What is the PV Factor formula for a 3-year project with a Discount Rate of 4.2%?

What is the PV Factor formula for a 3-year project with a Discount Rate of 4.2%?

• A. PVF = (1.042)^-3
• B. PVF = (1.042)^-2
• C. PVF = (1.042)^-4
• D. PVF = 1 / 1.042

Answer: (A)

Discount future cash flows back to present value by using a factor that accounts for one year of time value for each year in the horizon. The PV Factor for a cash flow n years from now is 1 divided by (1 plus the discount rate) raised to the n-th power. So with a discount rate of 4.2%, the factor for a cash flow three years out is PVF = 1 / (1.042)^3, which is the same as (1.042)^-3. This correctly discounts the value three years into the future. That matches a 3-year horizon because you’re applying three compounding periods of discounting. Expressions with exponent -2 or -4 would correspond to two years or four years, respectively, and 1 / 1.042 is the factor for one year, not three. Numerically, (1.042)^3 ≈ 1.131, so the PVF is about 0.884.

Discount future cash flows back to present value by using a factor that accounts for one year of time value for each year in the horizon. The PV Factor for a cash flow n years from now is 1 divided by (1 plus the discount rate) raised to the n-th power. So with a discount rate of 4.2%, the factor for a cash flow three years out is PVF = 1 / (1.042)^3, which is the same as (1.042)^-3. This correctly discounts the value three years into the future.

That matches a 3-year horizon because you’re applying three compounding periods of discounting. Expressions with exponent -2 or -4 would correspond to two years or four years, respectively, and 1 / 1.042 is the factor for one year, not three. Numerically, (1.042)^3 ≈ 1.131, so the PVF is about 0.884.