Trying to calculate net present value....

[allysonac]

Outflow is $110,000
Savings to company is $30,000 per year
Period of time is 5 years
Discount rate is 10% per year

I need to know how to calculate the discount factor for each year and how to calculate the NPV for each year.

I know that the discount factor for year 0 is 1.000 and that the NPV for year 0 is -$110,000.

Year 1 Discount factor? NPV?
Year 2 Discount factor? NPV?
Year 3 Discount factor? NPV?
Year 4 Discount factor? NPV?
Year 5 Discount factor? NPV?

I am a returning to college student who is working full time and I have run out of steam to finish this last piece of my homework. Brain fried.

 

[allysonac]

Thank you very much but......

As I mentioned I am a returning student who has forgotten ALL her math. Can still do all sorts of basic math but cannot comprehend your formula PV = P[(1 - 1/(1 + i)^n] / i

I understand that I must take the annual payment $3,000 then do a separate calculation 1 - 1 (why do this?) then take this answer (0?) and divide it by the sum of 1 plus interest rate (11%?) not sure what the > symbol means and then divide the answer (?) by the .10 interest rate.

This is the table I am trying to complete... I don't know if my 26,790 is correct or not...

	Inflow (Savings)	Outflow	Netflow	Discount factor	NPV
Year 0		$110,000	-110,000	1.0000	-110,000
Year 1	$ 30,000		$ 30,000	0.8930	26,790
Year 2	$ 30,000		$ 30,000
Year 3	$ 30,000		$ 30,000
Year 4	$ 30,000		$ 30,000
Year 5	$ 30,000		$ 30,000
Total

No need to calculate each year (imagine one for 100 years!!);
the following formula does it:
PV = P[(1 - 1/(1 + i)^n] / i
where:
PV = present value (?)
P = annual payment (30000)
i = interest (.10)
n = number of years (5)
PV = 30000(1 - 1/1.10^5) / i = 113,723.60

So NPV = 113,723.60 - 110,000 = 3,723.60

Means the same as borrowing $113,723.60 over 5 years, annual payments $30,000.00, 10% rate:

YEAR     PAYMENT      INTEREST     BALANCE
  0          .00           .00  113,723.60
  1   -30,000.00     11,372.36   95,095.96
  2   -30,000.00      9,509.60   74,605.56
  3   -30,000.00      7,460.56   52,066.12
  4   -30,000.00      5,206.61   27,272.73
  5   -30,000.00      2,727.27         .00

Clear nuff?

Suggest you find sites that deal with these, like:
http://www.investopedia.com/articles/03/101503.asp

 

[allysonac]

I believe you are correct... need a face to face tutor.

Too many years without having to do Math. But thank you very much indeed for your help.

Allyson..

Well, 1 - 1/(1 + i)^n means:

        1
1 - =========
    (1 + i)^n

^ means "to the power", as example 3^2 = 9

1 + i becomes 1 + .10 which becomes 1.10
However, this is VERY basic, meaning you need a face-to-face tutor;
it is impossible to conduct a classroom from here.