Bond Valuation

BOND VALUATION

The financial value of any asset, be it a security, real estate, business, etc., is the present value of all future cash flows. The easiest thing to value (conceptually) is a bond since the promised cash flows are known with certainty.

Consider a bond that pays a 10% coupon (or stated) rate of interest, has a par (or stated) face value of $1,000 and matures in 5 years. Suppose also that the market rate of interest for such a bond (i.e., your required rate of return, k) is 8%. Thus,

Par = $1,000

Coupon Rate = 10%

Maturity = 5 years

K = 8%

The cash flows that are promised by the company include interest payments of $100 per year (although most corporate bonds pay interest semi-annually, we will assume annual payments—we have already seen how to adjust for semi-annual cash flows) for five years and the payment of the face value (stated, or par, value) of $1,000 at the end of five years.

0 1 2 3 4 5

100 100 100 100 100

1,000

1,100

PVIFA 8%,4 = 3.3121

331.21

PVIF 8%,5 = .6806

748.66

$1,079.87

The value of the bond is $1,079.87 which is selling at a premium relative to the par value of $1,000. (A bond selling at less than par is said to be selling at a discount.)

What does the premium represent? As we saw when we looked at present values, it represents the present value of the additional interest of $20 per year (because it pays $100 in interest when we only require $80 for a $1,000 investment ($20 * 3.9927 = $79.85 with two cents rounding error). Any time the market rate of interest is less than the coupon rate of interest, the bond will sell at a premium. Similarly, when market rates of interest are greater than the coupon rate, the bond will sell at a discount. Recall from economics...