# Wrong way to use Present Value formula (in my opinion)

Dear all,

I'm preparing for PMP certification using practice test solution and I'm believing that a question related to Present Value is incorrectly answered.

Present Value concept consequence is that for same revenue, investing same money spread on a period is better than investing it at start of the period. Similarly, for same invested amount, getting the same revenue spread on the year is better than getting it at the end of the year. The 2 benefits are cummulated when spreading investment and revenues over the year compared to investment done at start of year and revenue obtained at end of the year.

The following question compare revenues of $12'000'000 invested for 1 year in a bank that will provide 15'600'000 revenue and the same investment evenly spread on a year used to run a project that will bring same revenue, evenly spread on 4 quarter

The issue is, I think, the way the problem has been modeled to argue the response of the question: using the Planned Value formula for the project cost is OK but Future Value should be computed for revenues to be able to compare with bank revenues. In other terms, PV should be used to compare investments of the 2 options, or the revenues of the 2 options, not investment and revenue of a given option.

Here is the question:

The banks in Ukraine have raised the annual interest rates sharply to 30 percent. You have the option to invest your money either in Ukrainian banks or to build a small factory for a client. The total cost of building the factory will be $12 million but it will spread evenly over one year ($1 million payable by the end of each month for the next 12 months). The client will make a payment of $3.9 million at the end of each quarter from the start of the project. Which of the following is the best option (if you are only considering the return on investment)?

Here are possible answers:

A. Invest the money in the bank for a year

B. Information given is insufficient to determine the best option

C. Build the factory for the client

D. Both options offer the same payoff

The exam prep tool state that right answer is A with the following details:

In this scenario you are considering investing your money in the bank or building a factory. Since all transactions are not happening at the same point in time, we need to discount the cash flows and then determine the return on investment. Since the bank is offering a 30% annual interest rate (the opportunity cost if you decide to build the factory), you need to discount all the cash flows for the factory project by 2.5% (30% / 12) on a monthly basis. The discount formula is: Present Value (PV) = Future Value / (1 + interest rate)^period.

Let’s use this formula to determine the net present value of all cash outflows:

Month 1: PV = 1,000,000/(1+2.5%)^1 = 975,610

Month 2: PV = 1,000,000/(1+2.5%)^2 = 951,814

...

Month 12: PV = 1,000,000/(1+2.5%)^12 = 743,556

Adding these up we get the total PV of outflows = 10,257,765

Now let’s calculate the PV of all inflows using the same formula:

Quarter 1: PV = 3,900,000/(1+2.5%)^3 = 3,621,538

Quarter 2: PV = 3,900,000/(1+2.5%)^6 = 3,362,958

Quarter 3: PV = 3,900,000/(1+2.5%)^9 = 3,122,841

Quarter 4: PV = 3,900,000/(1+2.5%)^12 = 2,899,868

Adding these up we get the total PV of inflows = 13,007,204

The return on investment (today) = (13,007,204 - 10,257,765)*100 / 10,257,765 = 27%

Since the bank is offering an annual 30% return on investment, it is advisable not to undertake the project and leave the money in the bank account.

Thanks for help