The discount factor tells you the value today of $1 receivable at some point in the future. If we can earn a return of 25% on our investments, then we only need to invest $0.80 today to have $1 in one year, since 1.25 × $0.80 = $1.00. This means that a dollar in a year’s time would only be worth eighty cents to us today, and we say the one-year discount factor is 0.80.
The key idea of the time value of money is that a cash flow received in the future is worth less than the same amount of cash received today. If the one-year discount factor is 0.80, then $200 received in one year’s time only has a present value of 0.80 × $200 = $160 (since each of those two hundred dollars, receivable in one year, is worth only eighty cents of today’s money). The general formula linking present value, future value and the discount factor is:
The discount factor depends on the time, t, until the future payment is made, and on the discount rate, r (also called the “cost of capital”). If there is a long time t for compound interest to grow our investment, we don’t need to invest very much today to have $1 by time t, so the present value of $1 at that future time (i.e. the discount factor) is low. As a result, the further into the future the cash flow is received, the lower the discount factor, and the present value of the future payment is less. Similarly, the better the rate of return r we can get on our investment, the lower the discount factor, since we don’t need to invest so much today to have $1 in the future. The general formula is:
This worksheet is designed for MBA or undergraduate students taking a Finance class. It covers several common topics: how to find a discount factor, how to apply a discount factor to find the present value, and how to rearrange the formula so we can calculate the discount rate from the discount factor. Answers are provided on the second page.
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