Net Present Value Interpretation

[Adi]

Just a bit of a theoretical question about NPV. I've just learnt recently that the NPV of an annuity can be calculated by finding the sum of the discounted cashflows using the formula:

NPV=cf0+cf1/(1+r)+cf2/(1+r)^2.....cfn/(1+r)^n.

Where r is the taken to be the interest you would gain if you had the money now instead of in the the future.

I was just wondering if I could apply this formula to to a debt repayment. If I assumed an annual inflation rate of 2% could I set r= the inflation rate to calculate how how much future debt payments set in nominal terms would be worth in today's dollars?

 

[tkhunny]

Just a bit of a theoretical question about NPV. I've just learnt recently that the NPV of an annuity can be calculated by finding the sum of the discounted cashflows using the formula:

NPV=cf0+cf1/(1+r)+cf2/(1+r)^2.....cfn/(1+r)^n.

Where r is the taken to be the interest you would gain if you had the money now instead of in the the future.

I was just wondering if I could apply this formula to to a debt repayment. If I assumed an annual inflation rate of 2% could I set r= the inflation rate to calculate how how much future debt payments set in nominal terms would be worth in today's dollars?

r is an interest RATE, not an amount, and the difference between cf2 and cf2/(1+r)^2 is the interest you LOSE by taking the money now, rather than in the future.

The same ideas apply when discussing a loan or debt. A typical loan arrangement starts with a cash flow in one direction and then other cash flows in the opposite direction. If the loan repayment is level, it is found by solving:

L = Original Loan
d = level loan repayment amount
r = periodic interest rate
v = periodic discount rate = 1/(1+r)
n = number of periods to pay

L = d(v + v^2 + v^3 + ... + v^n) = dv(1+v^n)/(1-v)
There are various other forms and simplifications for certain purposes or enlightenment.

 

[JeffM]

Just a bit of a theoretical question about NPV. I've just learnt recently that the NPV of an annuity can be calculated by finding the sum of the discounted cashflows using the formula:

NPV=cf0+cf1/(1+r)+cf2/(1+r)^2.....cfn/(1+r)^n.

Where r is the taken to be the interest you would gain if you had the money now instead of in the the future.

I was just wondering if I could apply this formula to to a debt repayment. If I assumed an annual inflation rate of 2% could I set r= the inflation rate to calculate how how much future debt payments set in nominal terms would be worth in today's dollars?

Yes.