‎The time value of money ‎One of the basic principles of finance is that a sum of money today is worth more than ‎the same sum in the future. If offered a choice between receiving ₦10,000 today or in 1 ‎years‟ time, a person would choose today. A sum today can be invested to earn a return. ‎This alone makes it worth more than the same sum in the future. The time value of ‎money concept states that the value of N1 today will not be the same in a year's time, due ‎to depreciation in the real value of naira. In order words, what a naira can buy today in a ‎year‟s time an amount above a naira would be required to purchase that same article. ‎Thus a naira invested today should yield an amount over and above the naira invested. ‎Devaluation of money allows for this. However, in a relatively stable economy, the ‎interest rate could be taking to account for devaluation in naira. The interest rate per naira ‎is the compensation for the loss of value by the naira amount. Hence the interest rate is ‎used for discounting. This is referred to as the time value of money. The impact of time ‎value can be estimated using one of two methods: ‎ Compounding which estimates future cash flows that will arise as a result of investing an ‎amount today at a given rate of interest for a given period. ‎i. ‎An amount invested today is multiplied by a compound factor to give the amount ‎of cash expected at a specified time in the future assuming a given interest rate. ‎ Discounting which estimates the present day equivalent (present value which is usually ‎abbreviated to PV) of a future cash flow at a specified time in the future at a given rate of ‎interest ‎i. ‎An amount expected at a specified time in the future is multiplied by a discount ‎factor to give the present value of that amount at a given rate of interest. ‎ii. ‎The discount factor is the inverse of a compound factor for the same period and ‎interest rate. Therefore, multiplying by a discount factor is the same as dividing by a compounding factor. ‎iii. ‎Discounting is the reverse of compounding. ‎Formula for Discounting Factor ‎ ‎ ‎ ‎ ‎Where: ‎r = the period interest rate (cost of capital)12This formula can be used in determining the present and future value of an investment as ‎follows. ‎Future Value (FV) = Amount Today X ‎ ‎Present Value (PV) = Future Value X ‎ ‎ ‎ ‎b. Money and Real Interest Rate ‎The scientific method assumes therefore that the interest rate used is the real interest rate ‎and not the money interest rate. The real interest rate is the after tax interest rate while the ‎money interest rate is the before tax interest rate. The scientific method makes use of the ‎real interest rate asking for granted that inflation rate will be equal the tax rate. Since ‎normally the value of good should only be inflated by the tax paid thereon. ‎For example, the money interest rate is 20% and the tax rate is 30% the real interest rate ‎will be (1-0.30) (20%) = (0.70) (20%) = 14%. ‎Scenario 1 ‎Mr Filafa expects to receive ₦150,000 in five years‟ time. If Mr Galadima faces an interest rate ‎of 20%, what is the present value of the ₦150,000? ‎Scenario 2 ‎Abdusomad want to invest 35,000. What is will be the future value of his investment in three ‎years‟ time if the interest rate is 15%? ‎Net Present Value Method ‎The net present value method is the total present value of a project which should be greater than ‎the initial capital outlay of the project before such project could be accepted. ‎Calculating the NPV of an investment project ‎Step 1: List all cash flows expected to arise from the project. This will include the initial ‎investment, future cash inflows and future cash outflows. ‎Step 2: Discount these cash flows to their present values using the cost that the company has to ‎pay for its capital (cost of capital) as a discount rate. All cash flows are now expressed in terms ‎of „today‟s value‟. ‎Step 3: The net present value (NPV) of a project is difference between the present value of all the costs incurred and the present value of all the cash flow benefits (savings or revenues).i. ‎The project is acceptable if the NPV is positive. ‎ii. ‎The project should be rejected if the NPV is negative

Step 1: Identify the given values for Scenario 2. The amount to invest today (Present Value, PV) is ₦35,000. The interest rate (r) is 15% or 0.15. The number of years (n) is 3. Step 2: Use the future value formula. The formula for future value is: FV = PV × (1 + r)^n Step 3: Substitute the values into the formula and calculate. FV = ₦35,000 × (1 + 0.15)^3 FV = ₦35,000 × (1.15)^3 FV = ₦35,000 × 1.520875 FV = ₦53,230.625 FV ≈ ₦53,230.63 The future value of Abdusomad's investment in three years will be approximately ₦53,230.63. ₦53,230.63 That's 2 down. 3 left today — send the next one.