Discounting Project Cash Flows to Calculate Net Present Value
Summary
The example asks how to calculate the net present value of a property project with an upfront purchase, renovation payments over several months, and a later sale. The answer’s method is to place each cash flow on a timeline, convert the annual financing rate to a period rate, and discount each amount according to when it occurs. It notes that the same discounting procedure applies to the interim renovation costs and the sale proceeds.
The answer reports an NPV and assumes no taxes, but its rate conversion needs care: the question specifies an annual effective rate, while the answer divides the annual rate by twelve, which corresponds to a nominal monthly convention. For an annual effective rate, the monthly rate should instead be derived by taking the twelfth root of one plus the annual rate, then subtracting one. The example is a basic capital-budgeting illustration rather than a trading strategy.
Key ideas
- NPV combines project cash flows after discounting each one to the same valuation date.
- Cash flows at different dates require discount factors matched to their timing.
- The annual rate convention matters when converting a rate to monthly periods.
- Taxes and other project assumptions can change the calculated NPV.
Tags
Full text
# How to calculate the NPV (Net present Value) in this question? # How to calculate the NPV (Net present Value) in this question? > 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. ## Answer by ApplePie (score 2, accepted) https://quant.stackexchange.com/a/25109 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.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.