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Management and the Technology Professional

## Financial analysis using interest and present values

If you lend me £500 today, I will repay you £10,000 in 30 years.

Would you lend the money?

Time value of money is a fundamental concept.

Several factors contribute to the determination of a rate of interest.

Simple interest

Let P be invested at a fixed interest rate of R per investment period. Let that interest be added just once at the end of an investment duration consisting of N investment periods. Let V be the total value including the investment and interest earned.

Compound interest

Let P be invested at a fixed interest rate of R per investment period. Let that interest be added at the end of each investment period, which is called compounding. Let N be the number of investment periods during the whole investment duration. Let V be the total value including the investment and interest earned.

£5,000 is invested at a rate of 8% per annum. What is the total value after 4 years if interest is compounded annually?

£5,000 is invested at a rate of 5% per quarter. What is the total value after 4 years if interest is compounded quarterly?

A rate of interest is assigned for a specific period of time, e.g. annual, quarterly, monthly or weekly. If the compounding period is not the same as the period of interest, then you need to calculate the effective rate of interest.

£5,000 is invested at a rate of 5% per annum. What is the total value after 4 years if interest is compounded every 6 months?

£3,000 is invested at a rate of 12% per annum. What is the total value after 4 years if interest is compounded every 3 months?

Present value analysis is based on the concept of compound interest.

Using a discount rate of 6.1%, how much is £10,000 payable in 30 years worth today?

The price of a new house is estimated to be £225,000 when the construction is finished in 2 years time. Using a discount rate of 8.2%, what is the house worth today?

Be careful of decimal places when using discount rates!

Discounted cash flow (DCF) valuation is the process of calculating the risk-adjusted present value of a future value to determine its value today. DCF is used to compare and make investment decisions.

Net present value (NPV) is the difference between the expenses and income (cash flows) of an investment project, which has been adjusted for risk using DCF valuation. Cash flows are typically applied at the end of each investment period.

The decision rules when using the NPV capital analysis method are:
1. Accept a project for which the NPV is positive.
2. Reject a project for which the NPV is negative.
3. Where the NPV is zero, the project is acceptable in meeting the cost of capital, but, gives no surplus to its investors.

When a duration for an interest or discount rate is not specified, then, the default period is one year.

NPV is not the same as profit!

A piece of land may be purchased for £610,000 to use for coal mining. Annual income would be £200,000 per year for 10 years. At the end of 10 years, the government requires the land to be restored, which is estimated to cost £1.5 million. Using a discount rate of 10%, determine whether to accept the project.

A machine is available to automate a computer assembly process. The machine could save £50,000 in reduced labor costs each year. The purchase price of the machine is £200,000 and it could be used for a period of 10 years. It has a salvage value of £10,000 at the end of its useful life. The machine requires an annual maintenance cost of £9,000. Using a discount rate of 10%, determine whether to purchase the machine.