Question

What would be the net present value of a microwave oven that costs $205 and will save you $84 a year in time and food away from home? Assume an average return on your savings of 8 percent for 5 years

Answer 1

Definition of 'Net Present Value - NPV'
The difference between the present value of cash inflows and the present value of cash outflows. NPV is used in capital budgeting to analyze the profitability of an investment or project.




interest is 8 percent so i = 0.08

year 1 you get 84 dollars
year 2 you get 84 dollars
year 3 you get 84 dollars
year 4 you get 84 dollars
year 5 you get 84 dollars

if i offered you 10 dollars now or 11 dollars if twenty years time you would choose the 10 dollars now

the 84 dollars in year1 is worth a net present value of 84/1.08 = 77.7777778

year 2 is worth a net present value of 84/((1.08)^2)=72.0164609
year 3 is worth..... 84/((1.08)^3)=....
year 4 is .......
adding up these 5 figures gives you your net present value of the future saving and you would expect it is less than 5*84=420



now take away the price of the mircowave and there is your answer

the general formual for this is work out as below
let see
let S = savings
net present value (NPV)= P
saving is R
interest is i
so the formula
NPV =R/i *(1-1/(1+i)^n)

here the link looks better
http://en.wikipedia.org/wiki/Annuity_(finance_theory)

so in you r case
npv = 84/0.08 * (1-1/(1.08)^5)
=1050*(0.319416803)
335.387643

and dont forget to take away the mircowave price

you should get the same answer for both ie 335.387- the mircowave

Hope this explains it