USA Calculating PV of annuity that changes payments using tables.

[Alex LaPorta]

I've been working on a problem that asks the reader to choose the best option for a payout. One is a lump sum, the other is an annuity for 20 years and the other is an annuity that lasts for 10 years and then is replaced by a larger annuity that lasts 10 more years.

I only have a question about the changing annuity so here are the details.

Years 1-10
PMT = 50,000
n = 10
i/r = 6%

Years 11-20
PMT = 80,000
n = 10
i/r = 6%

So, I tried to do a simple calculation of PVA1-10+PVA11-20 but I know that isn't correct. Unfortunately, the book never goes into the calculations involved.

I found several pages that demonstrate how to solve the problem using (a) a series of PV formulas and (b) the NPV function on excel.

I'd like to know how to solve this problem using the PV/PVA tables. I don't like relying on technology when I don't understand the work behind them and I don't want to be stuck calculating PV formulas to the nth degree.

I was able to find this example of a similar problem.

50,000 for 10 years then 70,000 for 10 years

i = 8%

Table
50,000*6.7101 = 335,505
+ 70,000 * 6.7101 * 0.4632 = 217,568

So I don't understand the logic or the procedure behind that last calculation that arrives at an additional multiplication of 0.4632.

Thanks for reading!

 

[kirby]

The 70K annuity starts 10 years from now. So they used the present value of a $1 table for 8% in 10 years to get the 0.4632 factor that values the $70K annuity 10 years from now.

 

[Alex LaPorta]

Thank you! I get it! The value received from periods 11-20 need to be adjusted because even with the PVA calculation, it still represents a value in the future! So the calculation is to find the present value of an annuity in the future, then find the present value of THAT present value in today's dollars.