Calculating Bond and Stock Prices: Videos & Practice Problems

To calculate the present value of a bond, you need to discount all future cash flows (interest payments and the principal repayment) to their present value. The formula used is:

${\mathrm{PV}}_1=\frac{\mathrm{FV}+\mathrm{CF}}{{(1+r)}^{-n}}$

Here, $\mathrm{PV}$ is the present value, $\mathrm{FV}$ is the future value (principal), $\mathrm{CF}$ is the cash flow (interest payments), $r$ is the interest rate, and $n$ is the number of periods. Sum the present values of all cash flows to get the bond's price today.

The formula for calculating the price of a stock with growing dividends is:

$P=\frac{D_1}{r-g}$

Here, $P$ is the price of the stock today, $D_1$ is the dividend expected next year, $r$ is the required rate of return, and $g$ is the growth rate of the dividends. This formula accounts for the time value of money and the expected growth in dividends.

The time value of money (TVM) is the concept that money available today is worth more than the same amount in the future due to its potential earning capacity. This principle is crucial in bond and stock pricing. For bonds, TVM is used to discount future interest payments and the principal to their present value. For stocks, TVM is applied to discount future dividends, considering their expected growth. Understanding TVM helps investors determine the present value of future cash flows, enabling them to make informed investment decisions.

Interest rates have an inverse relationship with bond prices. When interest rates rise, the present value of a bond's future cash flows decreases, leading to a drop in the bond's price. Conversely, when interest rates fall, the present value of future cash flows increases, causing the bond's price to rise. This relationship is due to the fixed nature of bond payments; as market interest rates change, the attractiveness of the bond's fixed payments changes relative to new bonds issued at current rates.

The key differences between valuing bonds and stocks lie in their cash flows and the methods used. Bonds have fixed interest payments and a principal repayment at maturity, which are discounted to present value using the time value of money. Stocks, on the other hand, generate dividends that are expected to grow over time. The stock price is calculated using the formula:

$P=\frac{D_1}{r-g}$

where dividends are expected to grow at a constant rate. Bonds are generally less risky and have a defined maturity, while stocks offer potential for growth but come with higher risk.