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PV Examples:
You are valuing a project that is expected to earn a one-time cash flow of $500m in five years. You estimate a discount rate of 11%. What is the present value of this cash flow? PV =
500 = $296.73m (1 + .11) 5
What is the present value if the project instead pays cash flows of $100m per year for each of the next five years? ⎛ 1 − (1 + .11) −5 ⎞ ⎟⎟ = $369.59m PV = 100⎜⎜ .11 ⎠ ⎝
What is the present value if the project instead pays cash flows that grow at a rate 10% per year for five years, starting with a cash flow of $100m next year? 5 ⎛ 1 − (11..10 ⎞ 11 ) ⎟ PV = 100⎜ = $442.41m ⎜ (.11 − .10) ⎟ ⎝ ⎠
You are valuing a firm that is expected to earn cash flows of $100m per year in perpetuity. You estimate a discount rate of 11%. What is the present value of these cash flows? PV =
100 = $909.09m .11
What is the present value if the firm instead earns cash flows that start at $100m next year and grow at 5% in perpetuity thereafter? PV =
100 = $1666.67 m (.11 − .05)
1
PV Examples:
You are valuing a firm that is expected to earn cash flows that grow at 10% for the first five years and at 5% in perpetuity thereafter. The forecasted cash flow next period is $100m (which includes the 10% growth) and you estimate a discount rate of 11%. What is the present value of these cash flows? 0
