How do I discount?

Question

I want to do a calculation of dicounted future costs and I am not sure what to do. I have the following bits of information
1. A one time cost of $100
2. Yearly costs of $10,000 for 12 years.
3. A discount rate of 5%.

Now what do I do? Am I correct in supposing that the 2nd year becomes period 1 while this current year is period 0.

The 10,000 is incurred at the beginning of the period.

Answer 1

I believe this is what you want:

Let r = 1/1.05. Then $10000 one year from now is equivalent to $10000*r now, that is, $9523,81. Also $10000 two years from now is equivalent to $10000*r^2 now. Etc. for 12 years.

Money spent later converted to an amount now is called its "present value". So the discounted amount is the present value of all moneys spent in the future. In this case, it is

100 + 10000*[r +r^2+r^3+...+r^12].

Using a formula for the sum of this geometric series, one gets

100 + 10000*(r-r^13)/(1-r), which equals $88732.52.

Answer 2

At time 0 you bear the one time cost of $100.

Yearly costs depend upon whether the cost is born at the end of the period (which I think is what this means) or the beginning of the period, in which case time 0 would be 10,100. You need to verify with the person which they mean, or alternatively perform both calculations.

Answer 3

Assuming the discount of 5% is for future years, you would indeed call the first year zero, and the second year, year one.

Year One: 10,100
Year Two: 9,500

The question is - does the discount of five percent come out of the new balance, or the original balance? If you get an additional five percent for each year, then the third year would be:

Year Three: 9,500 - 450 = 9,005

Otherwise, you remain at 9,500 each year...