# Net present Value

#### omron

Hi, I am setting up my own business and am wanting to learn how or which option to go for in investment terms, mainly for decision making purposes. I am wondering if someone could give me an answer to the problem below to see if it matches with mine. Thanks for all inputs

You are considering the purchase of a motorised caravan from Bluebird limited.
The company offer two means of purchase:

Payment of the full purchase price of £55000 plus a recommended service agreement and extended guarantee costing £500 per year or an initial deposit of 20% of the purchase price plus 8 annual payments of £8700 plus a finance arrangement fee of 2% of the purchase price.

a) Assuming that the cost of capital is 10% use the NPV method to evaluate which option represents the most economic choice.

#### ArcSine

You know the drill for homework problems: You show your work and your proposed answer (or explain where you're stuck), and then you get assistance.

#### iNinjaNotes

Your going to have to PV the lump sums, and contrast them against the payment option which is the PV of an annuity.

the equations are..

FV = PV(1+r)^t which is future value = pv * (1 + discount rate) to the power of years.
Rearrange this formula to solve for PV.

PV of an annuity is..

PV = [1-[1/ (1+r)^t ] divide by r ] multiply by payments.

so that means. do this.. (1+ discount rate) to the power of terms.
next, 1 divide by the result of the first step.
next, 1 minus the result of the last 2 steps.
next, divide the result by discount rate.
next, multiply the result by the payments, like the car payments.

Then compare the PV of each and see which has a greater cost.