## Introduction to Discounted Cash Flow – NPV

In this lecture we will be looking at how the Financial Manager should go about making capital investment decisions. For example, they may have to decide whether or not it is worthwhile investing $1,000,000 in a new factory. Alternatively they may have to make the choice between several available investments.

## Discounted Cash Flow – Net Present Value

This approach looks at the expected cash flows from the investment in question. If over the life of the investment there is an expected cash surplus, then the project will be accepted, whereas if an expected cash deficit the project will be rejected.

To account for the fact that money will be tied up in the project over a period of years (and will therefore either result in interest being paid on money borrowed for the investment, or interest lost on the money invested), the cash flows are discounted at the cost of money (or cost of capital) to the company before calculating the net surplus or deficit and making the decision.

View all ACCA Paper F9 lectures >> | This ACCA F9 lecture is based on OpenTuition course notes, view or download lecture notes here>> |

Maria says

Mr. Moffat please i have got a question on your example of investment appraisal/discounting. I’m struggling a little bit in digesting the concept of COST OF CAPITAL.

You gave an example of an initial outlay of US$50,000 and the future cash flow in two years is US$60,000. I’ll use your subsequent lecture on dividends to interpret this…..If i expect a cashflow of US$60,000 and require a return of 10% in two years then the present value or what i am willing to pay today is US$49,587(I understand that clearly).

Then does COST OF CAPITAL (discount rate) mean that my cost is US$50,000, but should have been US$49,587? So I’m losing US$413? So in other words I paid US$50,000 to get US$60,000 in the future instead of paying US$49,587, thus I’m US$413 poorer?

I understand the term when you call it the rate of return as in the dividend example, but I’m struggling to understand the term when you call it a discount rate. Would really appreciate it if you could explain.

John Moffat says

What you write is correct.

If we require a return of 10% then either we need to get more than 60000 from our investment of 50000, or alternatively we would only be prepared to invest a maximum of 49587 to get the return of 60000.

If we did choose to invest 50000 and get 60000 back, then we would effectively be losing 413, and so we would prefer not to invest.

There is nothing magical about the word discount. Discounting is simply the word we give to working out the equivalent amount now of a future cash flow. We can call the interest rate we use to do the discounting the discount rate.

yasminis says

Hello, I can see that the below has been deleted from the syllabus, however it is not quite clear for me. Do we not have to calculate the present values of cash flows (using figures from the tables) for the Dec 2013 sitting?

a) Explain and apply concepts relating to interest

and discounting, including: [2]

i) the relationship between interest rates and

inflation, and between real and nominal

interest rates

ii) the calculation of future values and the

application of the annuity formula

iii) the calculation of present values, including

the present value of an annuity and

perpetuity, and the use of discount and

annuity tables

iv) the time value of money and the role of cost

of capital in appraising investments

John Moffat says

It is all assumed knowledge from Paper F2, and everything is still examinable (and is examined – the syllabus changed at the beginning of 2013 and all the above was examined in June 2013)

yasminis says

thank you, thought it iwas no more examinable.

fahim231 says

i am still slightly confused as to why he did 60,000 divided by (1.1)^2 to get £49,587? – I fail to understand the concept regarding this, can anyone reword it berrer? thanks.

John Moffat says

Discounted cash flow is assumed knowledge from Paper F2, so for a fuller explanation have a look at the relevant Paper F2 lectures on here.

bwix77 says

Brilliant! Well explained lecturers. Thank you so much OT for making my life easy.

jmohan says

Alresford Ltd is considering the purchase of 100 per cent of the ordinary shares of the all

equity-financed Gibson Ltd. Gibson operates in two divisions – North and South – and a head

office. The divisions operate independently of each other; the only joint costs of Gibson, not

attributable directly to either division, are those of the head office. Gibson’s management is

currently committed to operating both divisions for 4 years and have estimated operating

cash flows and the taxable operating profits of each division as:

Operating Cash Flows Taxable Operating Profits

Division Division

Year North ($000) South ($000) North ($000) South ($000)

1 12,000 12,000 8,000 12,000

2 12,000 8,000 12,000 8,000

3 16,000 8,000 16,000 8,000

4 20,000 4,000 24,000 4,000

The above figures exclude:

1. Head office costs of $ 4,000,000 per year.

2. Planned capital expenditure by North division in year 1 of $ 8 million and its tax

consequences. The capital expenditure is necessary for North division’s continued

operations and the above figures assume it will be undertaken.

3. The salvage values of Gibson’s assets. Salvage values will be received at the end of year

4 and are estimated at

North division $ 24 million

South division $ 12 million

Equipment used at head office is all rented on short-term operating leases and

therefore has no salvage value to Gibson at any time.

The above details are widely known and would continue to apply to Gibson after any

takeover, except that

1. Some of Gibson’s administrative activities would be undertaken by Alresford, resulting

in savings of head office costs of 50% in years 1 and 2 and 75% in years 3 and 4.

2. At year 4, North division’s assets would be used by Alresford to substitute for capital

expenditure of $ 28 million planned for year 4.

Alresford’s Director of Strategic Planning has suggested that if a takeover is completed then

various options are available to Alresford. She has detailed the options, but has made no

attempt to appraise their financial desirability. The details are:

1. Early termination of South division’s operations. This would change the estimated

salvage values which would be realized immediately on termination of the division’s

activities. Early termination would also enable operating cash flows, and taxable

profits, to be increased by a constant amount for each year of the division’s revised

life, the level of the constant increase being dependent upon the date of termination.

The revised figures are:

Operations terminated at

end of year

South division

Revised salvage value

2 $ 20 million $ 4 million

3 $ 16 million $ 3 million

Increase in annual cash

flows for each year until

termination

2. Alresford’s own transport department could be used to carry out North division’s

deliveries, thereby saving the division $ 600,000 per year in transport costs. However,

this policy would cause Alresford’s transport department to modify its planned

replacement cycle, and expenditure of $ 1.6 million, scheduled for both year 3 and 5,

would be increased to $ 2 million and would occur earlier, in year 1 and year 4.

Thereafter all planned replacements would be unchanged.

3. By incurring additional advertising of $ 3.6 million in year 1, sales of North division

would increase producing additional profit, and cash flow, of $ 2.4 million for each of

years 3 and 4.

Alresford’s Financial Director believes that an appropriate risk-adjusted after-tax discount

rate to be applied to all cashflows relating to the consequences of the proposed acquisition

is 18%.

The corporate tax rate is 30%, with taxes payable in the year that taxable profits arise.

Alresford Ltd. has exclusively overseas resident shareholders, and so is not integrated into

the dividend imputation system. To stimulate the economy, the government has recently

announced that all capital expenditure may now be fully depreciated at the time it is made

for tax purposes (so that capital expenditure can be treated as an allowable expense in this

question). All sales of assets will be subject to taxation. Assume all cash flows occur on the

last day in each year.

Part A of the Assignment (12 marks):

Clearly state any assumptions you make and explain all calculations in full. Use an 18% aftertax

cost

of

capital.

(a) Estimate the market value of Gibson Ltd in the absence of any take-over possibilities.

(4 marks)

(b) Advise Alresford Ltd. on the maximum amount it should be prepared to pay for Gibson

if the Strategic Planning Manager’s suggestions are completely ignored.

(4 marks)

(c) Determine which of the Strategic Planning Manager’s suggestions should be

undertaken and specify the optimum life of South division. Advise Alresford Ltd. of the

maximum amount it should now be prepared to pay for Gibson.

(4 marks)

John Moffat says

Why have you typed out an entire question?

Surely you do not expect us to provide an entire answer?!

If you have specific problems (after having watched the relevant lectures) then by all means post them in the Ask the Tutor forum, and we will try and help.

jmohan says

Can you help me to find the IRR

John Moffat says

I am not sure why you want the IRR since it is not asked for!

However since you have presumably calculated the NPV at 18%, you need to guess a second discount rate and calculate the NPV at that rate also.

Then interpolate/approximate between the two as per my lecture.

jmohan says

I am going beyond the rate of 100% and still not getting a negative NPV. Could help me please

John Moffat says

I can only think that you have got your cash flows wrong (and I am still puzzled about why you want the IRR )

saulat says

in investment appraisal , when we calculating inflation for sales variable cost and etc , how many digits after decimal place has been taken ? like in CJ question of capital investment appraisal , i have just rounded of the sales and variable cost per unit and its given quite alot of difference in the values . i have calculated everything properly , but just due to round of difference , the NPV according to the question is in 700 ….. and my answer gives me sumthing in 1200 …. so , if any how i round of amounts in exam ,,, will they give relief ? or what is the appropriate way ? 3 digits to decimal places (when calculating per unit costs)? my another question is , that unless stated , workin capital should be recovered in the last year ? like if the examiner is silent , shall the wrking capital be recovered in the final year or what ? Thankyou.

John Moffat says

There is no firm rule about rounding. For the cash flows themselves, usually do them to the nearest thousand.

In CJ, you certainly need to keep the unit costs to three decimal places because otherwise when you multiply by the sales it will not end up being to the nearest thousand! You would lose some marks for having rounded too much.

(However, there is absolutely no need to work out the unit price and cost each year. All you need do is work out the total sales and total cost in the first year, then apply the inflation to the totals, and then round to the nearest thousand)

With regard to working capital, usually assume that it is recovered in the last year. Obviously in this question we do not because the question specifically said not do (which is because we are evaluating over a four year planning period, even though the project itself will presumably last longer).

saulat says

much of my confusion has been sorted , but if i mention in exam that ” i have taken just 2 decimal places , ” as calculating for per unit costs , then , will they still deduct my marks ? And regarding to Working capital , if question is silent , than obviously v will recover every amount in the final year of operation, but in CJ (question of investment appraisal) the examiner is silent about the working capital recovery in the final year of operation and also in the solution they had nt Recovered the amount in the final year , WHY ? its what making me so confused n contradictory ! kindly put some light regarding this issue , Thank you.

John Moffat says

You would lose some marks because you really should do it the way I said in my previous reply (i.e. in total).

In CJ, the examiner is not silent about working capital recovery – the question specifically says ‘ignoring any scrap value or working capital recovery’ in the last paragraph.

Oboro says

Thank you so much sir. This platform is simply the best. In my country, you pay heavily to receive ACCA lectures and now OT has made it free. Not only is it free, but the lecturers know their jobs well. Looking forward to asking you questions sire soonest. Godbless. Long live open tuition

pamelah says

Thanx for explaining so well

suthan says

Very good lecture

Mahoysam says

Thank you for this explanation, it was not boring, it was actually necessary!

I took this in college and never understood it, I just found it very confusing. I took it in F2 but I was not studying F2 here on open-tuition and I ALSO found it confusing, I was able to solve questions but very confused! This is the first time I feel that I understand the logic and the meaning of discounting. I think it is a confusing thing but it is understood now and true that there is no use of going any further if the basic thing is not clear, this is exactly the problem with most tutors, they go on teaching without clarifying the basics, it results in a waste of time really!

Thank you!

emanyani says

Wonderful lecture, i sjould have discovered this site earlier! thank you very much OT team.

nickyckelly says

Wonderful thank you guys so much, you make what seems complicated quite easy

tandi says

That was brilliant. Thank you.

martial28 says

please do it is for the p4 classe i really need to interact with other student doing p4

John Moffat says

I am not sure what it is you want me to do

martial28 says

are your debate on the investment appraisal for free cash flow for level P4 ? if so what is the problem

siti says

for the example,why don’t we used the interest 1.2 instead of 1.1?is’t because the interest only be charged starting Feb?

Jagjeet says

1.1 = interst rate of 10%.

in a formula you will have (1+r)

R = interest rate

1= always adding on from the last figure.

nothing to do with Feb.

so interest rate of 5% would be 1.05

arheen says

Fantastic lecture,loved it