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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.

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.

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.

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.

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?

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:

Net present value (NPV) is

The decision rules when using the NPV capital analysis method are:

- Accept a project for which the
**NPV is positive**. - Reject a project for which the
**NPV is negative**. - 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**.

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**.