Discounted cash flow （DCF） techniques
Discounted cash flow
Discounted cash flow （DCF） is an investment appraisal technique which takes into account both timing of cash flows and also total profitability over the project’s entire life.
Key features:
（1）The use of cash flows and not accounting profits
（2）Only future incremental cash inflows and outflows are considered.
（3）The time value of money
3.2 What cash flows should be included?
>> Cash inflows:
The project's revenues
Government grants
Resale or scrap value of assets at the end of project
Tax receipts
Saving
>> Cash outflows:
Initial investment in acquiring the assets
Projected costs （Labor, materials, overheads）
Working capital investment
Tax payments
3.3 Time value of money
There is a time preference for receiving the same sum of money sooner rather than later. Conversely, there is a time preference for paying the same sum of money later rather than sooner.
Reasons for time preference
.Inflation
.Risk preference – risk diminishes as the period before forecast cash inflows shortens and disappears once cash is received.
.Investment preference – money received can be invested in the business, or invested externally.
.Consumption preference – money received now can be spent on consumption.
3.4 Timing of Cash Flows
.A cash outlay to be incurred at the beginning of an investment project occurs in year 0 （now）. The present value of $1 now, in year 0, is $1 regardless of the discount rate.
.A cash flow which occurs during the course of a time period （say, during a year） is assumed to occur all at once at the end of the time period （i.e. at the end of the year）.
.A cash outlay or receipt which occurs at the beginning of a time period （say at the beginning of year 2） is taken to occur at the end of the previous year （i.e. at the end of year 1）.
3.5 Compounding and Discounting
Compound interest
>> Compounding means the interest earned one period will earn interest in the next period.
>> Compounding tells us how much an investment will be worth at the end.
Formula
The formula for compound interest is
FV＝ PV （1＋r）n
where FV = Future value after n periods
PV = Present or Initial value of the investment
r = Compound rate of return per period,
expressed as a proportion
n = Number of periods
3.6.1 Normal Annuity
The annual cashflow starts from Year 1.
What is the present value of $1,000 in contribution earned each year from years 1-10, when the required return on investment is 11%?
Answer: PV = $1,000 x 5.889 = $5,889
3.6.2 Deferred Annuity
The annual cashflow starts from the year later than Year 1.
What is the present value of $2,000 incurred each year from years 3-6 when the cost of capital is 5%?
3.6.3 Immediate annuity
The annual cashflow starts from Year 0.
3.6.4 Perpetuity
A perpetuity is an annual cash flow forever.
The perpetuity with growth keeps appearing in the exam so you need to be very familiar with it.
The examiner often implies a perpetuity by simply stating "The cash flows will occur for the foreseeable future”.
（a） Normal perpetuity
（b） Deferred Perpetuity
Back：Accounting rate of return （ARR）
Next：Net Present Value
Discounted cash flow （DCF） is an investment appraisal technique which takes into account both timing of cash flows and also total profitability over the project’s entire life.
Key features:
（1）The use of cash flows and not accounting profits
（2）Only future incremental cash inflows and outflows are considered.
（3）The time value of money
3.2 What cash flows should be included?
>> Cash inflows:
The project's revenues
Government grants
Resale or scrap value of assets at the end of project
Tax receipts
Saving
>> Cash outflows:
Initial investment in acquiring the assets
Projected costs （Labor, materials, overheads）
Working capital investment
Tax payments
3.3 Time value of money
There is a time preference for receiving the same sum of money sooner rather than later. Conversely, there is a time preference for paying the same sum of money later rather than sooner.
Reasons for time preference
.Inflation
.Risk preference – risk diminishes as the period before forecast cash inflows shortens and disappears once cash is received.
.Investment preference – money received can be invested in the business, or invested externally.
.Consumption preference – money received now can be spent on consumption.
3.4 Timing of Cash Flows
.A cash outlay to be incurred at the beginning of an investment project occurs in year 0 （now）. The present value of $1 now, in year 0, is $1 regardless of the discount rate.
.A cash flow which occurs during the course of a time period （say, during a year） is assumed to occur all at once at the end of the time period （i.e. at the end of the year）.
.A cash outlay or receipt which occurs at the beginning of a time period （say at the beginning of year 2） is taken to occur at the end of the previous year （i.e. at the end of year 1）.
3.5 Compounding and Discounting
Compound interest
>> Compounding means the interest earned one period will earn interest in the next period.
>> Compounding tells us how much an investment will be worth at the end.
Formula
The formula for compound interest is
FV＝ PV （1＋r）n
where FV = Future value after n periods
PV = Present or Initial value of the investment
r = Compound rate of return per period,
expressed as a proportion
n = Number of periods
3.6.1 Normal Annuity
The annual cashflow starts from Year 1.
What is the present value of $1,000 in contribution earned each year from years 1-10, when the required return on investment is 11%?
Answer: PV = $1,000 x 5.889 = $5,889
3.6.2 Deferred Annuity
The annual cashflow starts from the year later than Year 1.
What is the present value of $2,000 incurred each year from years 3-6 when the cost of capital is 5%?
3.6.3 Immediate annuity
The annual cashflow starts from Year 0.
3.6.4 Perpetuity
A perpetuity is an annual cash flow forever.
The perpetuity with growth keeps appearing in the exam so you need to be very familiar with it.
The examiner often implies a perpetuity by simply stating "The cash flows will occur for the foreseeable future”.
（a） Normal perpetuity
（b） Deferred Perpetuity
Back：Accounting rate of return （ARR）
Next：Net Present Value
