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STREETSMART GUIDE TO VALUING A STOCK
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ing of the expected cash flows and the risks associated with receiving the expected cash flows. The discount rate is a function of both time and risk: discount rate f (time, risk). The discount rate should increase with increasing default risk (e.g., a WorldCom bond) and decrease with lower default risk (e.g., U.S. Treasury bonds) associated with the expected cash payment. Similar to the discount rate, the discount factor takes into account both the discount rate and the timing of the expected cash flow. The discount factor is a function of both time and the discount rate: discount factor f (time, discount rate). For example, the discount factor for a one-year cash flow, whose discount rate is 6 percent, is simply equal to one divided by (1.06) which in equation form looks like this: 1/(1.06) .9434. The discount factor for a two-year cash flow, whose discount rate is also 6 percent, is equal to one divided by (1.06) .9434, that amount divided again by (1.06) .9434/(1.06) .8900. This process for a three-year cash flow continues with a third division by (1.06). And so on, ad infinitum. As you can see from this example, the discount factor decreases with increasing time to the payment of a cash flow, and it also decreases with an increasing discount rate. The value of an investment, known as the present value (PV), is found by taking the sum of the expected cash flows multiplied by their respective discount factors. For example, using a 6 percent discount rate, a discount factor of (.9434), and an expected $100 cash flow in one year, the present value of that cash flow would be $100 times (.9434): $100 * (.9434) $94.34. Using a 6 percent discount rate, a $100 cash flow expected in two years, and a discount factor of (.8900), the present value of that cash flow would be: $100 * (.8900) $89.00. The value of an investment is the sum of the present values of all of the expected cash flows. The present value of the two cash flows described above is: PV $94.34 $89.00 $183.34.
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Mary s Mortgage: A DCF Example Valuation
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To understand the DCF process better, consider a home mortgage. Mary wants to purchase a new house, so she borrows $100,000 from the bank and is the obligor on an 8-percent, 30-year mortgage. The
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Stock Valuation: Some Preliminaries
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DCF Example for Mary s Mortgage
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monthly mortgage payment is $734 for 360 months, as shown in Exhibit 3-1. Mary s $734 monthly payments are the cash flows that she is obligated to pay under her mortgage agreement and that the bank expects to receive for lending her the money. Over the life of the mortgage (assuming that she doesn t prepay it), Mary will pay a total of $264,240 ($734 * 360 months) to the bank $100,000 is the return of principal and $164,240 is the payment of interest. The initial mortgage amount of $100,000 represents the present value to the bank of the 360 monthly payments of $734 each discounted using a rate of 8 percent and the appropriate discount factor. The 8-percent mortgage rate is the discount rate, or yield, that the bank requires to lend Mary the money. The discount rate is a function of the general level of interest rates in the economy, as represented by the yield on a U.S. Treasury bond with a similar maturity, plus a risk premium for the bank to compensate it for the possibility that Mary may not make her payments. U.S. Treasury bonds are risk free because Uncle Sam can always print more money to repay its loans! The interest or discount rate that the bank requires on Mary s mortgage depends upon the market interest rate at the time she gets her loan. If interest rates change, the present value of the mortgage could increase or decrease. Consider these two scenarios: 1. If interest rates rise, the bank will increase its lending rates on new mortgage loans in order to cover the higher market interest rates that the bank offers to attract deposits. For example, if interest rates rise 1 percent (also known as 100 basis points), the
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