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Valuation of Single Cash Flows Summary

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Valuation
Valuation of single cash flows
A single cash flow will be discounted by the appropriate rate and time, using
Table A2.1. Read across for the discount rate and down for the number of
periods. Multiply the cash flow by the present value interest factor (PVIF
i,n
) to
get the present value of the cash flow.
Valuation of multiple cash flows
Valuation of a series of equal cash flows is the valuation of an annuity stream. If
the discount rate is the same and all cash flows are the same, then you have an
annuity (if the cash flows go on indefinitely, it is a perpetuity). The annuity can
be valued by using Table A2.2. You will have the cash flow, the discount rate and
the number of periods of the same cash flow, so read across for the interest rate
and down for the number of periods. Multiply the cash flow by the present value
annuity interest factor (PVAIF
i,n
) to get the present value of the annuity stream.
With the valuation of the annuity, it is assumed that the first cash flow occurs at
the end of year 1. If the cash flow starts immediately there is an adjustment that
needs to be made. Multiply the PVAIF
i,n
by (1+interest rate). This reflects the fact
that the first cash flow is one year earlier. All the present and future value tables
assume that the cash flow is at the end of the year.
With valuation you are bringing future cash flows back to a present value.
Valuation of bonds
Bonds will usually have a fixed life, eg, five years, ten years, fifteen years, etc. A
very small number of bonds are irredeemable, which means they are
perpetuities, the bond will keep paying cash flows indefinitely.
A bond will have a face value at which it is issued and redeemed. This face value
is £100 in the UK and $1,000 in the US. There are other terms that are used for
this value; nominal value, redemption value. So the bond will be issued at £100
and at the end of the bond’s life, at maturity it will be redeemed for £100. The
bondholder has lent the company a £100 and at the end of the period, the
bondholder is repaid the £100. In the intervening years the bondholder is paid a
coupon (cash). This is the income the bondholder gets for lending the company
the £100. The level of the coupon depends on the creditworthiness of the
company. The more creditworthy the company, the lower the coupon, because
there is low risk of the bondholder not being repaid at the maturity of the bond.
So the bond has a face value (£100), it has a coupon (say 5%) and it has a fixed
term (say 5 years left to maturity). With that information we can lay out the cash
flows to the bond and value the bond. The value of the bond will be the

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discounted value of all its future cash flows. The cash flows of the bond will be
discounted at the appropriate interest rate for the timing of each cash flow. For
example, assume the bond is a UK Government bond, this will be a risk free bond,
there is no risk of non-payment, so the cash flows will be discounted by the risk
free rate of interest for each time period.
Price = 5 + 5 + 5 + 5 + 105
The first cash flow will be discounted by the one year spot rate (1+
0
s
1
), the
second cash flow will be discounted by the two year spot rate (1+
0
s
2
)
2
and so on
through to the end of year 5.
The interest rates will be the set of spot rates from the term structure of interest
rates. This is a set of interest rates that are not fixed but can fluctuate on a daily
basis according to the economic conditions in a country. There is an example of
a term structure with this link; http://markets.ft.com/markets/bonds.asp
The cash flows are discounted and the discounted cash flows added up to give
the bond price. Once you have the bond price, the yield to maturity (YTM) can be
worked out. This is the average return on the bond, given today’s price if held
through to maturity.
Valuation of Equity
We have seen how to value simple cash flows, annuity cash flows and bond cash
flows. We now move on to valuing the equity of a company. This is different
from valuing the bond. With the bond we were valuing certain cash flows (the
coupon payments), with equity we are valuing uncertain cash flows. Equity is
risky, shareholders only get the residual cash flow that a company generates.
Before the shareholders get their return the bondholders have to be paid their
interest (the coupon payments).
The cash return to the shareholder is the dividend. The total return to the
shareholder is the dividend plus the capital gain. The dividend is the only cash
that is paid out by the company, so the valuation is based on that cash flow.
Bonds have fixed lifetimes of 5 years, 10 years, etc. Equities have an indefinite
lifetime. When shares are floated on to the stock market, the assumption is that
the company will keep on going indefinitely. A company does not sell shares on
to the stock market for 5 or 10 years like the bond. So a company on the stock
market is perpetuity. A company on the stock market will want to increase its
dividend each year to reward investors. So the company’s shares can be valued
like a growing perpetuity.
The formula for a perpetuity is; cash flow/ interest rate
The formula for a growing perpetuity is; cash flow/(interest rate growth rate)
Adapted for share valuation, this becomes;
P0 = D
1
/(r g)

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Valuation Valuation of single cash flows A single cash flow will be discounted by the appropriate rate and time, using Table A2.1. Read across for the discount rate and down for the number of periods. Multiply the cash flow by the present value interest factor (PVIFi,n) to get the present value of the cash flow. Valuation of multiple cash flows Valuation of a series of equal cash flows is the valuation of an annuity stream. If the discount rate is the same and all cash flows are the same, then you have an annuity (if the cash flows go on indefinitely, it is a perpetuity). The annuity can be valued by using Table A2.2. You will have the cash flow, the discount rate and the number of periods of the same cash flow, so read across for the interest rate and down for the number of periods. Multiply the cash flow by the present value annuity interest factor (PVAIFi,n) to get the present value of the annuity stream. With the valuation of the annuity, it is assumed that the first cash flow occurs at the end of year 1. If the cash flow starts immediately there is an adjustment that needs to be made. Multiply the PVAIFi,n by (1+interest rate). This reflects the fact that the first cash flow ...
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