What is the discount factor?

What is the discount factor?

• A. 1/(1+r)^n
• B. (1+r)^n
• C. 1 - r^n
• D. r^n

Answer: (A)

The discount factor tells you how much a future amount is worth in today’s terms, taking into account the time value of money at the discount rate r over n periods. For a cash flow of 1 unit received after n periods, its present value is 1/(1+r)^n. That number, the discount factor, is the factor you multiply the future amount by to get today’s value, and it’s the reciprocal of the growth/compounding factor (1+r)^n. The other expressions don’t reflect this time-value relationship: (1+r)^n grows money forward, not backward, and 1 − r^n or r^n don’t correctly capture how future value is converted to present value.

The discount factor tells you how much a future amount is worth in today’s terms, taking into account the time value of money at the discount rate r over n periods. For a cash flow of 1 unit received after n periods, its present value is 1/(1+r)^n. That number, the discount factor, is the factor you multiply the future amount by to get today’s value, and it’s the reciprocal of the growth/compounding factor (1+r)^n. The other expressions don’t reflect this time-value relationship: (1+r)^n grows money forward, not backward, and 1 − r^n or r^n don’t correctly capture how future value is converted to present value.