1. Net Present Value

2. Definitions Opportunity Cost of Capital Net Present Value (NPV)
Expected rate of return forgone by investing in a project
Net Present Value (NPV)
Present value of cashflows minus investment
BM&M p225

3. Example Mr Sharp is considering a property investment
He can lease a flat for 1 year for an upfront payment of £10,000
Mr Dim, his friend, has agreed to rent the flat from him for a year and will pay £12,000 in rent at the end of the year
Is this a good investment for Mr Sharp?

4. Opportunity Cost of Capital
The scheme is attractive to Mr Sharp, only if the payoff exceeds the rate of return offered by comparable investment alternatives
Assume that the £12,000 payment from Mr Dim is guaranteed
Assume that the rate of return on 1 year government bonds is 5%, this is the rate of return which Mr Sharp will forgo by investing in the project
How much would you have to pay to receive £12,000 at the end of the year?
Initial investment = £12, = £11,429
1.05
Mr Sharp’s required initial investment = £10,000
NPV = PV of cashflows minus investment = £11,429 - £10,000 = £1,429
NPV Rule – Managers increase shareholder value by accepting projects that are worth more than they cost and should accept projects with a positive NPV

5. Will Mr Dim pay up? Key assumption Risks
Mr Dim’s £12,000 future payment is guaranteed
Risks
Mr Dim may lose his job
Mr Dim may be run over by a bus
Mr Dim may be dishonest
Not all investments are equally risky
A risky investment requires a greater return than a safe one to compensate for potential losses
Opportunity Cost of Capital should reflect the riskiness of the project

6. Risk and Opportunity Cost of Capital
The scheme is attractive to Mr Sharp, only if the payoff exceeds the rate of return offered by comparable investment alternatives
The rate of return on 1 year government bonds is 5%, however, the rate of return on projects which offer a similar level of risk as Mr Dim is 15% - this is the rate of return which Mr Sharp will forgo by investing in the project
How much would you have to pay to receive £12,000 at the end of the year?
Initial investment = £12, = £10,435
1.15
Mr Sharp’s required initial investment = £10,000
NPV = PV of cashflows minus investment = £11,429 - £10,435 = £435
Mr Sharp should still accept the project, but the NPV is much lower

7. What if Mr Dim wants to rent the flat for 5 years?
Mr Sharp is required to pay £40,000 for a 5 year lease
He offers the flat to Mr Dim for £12,000 for the first year, with an increase of £1000p.a. thereafter
Is this a good investment?

8. Multiple Cashflows
Discount the future cashflows at the 15% Opportunity Cost of Capital
PV rental income= C1 + C2 +…+ C5 = £46,001
(1+r) (1+r)^2 (1+r)^5
NPV = PV rental Income – Initial Investment = £46,001 - £40,000 = £6,001
Mr Sharp should go ahead

9. Mr Sharp needs some Cash
Mr Sharp goes ahead with the project but immediately suffers a cashflow crisis
Mr Rich offers to buy his investment in the flat
How much should Mr Rich pay?
Mr Rich will be entitled to the future cashflows from the project
Value of the future cashflows = PV = £46,001
Mr Rich should pay Mr Sharp £46,001
Mr Sharp has outlayed £40,000 so his net gain is £6,001 which is exactly equal to the NPV of the project

10. Does a project have to generate positive cashflows to be attractive?
Not necessarily
Projects which offer cost reductions to the business will also positively impact upon profits in exactly the same way as cash generating opportunities
Discounting the cost reductions using the opportunity cost of capital will identify the increase in value to the firm
Some projects may generate negative net cashflows for the first few years and it is necessary to forecast associated cashflows over the long term
It should be noted that long term forecasting is itself subject to risk
Pentagon Law of Large Projects
Anything big takes longer and costs more than you are originally led to believe

11. Choosing between projects
Mutually exclusive projects are two or more projects which cannot be pursued simultaneously
Calculate the cashflows for each project, compare NPV’s and choose the most attractive

12. Example Mr Sharp has purchased a 5 year lease for £40,000
Mr Dim offers to pay rent for £12,000 for the first year, with an increase of £1000p.a. thereafter
Mr Bold offers to pay £25,000 rent for the first year, £20,000 for the second year and £5,000 p.a. thereafter
Which offer should Mr Sharp accept?
The NPV of Mr Dim’s proposal is £6,001
The NPV of Mr Bold’s proposal is £5,494
Mr Sharp should accept Mr Dim’s offer
Note – it is assumed that both offers carry equal risk and so the same opportunity cost of capital is employed

13. Payback
Payback period is the time until cashflows recover the initial investment in the project
Project A requires an initial investment of £50,000 and will generate income of £25,000 at the end of year 1, year 3 and year 5.
The payback period is 3 years because total income of £50,000 will have been received by the end of year 3.
Project B also requires an initial investment of £50,000 and will generate income of £30,000 at the end of year 1, £20,000 at the end of year 3 and £10,000 at the end of year 5.
The payback period is also 3 years because total income of £50,000 will have been received by the end of year 3.
The payback rule states that a project should be accepted is its payback period is less than a specified cutoff period
Ref:BM&M p230

14. Limitations of Payback
Payback is intuitive and answers the question ‘How long will it take to cover its costs?
However, there are limitations with payback
Payback ignores cashflows after the cutoff period, tends to favour short term projects and rejects long term investments
Payback gives equal weight to all cashflows arriving before the cutoff period
Payback does not consider whether the project increases shareholder wealth
Project B has a negative NPV and should be rejected,
Project A has a positive NPV and should be accepted
This is overlooked by the Payback rule.

15. Discounted Payback
The discounted payback measure answers the question ‘How long must the project last until it offers a positive NPV?’
The rule will never accept a project with a negative NPV
However, cashflows after the cutoff point remain ignored
Nevertheless may be useful for highlighting projects which have a long payback and the associated risks with long term forecasting

16. Internal Rate of Return
What is the actual return which the project will deliver?
PV opportunity cost of capital of 15% = £12, = £10,
NPV = PV of cashflows minus PV income = £11,429 - £10, = £435
Internal Rate of Return = Profit Investment = 12, , = 20%
Rate of Return Rule
Invest in any project offering a rate of return higher than the opportunity cost of capital

17. Internal Rate of Return and NPV
If the project is discounted at 15%, the NPV is £435
If the project is discounted at 20%, the NPV is zero
The rate of return on the project is the discount rate which gives an NPV of zero
Rate of return =20%
NPV Profile
Ref:BM&M p232

18. Calculating IRR for multiple cashflows
The project rate of return is the discount rate which gives the project an NPV of zero
Sometimes called the discounted cashflow (DCF) rate of return
Method of calculation
Linear interpolation
Spreadsheet Goal Seek function
Spreadsheet IRR function
Financial Calculator

19. Linear Interpolation NPV @ 20% = 793 NPV @ 21% = -135 Technique
= 928
135/928 = 0.145
21.00 – = 20.85
IRR = 20.85%

20. Goal Seek Function Values Formulae On the Tools menu, click Goal Seek.
In the Set cell box, enter the reference for the cell that contains the sum of the discounted cashflows, appears above as=SUM(E3:E8)
In the To value box, type 0
In the By changing cell box, enter the reference for the cell that contains the discount rate (appears above as )
Click OK.

21. IRR Function Values Formulae
IRR is calculated using the Excel IRR function on the cashflows

22. Pitfalls of IRR IRR does not distinguish between lending and borrowing
Where cashflows consist of multiple receipts and payments, it is possible to have more than one IRR figure
Mutually Exclusive Projects
High IRR does not always mean high NPV which is the objective for increasing shareholder wealth
Ref:BM&M p234

23. Lending and Borrowing Project A and Project B have the same IRR of 21%
Does this mean that the projects are equally attractive?
Project A involves lending £40,000 and receiving cashflows equivalent to interest of 21% p.a.
Project B involves borrowing £40,000, then paying interest at a rate equivalent to 21% p.a.
Project A is attractive, Project B is not
Calculate the NPV to determine which is a good proposition
Rule
When NPV increases as the discount rate increases, a project is acceptable only if its IRR is less than the Opportunity Cost of Capital

24. Multiple Rates of Return
Project C has an IRR of 8%
The NPV of project C using a discount rate of zero is 0 so Project C has an IRR of 0%
Is this possible?
Note – cashflow sign changes twice
There can be as many different IRR’s as there are changes in the sign of the cashflow stream
Opportunity Cost of Capital is 5% and NPV of the project is £148.43

25. NPV of Project C
IRR = 8%
IRR = 0%
Which IRR is correct?

26. Modified IRR
Combine the cashflows until only one change of sign remains
Use Opportunity Cost of Capital (5%) to discount the cashflows
The cashflows for Years 3,4 and 5 are discounted to year 3 to become a single cashflow of value 1075
Replace the cashflows for Years 3,4,5 with 1075 in year 3
Calculate IRR
Modified IRR = 5.42%
Note – NPV of £ remains unchanged

27. Mutually Exclusive Projects Mr Sharp, Mr Dim and Mr Bold
Mr Sharp accepted Mr Dim’s offer because it had a higher NPV - £6001 v £5494
The IRR from Mr Dim is 21%
The IRR from Mr Bold is 23%
Is this a contradiction?

28. Mutually Exclusive Projects Mr Sharp, Mr Dim and Mr Bold
The NPV profiles cross at 16.31%
Mr Dim’s offer has a higher NPV if the discount rate is greater than 16.31%
Mr Bold’s offer has a higher NPV if the discount rate is lower than 16.31%
Mr Dim
16.31%
Mr Bold
Higher IRR does not always mean higher NPV – shareholder wealth is paramount

29. Comparing NPV’s Investment Timing Decision Quality versus Price
Replacement Decision
Ref:BM&M p240

30. Investment Timing
Mr Careful is considering purchasing a second hand car
The car save him £2000 p.a. in bus fares and will cost £500 to run
If he buys the car now, it will cost £10,000 and will last for 10 years
Depreciation in the second hand market runs at 15% p.a.
His savings account pays 5% p.a.
Should he buy the car now or wait ?

31. Mr Careful
If Mr Careful purchases the car this year, he will save £1500 p.a. for the next 10 years
This saving must be discounted at Mr Careful’s opportunity cost of capital – his deposit account rate,5%
The car becomes 15% cheaper each year, this costs should also be discounted at Mr Careful’s opportunity cost of capital rate, 5%
Net Saving = PV Saving - PV Cost
The PV of the net savings are maximised if Mr Careful waits for 2 years and buys the car at a reduced price
The decision for investment timing is to choose the investment date which results in the highest NPV today

32. Quality versus Value Mr Careful decides he needs the car now
However, he could choose another car
This car provides net savings of £1500 p.a. but costs only £8000, however, it will only last for 8 years
Which car is best?

33. Comparison
At first sight, the longer life seems better since the savings are greater. But the longer life car provides a service for 2 more years.
Is the annual saving for the longer life car as good?
The savings are converted into annual equivalent figures
Equivalent annual annuity = present value of savings annuity
Select the car that has the highest equivalent annuity – Cheaper

34. Capital Rationing
Capital Rationing refers to the limit set on the amount of funds available for investment
Soft Rationing – capital rationing is not limited by investors but by management
Hard Rationing – firm has insufficient resources to invest in attractive projects
Profitability Index = NPV Initial Investment