1. PVfirm = PVdebt+ PVStock
Bond Valuation
The market value of the firm is the present value of the cash flows generated by the firm’s assets:
The cash flows generated by the firm’s assets are divided among the investors who pay for the assets. If these investors include only debt and equity holders, the market value of the firm can be expressed as:
PVfirm = PVdebt+ PVStock

2. Bond (Debt) Valuation
The price of bonds in the market place is the present value of the cash flows that bondholders have claim to:
These cash flows consist generally of two components, interest and principal. They are generally divided as follows:
That is, interest is paid every period, and the principal is paid at maturity, when the bond comes due.

3. Bond Valuation (Continued)
Terms:
Coupon Payment: the interest paid annually, or semiannually (I). Typically, these payments are fixed so that the interest paid each year is the same.
Principal: the amount borrowed, and repaid at maturity (P).
Coupon Rate: the annual interest payment divided by the principle (I/P)
Current Yield: the annual interest payment divided by the price (I/PV)
Capital Gains Yield: the change in price (over one year) divided by the price at the beginning of the year [(PV1-PV0)/ PV0]
Yield to Maturity: the return investors expect if they buy the bond and hold it until it matures. If the market is in equilibrium, the yield to maturity is also the return investors require given the bond’s risk (rd).

4. Bond Valuation (Continued)
Numerical Example: Suppose a bond with 10 years to maturity has a coupon rate of 10%, a principal amount of $1,000, and a yield-to-maturity of 10%. Assuming interest is paid annually and the bond is in equilibrium,
What is the price of the bond?
What is its current yield?
Current Yield = I/PV =
What is its expected capital gains yield?
Capital Gains Yield = [(PV1-PV0)/ PV0] =

5. Bond Valuation (Continued)
Suppose now that everything else remains constant, but the yield to maturity is 12%. What are the price, the current yield, and the expected capital gains yield?
Current Yield = I/PV =
Capital Gains Yield = [(PV1-PV0)/ PV0] =
What would cause the yield to maturity to be 12% instead of 10%?

6. Bond Valuation (Continued)
The yield to maturity, the return investors expect, is linked to the return investors require, rd.
The required return, rd , is a function of
The real rate of return - the return investors require for deferring consumption (that is, the time value of money)
The expected rate of inflation - the compensation investors require to guard against losses in their purchasing power.
The risk premium - the compensation investors require to accept the possibility that their return will be lower than what they were promised.
If rd is 12%, not 10%, one or more of the three components of the required rate of return must be higher in the second instance than in the first.
Why is yield to maturity linked to rd?

7. Bond Valuation (Continued)
Suppose the expected rate of return does not equal the required rate of return. If the bond above should be priced at $887 because the required rate of return is 12%, but it is priced at $1,000 to give an expected return of 10%, investors are not being compensated for the risk that they bare.
The NPV from buying the bond will be negative (887-1,000), so new investors will not buy.
The NPV from selling the bond will be positive (1, ), so existing investors will want to sell.
The combination of new investors not buying and existing investors wanting to sell will cause the price of the bond to fall.
How far? Why?

8. Bond Valuation (Continued)

9. Bond Valuation (Continued)

10. Bond Valuation (Continued)

11. Bond Valuation (Continued)
See