# How to calculate the NPV (Net present Value) in this question? [closed]

A company pays £1,200,000 to purchase a property. The company pays £30,000 at the end of each of the next six months to renovate the property. At the end of the eighth month the company sells the property for £1,500,000. The project’s cost of capital is an annual effective interest rate of 8%. What is the net present value of this project for the company?

What I tried- I know that NPV= Presnt value of sum of net cash flows-

below is the timeline for this cash flows I am having problem in calculating the present value of 30,000.

Please help me to solve this.

• Are you saying that you expect the answer to be 30k or that you are having trouble understanding how to calculate the PV of the 30k annuity ? – ApplePie Mar 27 '16 at 17:48
• How to calculate: You will need to calculate the discount factors for end of each month based on the 8% interest rate and choice of compounding (simple, compound, continuous). Then each payment will have NPV of the discount factor multiplied by payment (each payment of 30K will have different NPV). NPV of project will just be the sum of all discounted values. NPV comes to about 46K – compilation-error Mar 27 '16 at 18:45
• @AlexandreP.Levasseur yes how to calculate pv of 30K? – RajSharma Mar 27 '16 at 23:41
• @Romeet Could you please post the solution? – RajSharma Mar 27 '16 at 23:42
• Well... @AlexandreP.Levasseur's answer is pretty much the direction you would take to solve this. In case it helps clarify the concepts, look at this short but succinct example: quant.stackexchange.com/a/17354/13610 – compilation-error Mar 28 '16 at 0:49

## 1 Answer

I have laid out below one way of solving this kind of problem. You have your timeline right and I have reproduced it with the correct amounts. The way to discount your 30Ks is the same as discounting 1,500K if you do it this way. Basically, you need to compute a discount factor. To calculate this discount factor, you need to de-annualize your interest rate by dividing by 12 months. This amount is then compounded at each period. To help you understand, here is the formula I have in the first cell under Discount factor (C2):

=(1+0.08/12)^A2-1


As you can see. The annual rate is divided by 12, you add 1 to it and take the power of it in relation with the period. The first period has no discount factor given that no time has elapsed. Finally, note that I have subtracted 1 from the Discount factor so that you could see the relation between annual rate and effective rate but in reality the discount factor does not subtract 1 (see how in period 12 the rate is 8.30% instead of 8.00% ? that's the effective rate (EIR) instead of annual rate (APR)).

Finally, to calculate the discounted amount you need to divide the amount by its discount factor (in this case you would need to add 1 to it).

The final NPV is 46,474\$, assuming there is no tax involved. 