Module 1: Financial Decision Making, Arbitrage and the Time Value of Money Flashcards
What is 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 costs 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.
What is Present value?
The value today (opposite: Future value)
What is the Net present value (NPV)?
NPV = PV (Benefits) - PV (Costs) = PV (All project cash flows)
The NPV decision rule?
When making an investment decision, take the alternative with the highest
NPV (or at least as long as the NPV is positive). Choosing this alternative is
equivalent to receiving its NPV in cash today (regardless of your current cash
needs).
f NPV < 0, reject the project (potential losses)
if NPV = 0, no gain or loss
if NPV > 0, accept the project (potential gains)
What are the “Three Rules of Timeline”?
1) Comparing and combining values
- a dollar today and a dollar in one year are not equivalent
- to compare or combine cash flows that occur at different points iin time, you need to convert it into the same units or move them to the same point in time
2) Moving cash flows forward in time
- $1000 today equals $1100 in one year (rf=10%)
3) Moving cash flows back in time
- $1000 in one year is $909.09 today (rf=10%)
How to calculate more than one payment for the Present value of a cash flow stream?
Example: You want to buy a house in three years and for this purpose
you will be able to save € 20,000 p.a. in the next two years. You
expect a promotion after two years and can save € 40,000 p.a. in
the following year
PV= 20000/1+0.1 + 20000/(1+0.1)² + 40000/(1+0.1)³
= 64763.3358377
How to calculate more than one payment for the Future value of cash flow stream with a present value of PV?
Example: You want to buy a house in three years and for this purpose
you will be able to save € 20,000 p.a. in the next two years. You
expect a promotion after two years and can save € 40,000 p.a. in
the following year
FV = 64763.3358377 * (1+0.1)³ = 86200
What is “perpetuity”?
A perpetuity is a stream of equal cash flows that occur at regular intervals and last forever.
How to calculate a perpetuity?
You want to endow an annual MBA graduation party at your alma mater. You want the event to
be a memorable one, so you budget $30,000 per year forever for the party. If the university earns
8% per year on its investments, and if the first party is in one year’s time, how much will you
need to donate to endow the party?
PV = 30000/0.08 = 375.000 today
If you donate $375,000 today, and if the university invests it at 8% per year forever, then the
MBAs will have $30,000 every year for their graduation party.
What is “annuity”?
An annuity is a stram of N equal cash flows paid at regular intervals
How to calculate an annuity?
PV(annuity of C for N periods with interest rate r) =
C * 1/r *(1-(1/1+r)^N)
Example: You are the lucky winner of the $30 million state lottery. You can take your prize money either
as (a) 30 payments of $1 million per year (starting today), or (b) $15 million paid today. If the
interest rate is 8%, which option should you take?
PV= 1m * 1/0.8 * (1-(1/1.08)^29) = 11.16m today
What are growing Cash flows?
A cash flow which grows at a constant rate in each period
How to calculate Growing cash flows?
PV of a Growing Perpetuity = C / r-g
r= interest rate g= Grow rate
PV of a Growing Annuity = C * 1/r-g *(1-(1+g/1+r)^N)
What is the Internal Rate of Return (IRR)?
The rate of return, if the NPV of the cash flows is equal to zero, is
called the internal rate of return (IRR).
What is the Law of One Price?
f equivalent investment opportunities trade simultaneously in different
competitive markets, then they must trade for the same price in all markets
