Discounting and the Time Value of Money
A dollar today is worth more than a dollar tomorrow, because today’s dollar can be reinvested to earn a return. Discounting turns a future cash flow into its present value by dividing through a discount factor that compounds the cost of capital over time. Value depends on two things only, the magnitude of the cash flows and their timing. Larger and earlier cash flows are worth more. The discount rate reflects both the cost of funding the investment and the risk that tomorrow’s dollar may not arrive, so riskier cash flows are discounted harder. The discount factor itself is purely a cash-time mechanism, separate from any accounting accrual.
Why it matters
Money has a rent. If capital costs ten percent, then a dollar a year from now is only worth what you would need to set aside today to grow into that dollar, which is less than a dollar. Discounting just runs the clock backwards. The further out a cash flow sits, the more compounding shrinks it, so timing matters as much as size. The discount rate carries two ideas at once. What it costs to raise the money, and how confident you are the cash will actually show up.
Formulas
Worked examples
Two investments each promise US$1,000. One pays in one year, the other in five years. The cost of capital is 8 percent. Show why the earlier payment is worth more today.
The one-year payment has a present value of 1,000 divided by 1.08, which is about US$926. The five-year payment has a present value of 1,000 divided by 1.08 to the fifth power, about 1.469, which is roughly US$681. Same face amount, yet the earlier cash flow is worth about US$245 more today, purely because of timing. The longer the wait, the more compounding at 8 percent erodes the present value. Larger and earlier cash flows are always preferred.
Common mistakes
- ✗Two equal future amounts are worth the same regardless of timing. The earlier amount is worth more today, because it can be reinvested sooner. Discounting makes the timing difference explicit.
- ✗The discount rate reflects only the cost of funds. It also embeds the risk that the cash flow may not arrive, so riskier cash flows carry a higher rate and a lower present value.
- ✗A higher discount rate raises present value. A higher rate lowers present value, because each future dollar is divided by a larger compounding factor.
- ✗Discounting is the same as deducting inflation. Discounting captures the full opportunity cost and risk of capital, of which expected inflation is only one part.
Revision bullets
- •A dollar today beats a dollar tomorrow because it can be reinvested
- •Discounting converts a future cash flow to its present value
- •Value depends on the magnitude and the timing of cash flows
- •Larger and earlier cash flows are worth more today
- •A higher discount rate or a longer horizon lowers present value
- •The discount rate reflects both the cost of capital and risk
Quick check
Why is US$1,000 received one year from now worth more than US$1,000 received in five years?
Connected topics
Sources
- Titman & Martin, Ch. 2Titman, S., & Martin, J. D. Valuation: The Art and Science of Corporate Investment Decisions. Pearson.States that value depends on the magnitude and timing of cash flows discounted at a risk-reflecting rate.