38 - Bond and Stock Valuation Concepts

Question 1

What is the formula for finding the intrinsic value of a stock with an increasing dividend? (Words)

Answer 1

Next Expected dividend / (rate of return required by investor - dividend growth rate).
Note - if the stock dividend isn’t growing then it is just the dividend / rate of return required.

Question 2

For a stock to be undervalued it needs to have a stock price (higher/lower) than its intrinsic value?

Answer 2

Lower

Question 3

Bonds with lower coupon rates and longer maturities have a higher duration than bonds with higher coupon rates and shorter maturities, but why?

Answer 3

Coupon - If you have a 2% coupon bond and a 10% coupon bond and then interest rates drop by 1%, the lower coupon bond is now twice as good as new, similar issues, while the 10% bond is only a little better than a 9% bond.
Maturity - For long-term bonds, there is a greater probability that interest rates will rise (and by greater amounts) than for short-term bonds.Also, if interest rates rise for a short-term bond, they will be underpaid (compared to market rates) for a much shorter time than owners of long-term bonds.

Question 4

Why are call option premiums not just equal to the amount they are in-the-money? In other words, why aren’t all Call 70 options, when the stock price is at $73, selling for their in-the-money value of $3?

Answer 4

Because the premiums are made up of two parts. The first is their intrinsic value, but the second is their time value. If the strike price is $100 and the premium for a call is $5, I feel much better about the stock price rising that 5% (or more hopefully) over a year than over a week, so I may be willing to pay more for the option to buy the stock at $100 a year from now than just a week from now.

Question 5

The SML formula, which is risk-free return + (market return - risk-free return) * beta of the stock, is used to calculate what?

Answer 5

The investor’s required rate of return.

Question 6

Assume that a stock sells for $50 per share and pays an annual dividend of $3.50, and dividends are expected to grow at 7% per year into perpetuity. The stock has a beta of 1.2. The market rate of return is 16%, and the risk-free rate of return is 9%. The intrinsic value of this stock, based on the constant growth dividend valuation model, is __________?

Answer 6

The intrinsic value of this stock is $36.01, calculated as follows:

V = [Do(1 + g)]/(r-g) = [3.50(1 + .07)}/(.174-.07) = 3.745/.1040 = $36.01

This question requires the use of 2 formulas from the formula sheet: the constant growth model (top left corner) and the security market line (bottom left corner). While this question actually tells you to use the constant growth model, most questions will not and you should recognize that when a question asks you for the intrinsic value of a stock, most of the time you will need to use the constant dividend formula.

The constant growth model (a.k.a. dividend discount model) formula reads: The intrinsic value of a stock (V) is equal to (=) the dividend one year from today (D1), divided by: the required return (r) minus the growth rate of the dividend (g).

V = D1/(r-g)

The first hurdle is to realize that the $3.50 dividend is the dividend today, not one year from today. So you have to adjust it by multiplying by 1+ the growth rate to get the dividend next year.

D1 = D0(1+g)
D1= 3.50(1.07) = 3.745

Now when you look at the bottom of the fraction, you have a problem because the question does not tell you the required return (r). That means you have to solve for it using the SML.

r = Rf + (Rm-RF)B
r = .09 + (.16-.09)1.2
r = .174

Now you can finish the constant growth formula:

V = D1/(r-g)
V= 3.745/(.174-.07)
V=3.745/.104
V = 36.01

Note that this stock would not be attractive to the investor since its intrinsic value is less than its market price.

Question 7

Given a bond’s duration, coupon,, YTM, and % change in the interest rate, what can you calculate and using what formula (name)?

Answer 7

You can calculate the price change of the bond due to the change in the interest rate using the modified duration formula.

Question 8

Why are zero coupon bonds especially sensitive to changes in the interest rate compared to other types of bonds at similar maturity?

Answer 8

Interest payments are what makes a bond’s duration less than its maturity so since there is no interest payments (coupon rate of 0% after all), the duration is equal to its maturity, which is isn’t true of any of the other bonds paying interest along the way, regardless of rate.

Question 9

Mr. Wood has a 17% required rate of return. He is contemplating investing in SDF Corporation, which is selling for $120 per share and now pays a dividend of $4.40 annually. He expects the dividends and earnings to increase at an annual rate of 12%.

• What is the expected rate of return for SDF?
• Is the stock overvalued or undervalued?

Answer 9

16.1%; overvalued

The stock is overvalued because the expected rate of return is below Mr. Wood’s 17% required rate of return.
r = D1 + g
P
D1 = $4.40(1.12) This is the first year dividend, which is the current dividend increased by 12% growth.
P is the current market price of the stock, which is $120.
g is the growth rate of the stock, which is 12%.

When we enter these values in the formula we get:
r = 4.40 (1.12) + .12
$120
r = .0411 + .12
r = .1611 or 16.11%
The stock is overvalued because the expected rate of return is below Mr. Wood’s 17% required rate of return.