Net Present Value Flashcards

True or False, a project or policy always makes economic sense if the present value of benefits is greater than the present value of costs.

True, because if the net present value of costs is greater than the present value of benefits, then the benefits outweigh the costs

True or False a project’s costs occur earlier than the benefits, then the project always does not make economic sense if the costs are greater than the sum of benefits, without needing to calculate present value.

True, this is because if the costs incurred are greater than the total future benefits then we can assume that the costs outweigh the benefits because the present value of those benefits will still be less than the costs incurred.

True or False, if a project’s benefits occur earlier than the costs, then the project always does not make economic sense if the costs are greater than the sum of benefits, without needing to calculate present value.

False, in order to determine if future costs outweigh benefits, we need to discount future costs and find the Net Present value of costs to confirm if they are greater than or less than benefits. 

True or False, if the costs occur before the benefits, then a lower discount rate will increase the net-present benefits of a project or policy. 

True, because the formula for net present value implies that the discount rate needs to be smaller in order for benefits to be bigger since the future value is in the numerator, and the discount rate is in the denominator. 

True or false, if the benefits occur before the costs, then a lower discount rate will increase the net-present value of benefits of a project or policy.

True, because the formula for net present value implies that the discount rate needs to be smaller in order for benefits to be bigger since the future value is in the numerator, and the discount rate is in the denominator. 

What is the notation for FV, PV, r, T and t?

FV: Future Value

PV: Present Value

r- Interest Rate/ Discount

T-Finite end-period

t-period

What is the formula for a 1-time present value cost/benefit (Discrete)?

PV = FV/(1+r)^t

Present value of a onetime discrete cost/benefit is equal to the future value divided by 1 plus r with an exponent of t.

What is the formula for a infinite present value cost/benefit?

PV(Infinite) = PV=

∞ Σ FV/(1+r)^t = FV/r t=1

What is the formula for an infinite present value cost/benefit starting in year 0 (or treating a year as year 0)?

PV(Infinite) = PV=

∞ Σ FV/(1+r)^t = FV (1+r)/r t=0

What is the formula for present value for a finite cost/benefit- starting in year 0?

PV(Infinite) = PV=

∞ Σ FV/(1+r)^t = [[((1+r)^t)-1]/ [r(1+r)^t]] x FV t=0

What is the formula for present value for a finite cost/benefit- starting in year 1?

PV(Infinite) = PV=

∞ Σ FV/(1+r)^t = [[((1+r)^t)-1]/ [r(1+r)^t+1]] x FV t=1