Question

True or False: The sum of the present value discount factors for 1...n years equals the present value factor for an annuity at year n.

Answer 1

True,

The sum of the present value discount factors for 1...n years equals the present value factor for an annuity at year n.

We know that PV = C₁/(1+r)ⁿ where C₁ is cash flow at year end, when we sum the PV factor of each period that is 1,2,3..n, the resultant is nothing but the present value for an annuity at year n.

which can alternatively be calculated as Annutiy PV factor =1-(1+r)^-n/ r

For example i want to calculate the present value of series of payments of $1000 for 3 years based on 6% rate,

PV for year 1 = (1/1.06)³= 0.9434, similarly for year 2 =0.8900,year 3 = 0.8396.

The present value of an annuity at year 3 = 2.6730, which is again a total of the above values