Outline

1
Outline

1. Bond valuation
2. Bond yields
3. Stock valuation

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Bond valuation and yields

• A level coupon bond pays constant semiannual
  coupons over the bonds life plus a face value
  payment when the bond matures.
• The bond below has a 20 year maturity, 1,000
  face value and a coupon rate of 9 (9 of face
  value is paid as coupons per year).

Year 0 Year 0 0.5 0.5 1 1 1.5 1.5 . . . . . . 19.5 19.5 20 (Maturity Date) 20 (Maturity Date)


45 45 45 45 45 45 . . . . . . 45 45 45 1,000 45 1,000
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Market value of bonds

• To determine the market value of a bond, just
  determine the PV of the annuity of coupon
  payments and add the PV of the face value.
• In your calculator you can enter the semi-annual
  coupon payment as PMT and the face value as FV.
  Convert the yield to maturity to a semi-annual
  effective rate and enter as I/YR and enter the
  number of payments as N. Use PV to calculate the
  current market price of the bond.

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Bond market values continued

• Using the bond example given, calculate the
  market price if the quoted yield is
• 6
• 9
• 12
• What do you notice about the market price as
  interest rates rise?
• Relate the market price to the yield and coupon
  rate.
• Define selling at a discount and selling at a
  premium.

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Bond values self study

• Pure discount bonds (no coupons)
• Consols (no maturity, perpetuity of coupons)

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Determining bond yields

• Using our example, determine the bonds quoted
  yield if the current market price is 1,213.55.

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Stock valuation

• The fundamental of stock valuation is that the
  current price should reflect the present value of
  all future cash flows expected to accrue to the
  stockholder. This leads to two general models for
  valuation
• Discount the expected future dividends expected
  to occur from now on into eternity.
• Discount the expected future dividends expected
  to be received over the next defined time period
  and the expected price that can be received at
  the end of that time period.
• Note both methods are equivalent as the ending
  price in the second method should reflect
  dividends that are expected to occur further in
  the future.

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No-growth stock valuation

• Preferred stock have constant dividends that are
  continually paid as long as the company is
  healthy. The price of a preferred share is thus
  the present value of a constant perpetuity of
  expected dividends.
• E.g., a preferred share of the Royal Bank pays
  quarterly dividends of 0.40 per share. The
  relevant discount rate, given the risk of the
  shares, is 8 (note, stock returns are normally
  quoted as effective annual rates). What is the
  current value of this stock assuming the next
  dividend is to be paid in 2 months?

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Constant growth stock valuation

• A company with sales and profits expected to grow
  along with overall economic growth may be
  expected to approximate a constant growth of
  dividends through time. If this is the case, the
  growing dividends can be valued as a growing
  perpetuity. Note, though, that it does not make
  sense to have a growth rate for the stock greater
  than the long-term economic growth rate as that
  would imply that eventually the company value
  would be greater than the total value of the
  economy.
• Example Coca Cola stocks last dividends was
  0.75. Dividend are paid each quarter, the next
  dividend is in 1 month and each dividend is
  expected to grow by 1 each quarter. The relevant
  discount rate given Cokes risk is 12. What is
  the current price of Cokes stock?

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Other valuation models for stocks

• Sometimes stocks are valued assuming uneven
  dividends in the near future followed by
  dividends that grow at a constant rate. To value,
  the PV of each of the uneven dividends must be
  individually calculated, then the PV of the
  ending growing perpetuity can be added.
• Sometimes two growth rates are assumed for
  stocks an initial high growth rate over the near
  term followed by a more normal growth rate over
  the long term. To value, the PV of a growing
  annuity is calculated for the near-term dividends
  and then the PV of a growing perpetuity is
  calculated and added for the long-term dividends.

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Summary and conclusions

• For annuities and perpetuities, we must ensure
  the discount rate is effective and quoted over a
  period the same as the time period between cash
  flows.
• TVM principles are useful for valuing stocks and
  bonds.
• If you understand TVM principles, you do not need
  to blindly rely on another party to determine
  value or interest costs. You know what factors
  affect these and you can determine reasonable
  numbers for yourself.