Outline Bond Valuation and Yields

Outline

I. Bond valuation II. Bond yields III. Stock valuation

Bond valuation and yields

A level coupon bond pays constant semiannual coupons over the bond’s 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). 20 Year 0 0.5 1 1.5 . . . 19.5 (Maturity Date)

$45 $45 $45 . . . $45 $45 + $1,000

1 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 semiannual 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.

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”.

2 Bond values – self study

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

Determining bond yields

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

3 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.

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?

4 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 stock’s 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 Coke’s risk is 12%. What is the current price of Coke’s stock?

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.

5 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.