Valuing decisions Flashcards
analysis costs & benefits
need to evaluate benefits and costs in the same unit
ie value today or dollars
competitive market
a market in which goods can be bought and sold at the same price
interest rates and the time value of money
difference in value between money today and in the future is the time value of money
determined by the current interest rate
risk free interest rate (discount rate)
the interest rate at which money can be borrowed or lent without risk
interest rate factor
= 1 + rf
discount factor
= 1/(1+ rf)
value of investment today
105,000 in a year with a 7% risk free interest rate
= 105,000/1.07
= 98,130.84 today
the amount the bank would lend us if we promised to Pay 105,000 in a year
our decision is the same regardless if we look at the investment in dollars today or in a year
Net present value (NPV)
the difference between the present value of the investment and the present value of its costs
positive cash flow represents benefits
NPV and cash needs
should always maximise NPV regardless of preference of money today or future
Arbitrage
arbitrage is the practice of buying and selling equivalent goods in different markets to take advantage of price difference
an arbitrage opportunity occurs when its possible to make a profit without taking any risk or making an investment
normal market
a competitive market in which there are no arbitrage opportunities
the law of one price
if equivalent investment opportunities trade simultaneously in different competitive markets then they must trade for the same price in both
valuing a security with the law of one price
if security pays 1000 in a year with 5% risk free interest rate
bond price = 1000/1.05
if bond price is below, the difference is the net cash flow
firm considering a project of $10 mill investment today yielding $12mill in a year
considering raising additional funds by issuing a security that’ll pay investors $5.5 mill in a year.
rf = 10%
without new security NPV = 12/1.1 - 10 = $0.91 mill
with security:
price of security = 5.5/1.1 = $5 mill today
therefore firm only needs to raise 5 mill more to fund investment
firm will need to pay 5.5 mill in a year leaving them with $6.6 mill in a year
NPV = 6.5/1.1 - 5 = $0.91 mill
Valuing a portfolio
if C has same cash flows as A and B
the price of C should equal the price of A plus B
otherwise arbitrage opportunity
