow’s present value and summing all of
them. Invest if positive and don’t if negative, and it is optimal under some assumptions
Inflation rate (T ), Nominal IR (r), Real IR (i) i
-
=
i
r= π
+
Week 2
Annuity Assumptions
• First cash flow occurs at the end of first period, discount rate denoted by r
• Each cash flow must grow at constant rate g, occurring at constant intervals
• finite n periods between cash flows and PV valuation point is before first cash flow
Growth: PV
c[ )"]
= Normal:PV
c[in]
=
Perpetuity Assumptions
• First cash flow occurs at the end of period one and constant growth rate g
• CF at constant intervals, with same discount rate, n number of periods to infinity
• PV point is one period before first cash flow and discount rate r > g
Growth:PV Eg
= Normal:PV= I
,Week 3
Bonds are simply fixed-income securities that is issued by a borrower and purchased by an
investor with the main aim to raise money. Upon issue the investor is obliged to pay the issue
the bond price and expects pre-specified payments (with interest) over time
Par Value: nominal value of bond to be repaid at maturity (face value)
Coupon: the periodic payment of interest on the bond, with coupon rate being expressed as
a percentage of the bond’s par value
Maturity Date: the specified date on which the par value of bond must be repaid
Discount: when a bond is trading below its par value
Premium: when a bond is trading above its par value
Zero-coupon bonds: A bond that pays no annual interest but is sold below par so all the
compensation is paid to the zero coupon bondholder in the form of capital appreciation
Coupon bonds: bonds with interval coupon interest payments up to maturity plus par value
Yield to Maturity: a hypothetical discount rate that, when used to compute the PV of a bond’s
cash flow, gives you the bond’s market price as the answer. YTM is used rather than prices as
it can be very different across bonds due to differing coupon rates. Therefore, a higher bond
price must mean a lower YTM vice versa
Bond prices are natively related to interest rates. If the coupon rate is greater than the YTM,
price of bond will be above par (premium), vice versa
Stockholders are owners of the firm and have the right to vote on company policy and
strategy, whereas bond holders are not
Common Stock: security representing the share in ownership of a corporation
IPO: first sale of stock in a corporation to the public
Secondary Market: a market which previously issued shares are traded among investors
Dividends: payments made to shareholders by companies
Dividend Yield: ratio of annual dividend to share price
P/E Ratio: share price divided by the earnings per share
, Market Value: total stock market value of a firm’ stock (share price * shares)
Book Value: accounting value of the firm’s equity on the balance sheet
Liquidation Value: amount that would be available to shareholders if firm was liquidated
Pt currentprice
E t(D++) Ee(Pt-Pt)
=
E(r) =
+
P1+1 price after dividend paid
=
Pt Pt
Gordon growth
Po E(r)
=
(perquity) Po=Ig (with growth) formula for
pricing stocks
Payout Ratio: the ratio of dividends to earnings
Plowback Ratio: The proportion of earnings retained by the firm and used for investment
EPS
ROE is a measure of the amount of earnings that a pound of equity creates ROE: Book Value Equityper shoe
of
A firm’s earnings growth is: 9 ROEx Plowback Ratio
= Divided growth ROEX Plowback
=
The difference between the firm that plows back earnings and the firm that does not is called
the Present Value of Growth Opportunities (PVGO). P. E PVGO
= +
When re-arranging, EPS ratio understates the required returns for firms with large PVGO,
hence not good unless you adjust for growth
Week 4
Interest rates are not the same for different maturities. The spot interest rate ( ) is the rate
fixed today on a loan that is made over a specified time period t. Bonds are priced using this
Arbitrage: an investment strategy that has a positive cash flow today and zero cash flow
If we are guaranteed £100 in the future, borrow PV of £100 and pay in future for positive
cash flow today and zero cash flows in the future
Short Selling Bond: borrow the bond and sell it on the market, then compensate the broker
for any coupons that the bond pays, then buy the bond in market and return bond to broker.
Short sale is profitable when bond price goes down
If a bond has a no arbitrage price of £97 and was priced at £98 in the market, you can make
arbitrage profits. At t=0, you short the bond and go long the replicating portfolio to make
Michaelmas Term
Week 1
Discount Rates: interest rate used to compute the present value of future cash flows, also
known as the forgone opportunity cost of capital
Present Value: value today of future cash flows PV
rit
=
Future Value: amount an investment is willing to grow after earning interest FV ((1+r)T
=
Simple Interest ((1+ rn) Compound Interest C(1+r)
Stated Annual Rate: simple interest earned without compounding EAR= [1+ated] 1
-
Effective Annual Rate: interest that includes compounding (same as annual interest rate)
Net Present Value: computing each individual cash flow’s present value and summing all of
them. Invest if positive and don’t if negative, and it is optimal under some assumptions
Inflation rate (T ), Nominal IR (r), Real IR (i) i
-
=
i
r= π
+
Week 2
Annuity Assumptions
• First cash flow occurs at the end of first period, discount rate denoted by r
• Each cash flow must grow at constant rate g, occurring at constant intervals
• finite n periods between cash flows and PV valuation point is before first cash flow
Growth: PV
c[ )"]
= Normal:PV
c[in]
=
Perpetuity Assumptions
• First cash flow occurs at the end of period one and constant growth rate g
• CF at constant intervals, with same discount rate, n number of periods to infinity
• PV point is one period before first cash flow and discount rate r > g
Growth:PV Eg
= Normal:PV= I
,Week 3
Bonds are simply fixed-income securities that is issued by a borrower and purchased by an
investor with the main aim to raise money. Upon issue the investor is obliged to pay the issue
the bond price and expects pre-specified payments (with interest) over time
Par Value: nominal value of bond to be repaid at maturity (face value)
Coupon: the periodic payment of interest on the bond, with coupon rate being expressed as
a percentage of the bond’s par value
Maturity Date: the specified date on which the par value of bond must be repaid
Discount: when a bond is trading below its par value
Premium: when a bond is trading above its par value
Zero-coupon bonds: A bond that pays no annual interest but is sold below par so all the
compensation is paid to the zero coupon bondholder in the form of capital appreciation
Coupon bonds: bonds with interval coupon interest payments up to maturity plus par value
Yield to Maturity: a hypothetical discount rate that, when used to compute the PV of a bond’s
cash flow, gives you the bond’s market price as the answer. YTM is used rather than prices as
it can be very different across bonds due to differing coupon rates. Therefore, a higher bond
price must mean a lower YTM vice versa
Bond prices are natively related to interest rates. If the coupon rate is greater than the YTM,
price of bond will be above par (premium), vice versa
Stockholders are owners of the firm and have the right to vote on company policy and
strategy, whereas bond holders are not
Common Stock: security representing the share in ownership of a corporation
IPO: first sale of stock in a corporation to the public
Secondary Market: a market which previously issued shares are traded among investors
Dividends: payments made to shareholders by companies
Dividend Yield: ratio of annual dividend to share price
P/E Ratio: share price divided by the earnings per share
, Market Value: total stock market value of a firm’ stock (share price * shares)
Book Value: accounting value of the firm’s equity on the balance sheet
Liquidation Value: amount that would be available to shareholders if firm was liquidated
Pt currentprice
E t(D++) Ee(Pt-Pt)
=
E(r) =
+
P1+1 price after dividend paid
=
Pt Pt
Gordon growth
Po E(r)
=
(perquity) Po=Ig (with growth) formula for
pricing stocks
Payout Ratio: the ratio of dividends to earnings
Plowback Ratio: The proportion of earnings retained by the firm and used for investment
EPS
ROE is a measure of the amount of earnings that a pound of equity creates ROE: Book Value Equityper shoe
of
A firm’s earnings growth is: 9 ROEx Plowback Ratio
= Divided growth ROEX Plowback
=
The difference between the firm that plows back earnings and the firm that does not is called
the Present Value of Growth Opportunities (PVGO). P. E PVGO
= +
When re-arranging, EPS ratio understates the required returns for firms with large PVGO,
hence not good unless you adjust for growth
Week 4
Interest rates are not the same for different maturities. The spot interest rate ( ) is the rate
fixed today on a loan that is made over a specified time period t. Bonds are priced using this
Arbitrage: an investment strategy that has a positive cash flow today and zero cash flow
If we are guaranteed £100 in the future, borrow PV of £100 and pay in future for positive
cash flow today and zero cash flows in the future
Short Selling Bond: borrow the bond and sell it on the market, then compensate the broker
for any coupons that the bond pays, then buy the bond in market and return bond to broker.
Short sale is profitable when bond price goes down
If a bond has a no arbitrage price of £97 and was priced at £98 in the market, you can make
arbitrage profits. At t=0, you short the bond and go long the replicating portfolio to make
