Ch 3: Time Value of Money

$0.476 mil today or $ .5 mil in the future (10 mil / 1.05 = 9.524 - 10 = .476)

A major new customer has just pushed back the start of its contract with your company by a full year. The contract called for an upfront payment of $10 million at the start of the contract. If the interest rate is 5%, what is the cost to your company of the delay in receiving the upfront payment?

Save 71.43 (1500 one year from now / 1.05 = 1428.57 - 1500 = 71.43)

After saving $1,500 waiting tables, you are about to buy a TV. The store is offering a deal where you can take the TV home today and pay nothing until one year from now, when you will owe the store the $1500 purchase price. If your savings account earns 5% per year, what is the NPV to this offer?

1. r 2. PV 3. FV 4. C 5. n

Give notations for 1. interest rate 2. present value 3. future value 4. cash flow 5. number of periods

n = ln (fv/pv) / ln (1 +r) = ln (774/300) / ln (1.09) = 10.998 about 11 years

How many years will it take an initial investment of $300 to grow to $774 if it is invested at 9% compounded annually?

No, only the current prices in a competitive market matter

If we are transacting today, does it matter if you believe the value of a commodity will plummet over the next month?

106 (100 x 1.06)

If you put $100 in the bank at 6% interest, how much would you have in one year?

98.11 (104/1.06 -> make $1.89 extra)

If your friend offers to lend you $100 today in exchange for $104 in one year, how much would you need to deposit in the bank account today in order to have enough to pay hm back in one year? 6% interest

$2 bil - $1.481 bil = $0.519 billion; (1.6 bil/1.08 = $1.481 billion)

If your launch is delayed a year reducing your sales from $2 billion to $1.6 billion (8% interest rate), what is the cost of a delay of the first year's revenues in terms of dollars in 2005?

same, compounding, discounting

Three Rules: 1. It is only possible to compare/combine values at the s_____ point in time. 2. C___________: To calculate a cash flow's future value, you must compound it 3. D________________: to calculate the value of a future cash flow at an earlier point in time, we must discount it

positive, highest, cash

We accept a project if the NPV is _________________. When making an investment decision, take the alternative with the ______________ NPV, which is equivalent to receiving its NPV in ______ today.

385.54 (10000 / [1+.1]^10 ) (Rule of 72: 72/10% = 7.2 so value must at least double)

What is the PV of $1000 to be received 10 years from now discounted at an annually compounded rate of 10%?

FVn = C x (1+r)^n

What is the equation for a future value of a cash flow?

PV = C / (1 + r)^n

What is the equation for finding present value of a cash flow?

Today you can borrow 5660.38

You expect to have $6,000 in one year. A bank is offering loans at 6.0% interest per year. How much can you borrow today?

r = FV/PV ^ 1/n -1 = 1790.85 / 1000 ^ 1/10 - 1 = 6%

You have 1000. You want it to grow to $1790.85 in 10 years. What is the rate of interest compounded annually?

NPV = 754.71 (22,000 / 1.06), firm should do the 22,000 offer

Your firm has the opportunity to make a $20,000 investment that will return $22,000 for sure in one year. Alternatively, you could leave the money in the bank earning 6% interest. What is the NPV of the investment and what should you do?

Borrow the money at 4% and deposit it in the bank to get 5% interest (will make $9.52 for every 1000 deposited in one year)

Your two neighborhood banks are offering specials. One is offering a special rate on deposits (5%) and the other is offering a special rate on loans (4%). What does the NPV decision rule tell you to do?

competitive market

a market in which a good can be bought and sold at the same price (whenever this is the case, that price determines the VALUE of the good)

arbitrage opportunity

any situation in which it is possible to make a profit without taking any risk or making any investment

discount rate

appropriate rate to discount a cash flow to determine its value at an earlier time

compounding

computing the ROI over a long horizon by multiplying the return factors associated with each intervening period

discounting

finding the equivalent value today of a future cash flow by multiplying by a discount factor, or equivalently, dividing by 1 plus the discount rate

Law of One Price

in competitive markets, securities with the same cash flows must have the same price

interest rate factor

one plus the interest rate, it is the rate of exchange between dollars today and dollars in the future. It has units of "$ in the future/$ today"

arbitrage

practice of buying and selling equivalent goods to take advantage of a price difference

time value of money, more; interest rate

the difference in value between money received today and money received in the future; also, the observation that two cash flows at two different points in time have different values; "a dollar received today is worth _____ than a dollar received in one year"; In the case of money, what is the price?

compound interest

the effect of earning interest on interest

interest rate

the rate at which money can be borrowed or lent over a given period (Example: r = 10%, then we exchange $1 today for $1.10 (1 + .10 , interest rate factor) in one year; depends on supply and demand

Future value (FV)

the value of a cash flow that is moved forward in time

Valuation Principle, market, exceeds

the value of a commodity or an asset to the firm or its investors is determined by its competitive market price. The benefits and costs of a decision should be evaluated using those m__________ prices. When the value of the benefit e_____________ the value of the costs, the decision will increase the market value of the firm.

present value (PV)

the value of a cost or benefit computed in terms of cash today

discount factor; 1/(1+r)

value today of a dollar received in the future (money in the future is worth less today, so its price reflects a discount); What's the one year discount equation?

Rule of 72; 72/9 = 8 years

years to double your money is usually around 72 / (interest rate in percent); Example: if interest rate is 9%, how long should the doubling time be?