Question

A thirty year investment with an NPV of $200,0000 and a discount rate of 6% as an annual equivalent of what?

Answer 1

If net present value is $200,000

Then it means the present value of all annual cash flows for 30 years is the npv

We will discount future cash flows with discount rate

Let annual equivalent amount be X which we get for 30 years. Every year we get $X

Thus,

200,000 = X/(1.06) + X/(1.06^2) + ...X/(1.06^30)

We can use the Excel function = pmt for this.

=Pmt(rate,nper,pv) = pmt(.06,30,-200000)

= $14,529.78

Nper is the period which is 30 years.

Pv is taken negative as excel shows for this outflow amount, we get inflows of PMT every year.

We can also use equivalent annual cost formula

Equivalent Annual cost = npv/A

Where A = {1-(1/(1+r)^n}/r where r is discount rate and n is timd period.

A={1-(1/1.06)^30}/.06

Thus, annual equivalent amount is $14,529.78