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Finance 1

Chapter 3

Chapter 3. The Valuation Principle: The Foundation of Financial Decision Making Cost-Benefit Analysis -

Any decision in which the value of the benefits exceeds the costs will increase the value of the firm - Compare costs and benefits o In the same units o At the same point in time - Quantify all possible sources of cost and revenue - EXAMPLE: higher education - CBA in management decisions: marketing, HR, strategy, operations, product decisions etc. - EXAMPLE A jewellery manufacturer has the opportunity to trade 600 ounces of silver and receive 10 ounces of gold today 1. Convert them to a common unit MP of silver $20 per ounce 600 Oz x $20 = $12,000 MP of gold $1500 per ounce 10 Oz x $1500 per ounce = $15,000 2. Compare Therefore the jeweller’s opportunity has a benefit of $15,000 today and a cost of $12,000 today. In this case the net value of the project today is: $15,000-$12,000 = +$3,000

Market Prices and the Valuation Principle -

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In a Competitive Market… o A good can be bought and sold at eh same price o The price determines the value of the good. EXAMPLE You won a prize: 4 tickets to the Celine Dion concert (face value $100 each) OR 2 tickets to Justin Bieber’s sold-out show (face value $150 each). On eBay, tickets to the Celine Dion show run for $70 each and tickets to Justin Bieber’s show run for $180 each. What should you do? Market prices, not your personal preferences (nor the face value of the tickets), are relevant here: o 4 Celine Dion tickets at $70 each o 2 Justin Bieber tickets at $180 each Compare the market value and choose the highest one. o Market value Celine Dion tickets $280 (4 × $70) o Face value Celine Dion tickets $400 (4 × $100) o Market value Justin Bieber tickets $360 (2 × $180) o Face value Justin Bieber $300 (2 × $150) o Take the tickets to Justin Bieber based on Market Value o Take them even if you don’t want to go to his show.

Finance 1

Chapter 3 o Take them even if you want to see CD (take JB, sell for 360, buy CD for 280, enjoy extra 80 cash)

The Valuation Principle -

The value of a commodity or an asset to the firm or its investors is determined by its competitive market price The benefits and cost of a decision should be evaluated using those market prices When the value of the benefits exceeds the value of the costs, the decision will increase the market value of the firm Example o You have the opportunity to acquire 200 barrels of oil and 3,000 pounds of copper for a total of $25,000. Current MP of oil is $90 per barrel and for copper is $3.50 per pound. o What should you do? What if you expect prices to drop next month?  Oil 200 x $90 = $18,000 today  Copper 3000 x $3.5 = $10,500  Value of opportunity = $18,000+$10,500 - $25,000 = $3,500  Take the offer

Law of one price -

We cannot have two different competitive market prices for the same good The flood of buy and sell orders would push the two prices together until the profit was eliminated More generally, financial securities that profit was eliminated. Law of One Price: in competitive markets, the same goods must have the same price. More generally, financial securities that produce exactly the same cash flows must have the same price.

Arbitrage -

Arbitrage: the practice of buying and selling equivalent goods in different markets to take advantage of a price difference Arbitrage opportunity: any situation in which it is possible to make a profit without taking any risk or making any investment Principle of No Arbitrage: in normal competitive markets, supply and demand forces cause prices to adjust so that arbitrage opportunities are eliminated

The Time Value of Money -

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What would you prefer, $1000 now or in a year? What if the choice was between $1000 now and $1100 in a year? In general, a dollar today is worth more than a dollar in a year o If u have $1 today and you can deposit it in a bank at 7% you will have $1.07 at the end of one year The difference in value between money today and money in the future is the time value of money We can’t compare money today and money tomorrow directly. We need to account for TVM.

Finance 1

Chapter 3

Interest Rates Interest Rate (r) -

The rate at which money can be borrowed or lent over a given period. Converting cash across time – finding common “unit/price” to compare valies

Interest Rate Factor (1+r) -

It is the rate of exchange between dollars today and dollars in the future. It has units of “$ in one year/$ today”.

Future value Formula

PV Formula

Putting PV and FV together -

PV – the value of a cost or benefit computed in terms of cash today -$1869.16 FV – the value of a cash flow that is moved forward in time - $2,000 It’s the equivalent amount! Just in different points in time (-$1,869.16 today) x (1.07) = -$2,000 in one year

Discount Factor -

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Money in the future is worthless today so its price reflects a discount Discount Rate r o The appropriate rate to discount cash flow to determine its value at an earlier time Discount Factor o The value today of a dollar received in the future, expressed as : -------

EXAMPLE -

Revenues if released in 2005: $2B Revenues if released in 2006: $1.6B Interest Rate: 8% $1.6B in 2006/ 1.08 = $1.481B in 2005 Cost of delay of one year: $2B$1.481B = $0.519B ($519M) Delaying the launch delays the entire revenue stream by one year, so the total cost would be calculated in the same way by summing the cost of delay for each year of revenues.

1 1+ r

Finance 1

Chapter 3

Timelines Timelines: Linear representation of the timing of expected cash flows Example: Rob will repay you a loan in 2 installments 10,000 in 1 year and 10,000 in 2 years

Rule 1: Comparing and Combining Values -

Its only possible to compare or combine values at the same point in time Always compare in the same units Money today is always worth more than money tomorrow

Rule 2: Compounding To calculate a cash flow’s future value, you must compound it - $1,000 today, r=10% - $1,000 *1,1=$1,100 in a year - $1,000 *1,1=$1,200 in 2 years - Or simply $1,000*1.1*1=$1,000*(1.1) 2 = $1,210 in two years - (0-1) $100 earned on principal - (1-2)$100 earned on principal and $10 earned on $100 interest from 1st year Compound Interest The combination of earning interest on the original principal and earning interest on accrued interest

Finance 1

Chapter 3

Rule of 72 – simple shortcut -

How long does it take your money to double FVin n years = 1*(1+r)n=2 n≈72/(interest rate in %) Accurate for r>2% Example o r=9% o 1*(1.09n=2, n=8.04 o OR: n≈72/9≈8

Rule 3: Discounting -

To calculate the value of a future cash flow at in earlier point in time, we must discount it

Example – Formula Solution...