# Reconcile two different ways to calculate a discount rate for present value

• Apr 26th 2012, 03:51 PM
odonnellphil
Reconcile two different ways to calculate a discount rate for present value
A colleague and I are in disagreement on the correct way to calculate a discount rate for a present value equation and would like an opinion from some more knowledgeable folks. (Happy)

I have a single data point that a dollar today will be worth \$0.22 after 24 months. Given the present value equation: PVi = 1 / ( 1 + r ) ^ i ...

A) That is a rate of 78% over 24 months, so the monthly compounded rate is (1+.78)(1/24) - 1 = 0.024316, thus the discount rate (r in the PV equation) is 0.024316.

or

B) By plugging in 0.22 for PVi and 24 for i, we can rewrite the PV equation to solve for r as 1 - (1 / 0.22)(1/24) = 0.06512, thus the discount rate (r in the PV equation) is 0.06512.

Both these approaches seem valid to me, but obviously they will result in very different answers for Present Value. A) would give a PV24 of 0.56 per dollars and B) gives a value of 0.22 per dollar.

Can anyone help me figure out which approach is the correct one?
• Apr 26th 2012, 06:15 PM
HallsofIvy
Re: Reconcile two different ways to calculate a discount rate for present value
So you are expecting a sharp deflation after many years of inflation? Or do you mean an increase of \$0.22 so that, after two years, a dollar will be worth \$1.22?
• Apr 27th 2012, 08:07 AM
odonnellphil
Re: Reconcile two different ways to calculate a discount rate for present value
I suppose it most closely resembles inflation. So \$1 in month 24 is worth \$0.22 today.
• Apr 27th 2012, 12:37 PM
SpringFan25
Re: Reconcile two different ways to calculate a discount rate for present value
Quote:

A) That is a rate of 78% over 24 months, so the monthly compounded rate is (1+.78)(1/24) - 1 = 0.024316, thus the discount rate (r in the PV equation) is 0.024316.

you are not given a rate of 78% spread over 24 months. Your 0.22 will accumulate to \$1. that is a accumulation of about 400% over 24 months.
you have solved for the interest rate in b.
• Apr 27th 2012, 07:21 PM
Wilmer
Re: Reconcile two different ways to calculate a discount rate for present value
Quote:

Originally Posted by odonnellphil
I suppose it most closely resembles inflation. So \$1 in month 24 is worth \$0.22 today.

Why in heck don't you use something CLEAR...