Discounted cash flow methods
Net present value
The DCF can be used to calculate the net present value of a company or an investment
NPV is the net value of a capital investment or project obtained by discounting all cash outflows and inflows to their present values by using an appropriate discounted rate of return
It uses cash flows rather than accounting profits and ignores non cash items which including the initial cost of the project and any residual value in the calculation of net cash flows
Initial investments occur at the start of the year (To), other cash flows start at the end of the first year (T1)
The NPV method compares the present values of cash inflows with the present value of cash outflows for an investment
NPV = PV of cash inflows - PV of cash outflows
Decision rules
The project could be undertaken if its NPV is positive
When comparing mutually exclusive projects, the project with the highest positive NPV is selected
Positive NPV = returns from investment exceeds cost of capital
Nil NPV = returns from investment is equal to the cost of capital
Negative NPV = returns from investment are less than the cost of capital
Advantages
The NPV method of investment appraisal is superior to all other methods
It considers the time value of money through the discount rate
It is an absolute measure of return
It is based on cash flows not profits
Takes into account all cash flows throughout the life of a project
It maximises shareholder wealth by only undertaking projects with positive NPVs that ensures a surplus over and above the costs of finance
Disdavnatges
Can be difficult to explain as it uses cash flows rather than accounting profits
The calculation of discount rates can be challenging and requires knowledge of the cost of capital
It is relatively complex compared to non discounting methods such as the payback period and ARR
Discounting annuities
An annuity is a series of fixed payments made at regular intervals during a specific period of time
When a loan is repaid in annuity, each instalment is a fixed amount usually consisting of a repyamnent of part of the principal and the interest expense for the period
The principal repyamnet increases over time while the interest expense decreases
Annuity factors
An annuity factor is used to calculate the present value of an annuity
The PV of an annuity stream is the current value of future periodic payments calculated by multiplying the fixed periodic payment by the annuity factor
Annuity factors are based on the number of years involved and an applicable rate of return or discount rate
The AF is the sum of the individual discount factors
The PV of an annuity can be found using the formula
PV = annual cash flow x AF
AF = [1 - (1 + r)-n] / r
The above formula is used to find the PV when the FV of the annuity is known, the higher the discount rate, the lower the PV of the annuity
Discounting a perpetuity
A perpetuity is a type of annuity or a constant stream of cash flow that continues indefinitely
Certain types of government bonds pay annual fixed coupons for as long as the bondholders hold the bonds
Discounting a perpetuity is used in valuation methodologies to find the present value of a company's cash flow when discounted at an applicable rate of return
PV = annuity per period (cash flow) / discount rate)
Internal Rate of Return
IRR calculates the rate of return at which the NPV of all the cash flows from a project or investment equal 0
IRR is the discount rate at which NPV is 0, the discount rate that allows the project to break even
IRR uses the same concepts as the NPV method
Decision rules
Projects should be accepted if the IRR is greater than the cost of capital
If IRR is less than the target rate, the investment does not add value to the company
If the IRR exceeds the cost of capital or the discount rate, it is worth undertaking the project
If IRR is greater than the target rate, the investment adds value to the company
Calculating IRR
- Find a discount rate that gives a positive NPV and a negative NPV, if the NPV is positive use a higher discount rate to get a negative NPV. If the NPV is negative, use a lower discount rate to get a positive NPV
- Estimate a discount rate between these 2 rates that will product 0 NPV
- Calculate IRR using the following formula
IRR = L + [NPVL / (NPVL - NPVH)] x (H - L )
Where
L and NPVL represen the lower discount rate and its NPV
H and NPVH represent the higher discount rate and its NPV
The IRR method works well when cash flows have traditional patterns such as a cash outflow at the beginning of a project followed by a series of has inflows
Advantages
The IRR method evaluates potential returns and the attractiveness of potential investments
It uses real cash flows rather than profits which can be manipulated by the use of different accounting policies
It takes account of the time value of the money
It considers risk of future cash flows
Excess IRR over the cost of capital indicates the excess return fr the risk contained in the project
It gives a % rate that can be compared to a target (cost of capital). this is easier for management to understand and interpret than the concept of NPV
Disadvantages
IRR is a relative measure that gives a % rate that can be compared to a target cost of capital. It ignores other factors such as project duration, future costs and the relative size of the investments
It is not a measure of profitability in absolute terms
It is the most complex to caclulate
May not lead to value maximisation when used to compare mutually exclusive projects
It may not to lead to value maximisation of projects when used to choose projects when there is capital rationing
Cannot be used for non-conventional cash flows, a project that has large negative cash flows later I life may give rise to multiple IRRS
Assumes that the positive future cash flows are reinvested to earn the same return as the IRR
Discounted payback
The discounted payback period method helps determine the time period required by a project to break even
It combines the techniques used in payback period and DCF to calculate a discounted payback period
This involves discounting the cash flows and then calculating how many years it takes for the discounted cash flows to repay the initial investment
Discounted payback was developed to overcome the limitations of the traditional payback period method which ignores the time value of moeny
Discounted payback period = original cost of investment or initial cash / PV of annual cash flows
Advantages
The discounted payback method considers the time value of moeny
Uses cash flows not profit
Considers the riskiness of the projects cash flows (through the cost of capital)
Determines whether the investments made are recoverable
Disadvantages
The discounted payback method is subjective as it gives no concrete decision criteria that indicates whether the investment increases the firms value
It requires an estimate of the cost of capital in order to calculate the payback period
It ignores cash flows beyond the discounted payback period
Calculations can become complex if there are multiple negative cash flows during the projects life