Question

Second National Bank is considering adding 5 new ATM machines. Each machine costs $25,000 and installation costs are $15,000 per machine. Second National Bank expects the new machines to save $0.33 per transaction on 250,000 transactions per year on the new machines. It also expects the new machines to last for 15 years. If the bank needs to earn 14 percent return on this investment, what is the net present value of this investment?

Answer 1

1. Introduction:

NPV stands for Net Present Value of an investment:

• It is used in capital budgeting to assess and analyse the profitability from given viable project options.
• Its calculated as a difference between present value of Inflows and present value of Outflows. This difference may be positive or negative based on which conclusions are derived as to investmentment in project is recommeded or not.
• Positive NPV (Inflows are more than Outflows)of a project implies a profitable investment option, whereas Negative NPV (Outflows are more than Inflows) reflects th investment will result in loss and therefore, not a viable option.

2. Let us calculate NPV of the investment under consideration, step wise step:

A. Step 1:-

(a) NPV of Project Outflow:

• This is the first cash flow (outflow) at year 0. Since, this is today's outflow (usually paid upfornt) it doesn't need to be discounted.
• Outflow included machine cost ($25,000 per machine) as well as installation cost ($15,000 per machine)

Therefore, Outflow for 1 machine= $15,000 + $25,000, which equals to $40,000

Therefore, Total outflow for 5 machines comes to= $40,000*5 machines= $ 2,00,000 for all the 5 machines purchased and installed.

Therefore, NPV of Cash Outflow= $2,00,000

(b) Number of years that the new ATM machine will last for is given as 15 years, meaning there will be cash flows (inflows) flowing in to the bank on the investment made (each year a certain amount of inflows flowing)

(c) Discount rate given is 14%, signifying the rate of return expected by the shareholders of the Second National Bank, for calculating the NPV of the investment in ATM.

B.Step 2:-

(a) NPV of Project Inflow:

• Yearly inflows earned on account of investment made. These are the future payments which spreads accross 15 years time horizon, therefore it needs to be discounted or adjusted for the time value of money.
• Inflows (without adjusting for time value of money)= $0.33 per transaction* 2,50,000 per year on all the machines, that comes to $82,500 per year for 15 years.

(It is to be noted that for calculating inflows 2,50,000 transactions is not to be viewed as transaction per machine, carefully see it's written "transaction per year on new machines" and not per machine)

• $82,500 per year for 15 years is the inflow, so we have to calculate present value of annuity (since amount of inflow is fixed every year and are not fluctuating). PVAF of $82,500 (15years, 14%)

Let us calulate the present values of discount rates and its sum:

Therefore, NPV of Cash Inflows= $5,06,728.86

C. Step 3:-

Calculation of NPV= NPV of Cash Inflows - NPV of Cash Outflows

NPV= $5,06,728.86 - $2,00,000

Therefore, NPV of investment in ATM machines by Second National Bank= $3,06,728.86

Since the NPV is positive, it is a viable investment option and it is recommended to invest in the same.

Note: Alternatively, you may use financial calculator to calculate the NPV instead of using the tabular manual method.

Steps to be performed if NPV is to be calculated on calculator:

Step a) Press 2ND and CF (right besides 2ND) and again 2ND and CE/C for clearing the any previously entered fields.

Step b) Enter CFo (Cash outflow) as -$2,00,000. Enter and down arrow button.

Step c) Enter C01 as $82,500. Enter and down arrow button.

F01 as 15 (because a constant inflows will be earned over a period of 15 years. Enter and down arrow button.

Step d) Press NPV button, 'I' (Interest rate) would be asked, fill this I as 14%. Enter and down arrow button.

Step e) An NPV would appear on screen with no figures, Press CPT to compute the same.

Step f) NPV of investment $3,06,728.86 would appear as a resultant answer.