Net Present Value

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

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?

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 = £12,000 = £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

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

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 = £12,000 = £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

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?

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

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

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

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

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

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

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.

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

Internal Rate of Return What is the actual return which the project will deliver? PV income @ opportunity cost of capital of 15% = £12,000 = £10,435 1.15 NPV = PV of cashflows minus PV income = £11,429 - £10,435 = £435 Internal Rate of Return = Profit Investment = 12,000 10,000 = 20% Rate of Return Rule Invest in any project offering a rate of return higher than the opportunity cost of capital

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

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

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

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 0.20852709) Click OK.

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

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

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

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

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

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 £148.43 remains unchanged

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?

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

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

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 ?

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

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?

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 factor @5% Select the car that has the highest equivalent annuity – Cheaper

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