Time Value of Money (TVM) – formula with examples

Time Value of Money (TVM) – formula with examples

Time Value of Money Overview

Discounted cash flow analysis

  • It is a technique for evaluating the proposed investments to decide whether thy are financially worthwhile.
  • The expected future cash flows (inflows/outflows) from the investment are all converted to a present value by discounting them at the cost of capital ‘r’
  • Taking into account the concept of relevant cost.
  • It is usually assumed that cash flow early during a year should be treated as a cash flow as at the end of the previous year.

Present value Formulas

Discount factor = 1/(1+r)n

where
r = cost of capital
n = number of periods

Annuity factor = ( 1 – (1+r)-n /r)

Discounted Cash Flow

Time Value of Money

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  • In Net present value (NPV) analysis, all future cash flows from a project are converted into a present value.
  • NPV is the difference between present value of all costs incurred and present value of all benefits received.

Approach

  1. List all cash flows from the project (initial investments, future cash inflows/outflows).
  2. Discount these cash flows to present value using ‘cost of capital’ as discount rate.
  3. If present value of Benefits exceeds the present value of costs, the NPV is positive and if present value of benefits is less, then NPV is negative.
  • A project is worthwhile if NPV is positive.
  • The project commences at time ‘0’ where the cash flows are already at present value.
  • Changes in working capital included as cash flows. An increase usually at the beginning of the project in time ‘0’ is a cash outflow and reduction is a cash inflow.
  • It is the discounted rate of return on investment.
  • It is the average annual investment return from the project.
  • The NPV of the projected cash flows is ‘zero‘ when those cash flows are discounted at IRR.
  • A company might establish the minimum rate of return that it wants to earn on an investment:
    • If a project’s IRR is equal or higher than minimum acceptable rate of return, it should be undertaken.
    • If IRR is lower than the minimum required return, it should be rejected.
  • The following step are involved for calculation of a reliable Internal rate of return (IRR):
    1. Calculate NPV of the project at TWO different rates. One of the NPV should be positive and the other should be negative.
    2. Put the NPVs in the formula:

IRR formula

Discounted Cash Flow and Inflation

Time Value of Money

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  • The cash flows expressed in today’s price terms.
  • They ignore the expectations of inflation.
  • In order to incorporate real cash flows in NPV calculation, real cash flows should be discounted at the real cost of capital.

The following steps are involved:

  • Calculate real discount rate

= money cost of capital – 1
inflation rate

  • Calculate net cash flows at today’s prices.
  • Discount them using real discount rate.

This is the most common method used.

  • Money (nominal) cash flows are cash flows that include expected inflation.
  • Money cash flows should be discounted at the money cost of capital.

The following steps are involved:

  1. Calculate net cash flows at today’s price.
  2. Make adjustment for inflation (by doing this they will be converted into money cash flows).
  3. Use money cost of capital as discount rate.

*Both approaches give same solution, with a difference of rounding off.

Time Value of Money

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