Discounted cashflow techniques

Question 1

What is meant by the time value of Money?

Answer 1

Essentially the time value of money means that £100 now would be worth more(buy more) than £100 in a years time.
This is recognising the effects of inflation on the purchasing power of money or
That money now can be used the earn investment returns now that would not be earned on money later.

there is also the risk that money expected later may not be received.

Question 2

What is compounding and how is it calculated?

Answer 2

Compounding could be described as earning interest on interest…
So where an initial investment is left in place over a number of years each subsequent years interest will be calculated not only on the value of the initial investment but also on any interest earned on the investment in previous years.

By compounding a value we will be calculating its future or terminal value.

F=P(1+R)^N

Where:

F is final or terminal value

P is the value of initial investment

R is rate of interest

N is number of periods.

Question 3

How is the calculation of a present value for a single sum, annuity and perpetuity calculated?

Answer 3

• Discounting - where a discount factor is applied to calculate the present value of a future cash flow. the formula for this is - P = F/(1+R)^N, alternatively (and quicker) is to use discount tables referencing time period and cost of capital (interest)
• Annuities - An annuity is a fixed return for a stated period of time, i.e. £10k per year for 3 years, the present value can be calculated using the above formula on a period by period basis, the annuity factor calculated as PV = 1-(1+R)^-N/R or using an annuity table in a similar way to discount table, apply the annuity factor to the single annual payment value.
• Perpetuity - similar to an annuities but payment amount will continue for the foreseeable future, calculated as PV = Cash flow x 1/R . If the perpetuity is growing the formula changes slightly to Cash flow x1/(R-G)

Question 4

What is meant by a delayed or advanced annuity/perpetuity and how does this change the calculations?

Answer 4

The assumption is that the cash flows will start from the 1st year after the investment, where this is not the case it is referred to as advanced (received in year 0) or delayed (received later than year 1)

• Advanced annuities/perplexities can be calculated using the same formula with 1 added to the factor.
• Delayed annuities/perpetuities carry out the initial calculation as usual and then time discount the value to bring it back as if started in T0.

Question 5

What is the under laying idea with Cost of capital?

Answer 5

Cost of Capital is the term which includes:

• Interest rates
• Discount rate
• Required rate of return.

It is used to take in to account the costs of acquiring an investment

Question 6

What is Net present value and how is it used to appraise an investment?

Answer 6

Net present Value appraisal will take in to account all cash flows related to an investment which will include:

• Initial cost of the investment and any disposal proceeds expected at completion of the project
• Cash inflows relating to the project (relevant cash flows)
• Cash outflows relating to the project (relevant cash flows)
• Increased tax charges arising, and savings from Tax allowable depreciation.
• Increases/decreases to Working capital as a result of the project.

Each years cash flows will be adjusted for inflation and expected growth (depending on money or real terms) before being discounted back to present value.

The NPV will then give either a positive or negative indicator to invest in the project.

Question 7

How useful is NPV as a discounted cash flow appraisal method and why would it be chosen over other methods?

Answer 7

The NPV represents the surplus funds from an investment after taking in to account the time value of money, so inflation and cost of capital, along with other impacts to project cash flows such as increases to working capital and tax charges/Tax downloadable depreciation.

• It gives a clear signal on whether the investment should be approved, surplus or deficit funds.
• It covers the whole life cycle of the project, unlike payback period.
• It focuses on cash flows to give an absolute result not profit (ROCE) which can be subjective.
• Increasing shareholder wealth - cost of capital represents the investors required return then NPV reflects increase in wealth.

It is a more complicated method to carry out and explain to management.

Question 8

What is Internal Rate of Return (IRR) and how is it calculated?

Answer 8

IRR is the return rate that would produce a nil or break even NPV for an investment.

If IRR is greater than cost of capital - project could be accepted.

IRR can be calculated using linear interpolation:

1. Calculate two NPVs for the project using 2 different interest rates approx 5 apart.
2. use the following formula - L+ (N^l/N^l-N^H) x (H-L)

L= lower rate of interest, H= Higher rate of interest, N^L = NPV at lower rate, N^H= NPV at higher rate. NOTE - multiply out the parts in brackets to give a %age to add to L.

Or use the following spreadsheet formulea:

• IRR(Values) - assumes period between cashflows are equal
• XIRR(Values,Dates) - deals with cash flows over unequal time periods.

Question 9

What benefits and disadvantages are there with using IRR as a DCF investment appraisal method?

Answer 9

• IRR considers cashflows, not profits and does take in to account the full life of the project along with the time value of money however it is not an absolute measure of profitability.
• While interpolation is a manual calc the result is an estimate so use of a spreadsheet would be better, it also won’t work with uneven cash flows which can also give multiple IRR’s.
• The result it produces is simple to understand however the calculation is complicated and may prove difficult to explain.

Question 10

What impact does inflation have and how does this relate to real and nominal rates (Terms)?

Answer 10

Where inflation is curing fund provides will usually want to see their return broken down in to two parts:

• Real - the value of the return were inflation not to be occurring.
• Additional - the inflation related part of the return.
• Nominal - is the return total made up of the two parts above.

The formula for this is:

(1+i) = (1+R)(1+H)

i = money (nominal rate), R = real rate, H= inflation rate.

Cash flows not adjusted for inflation will be referred to as being in current or today’s prices.

Cash flows that have been adjusted will be in money terms.

Bear in mind inflate then discount!