Chapter 7: Valuation
I. Basic Valuation
a. Need to make some estimate the return from the investment in $ or as a percent of
investment.
b. Need to make some estimate of the risk associated with the investment
c. The value of any asset is equal to the Present Value of all future cash flows from the asset.
d. Discount rate for PV calculation includes risk premium
II. Bond Valuation
a. Discount Bond
i.
PVbond = Fvbond/(1+i)n
ii. I includes risk premium
b. Coupon Bond – Formula Page 186
i. Price is the Present value of the future income stream
ii. What is the value of a $1,000, 5 year bond that pays 7% if the discount rate is 7%
Year Payment Present Value
1 $70 $65.42
2 $70 $61.14
3 $70 $57.14
4 $70 $53.40
5 $1,070 $762.90
Total $1,350 $1,000.00
The value of the bond equals the par value when the discount rate equals the interest
rate. In this case 7% = 7%.
iii. What is the value of a $1,000, 5 year bond that pays 7% if the discount rate is 8%
Year Payment Present Value
1 $70 $64.81
2 $70 $60.01
3 $70 $55.57
4 $70 $51.45
5 $1,070 $728.33
Total $1,350 $960.07
The value of the bond is less than par value when discount rate is higher than the
interest rate. In this case 8% >7%
iv. What is the value of a $1,000, 5 year bond that pays 7% if the discount rate is 6%
Year Payment Present Value
1 $70 $66.04
2 $70 $62.30
3 $70 $58.77
4 $70 $55.45
5 $1,070 $899.57
Total $1,350 $1,042.12
The value of the bond is more than par value when discount rate is lower than the interest
rate. In this case 6% < 7%
III. When the bond is issued the interest rate must equal the discount rate or the bond won’t sell.
IV. But, since the interest rate is fixed and the discount rate may change, the bond value may
change
a. Changing economic conditions
i. Prevailing Interest rates
b. Change in risk premium for the firm
V. Yield to Maturity
a. Yield to maturity is the total return on the bond
b. It includes interest payments plus capital gains or losses
a. In the example above, buying the bond at a discount of $960 raises the YTM of the bond to
the 8% return required by the market. The $39.39 capital gain increases the effective
yield of the bond from 7% to 8%
b. In the example above, buying the bond at a premium of $1,042 lowers the YTM to the
required 6%. The $42 capital loss lowers the effective yield from 7% to 6%
VI. Common Stock Valuation
a. Same principle applies as for bonds but dividends with stocks are less certain.
b. To value stock you need some assumption about dividends
c. Note that capital gains are not relevant in stock valuation – page 192
d. Zero Growth Model
i. Same dividend expected each year
ii. Valuation is same a Perpetuity D/k
iii. Dividend is $3 and 15% return 3/.15=$20
iv. Most commonly used model
e. Constant Growth
i. Assumes exponential growth of company
ii. Not realistic beyond few years
f. Variable Growth
i. Need to make long term assumptions about growth of the company
ii. More commonly used when valuating start ups
iii. Often plan accelerated growth for a while tapering off to average growth.
VII. Required Returns
a. Valuations change because required returns change
b. Required Return = Risk Free Interest Rate + Risk Premium
c. Risk Free Interest Rate changes with monetary policy
i. At present risk free rates are low
ii.
ii. Fed cut interest rate 12 times in past 2 years
d. Risk Premium changes with other economic conditions
i. Slow down in the economy increases risk of bankruptcy
ii. Rising health threatens to balloon cost of pension benefits increasing the risk of
bankruptcy
ii. Dave Thomas, Sam Walton, Walt Disney die making the future of the company
uncertain
iv. People begin catching on to AOL
Chapter 7 Homework
Pricing of Discount Bond
How much should you pay for a $1,000 discount bond that matures in 5 years if you want a 7% return
on your investment?
What should you pay for the same bond if you want an 8% return on your investment?
What should you pay for the same bond if you want a 6% return on your investment?
What can you say about the relationship between bond prices and required returns.
Pricing of a Coupon Bond
What should you pay for a $5,000 coupon bond that matures in 5 years and pays 7% interest if the
required return is 7%?
Year Payment Present Value
1
2
3
4
5
Total
What should you pay for a $5,000 coupon bond that matures in 5 years and pays 7% interest if the
required return is 9%?
What should you pay for a $5,000 coupon bond that matures in 5 years and pays 7% interest if the
required return is 5%?