Transcript Risk, Return, and the Time Value of Money

Risk, Return, and the Time Value of Money
Chapter 14
Relationship Between Risk and Return
• Risk
– Uncertainty about the actual rate of return
over the holding period
• Required rate of return
• Risk-free rate
Types of Risk
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Business risk (Changing Economy)
Financial risk (Loan Default)
Purchasing power risk (Inflation)
Liquidity risk (Converting to Cash)
The Time Value of Money
• Money received today is worth more than money to be
received in the future
• Interest Rates
– Nominal Rates = Real Rates + Inflation
• Interest Rates are the rental cost of borrowing or the
rental price charged for lending money
• Simple Interest – Interest on the initial value only (Not
commonly used except for some construction loans)
• Compound Interest – Interest charged on Interest
(Typical in Lending and Savings)
The Time Value of Money
• Present Value (PV) - a lump sum amount of
money today
• Future Value (FV) - a lump sum amount of
money in the future
• Payment (PMT) or Annuity - multiple sums of
money paid/received on a regularly scheduled
basis
The Six Financial Functions
• Future value of a lump sum invested today
• Compound Growth
• FV = PV(1+i)n
• PV=value today, i= interest rate, & n= time
periods
• Example: where PV= $1, n=3, & i=10%
– FV = $1 x (1+.10) x (1+.10) x (1+.10)
– FV = $1 x 1.331
– FV = $1.331
The Six Financial Functions
• Present Value of a Lump Sum
• Discounting
– Process of finding present values from a
future lump sum
• PV = FV [1/(1+i)n ]
• Example: where FV= $1, n=3, & i=10%
– PV = $1 x [1/(1+.10) x (1+.10) x (1+.10)]
– PV = $1 x [1/1.331]
– PV = $1 x 0.7513
– PV = $0.7513
The Six Financial Functions
• Future Value of an Annuity
– FVA = PMT[((1+i)n -1))/ i]
– The future value of a stream of payments
The Six Financial Functions
• Present Value of an Annuity
– PVA = PMT[(1-(1/(1+i)n ))/ i]
– The present worth of a stream of payments
The Six Financial Functions
• Sinking Fund
– SF PMT = FVA [ i / ((1+i)n -1))]
– The payment necessary to accumulate a
specific future value
The Six Financial Functions
• Mortgage Payments (Mortgage Constant)
– MTG PMT = PVA [ i / ((1 - (1/(1+i)n )))]
– The payment necessary to amortize (retire) a
specific present value
Effect of Changing the Compounding Frequency
– Interest Rates are quoted on an annual basis
– Increasing the frequency of compounding increases
the amount of interest earned
– Increasing the frequency of payments for an
amortizing loan decreases the amount of interest
paid
Examples
• A Future Value Example:
– You have just purchased a piece of residential land
for $10,000. Based upon current and projected
market conditions similar lots appreciate at 10%
per year (annually). How much will your investment
be worth in 10 years? How about 20 years. Is the
effect of compounding 2 times greater?
Examples
• A Present Value Example:
– You have been offered the option of purchasing a
condo which will be sold for $150,000 at the end of
15 years. You need to make a reasonable offer for
the investment so that you can purchase it today.
You expect that similar investments would provide
an 8% return per year (annually). How much
should you be willing to pay (in one lump sum)
today for this investment?
Examples
• Future Value of an Annuity Example:
– You wish to save $2,000 per year over the 10 years
you operate an apartment property. You can invest
your savings at 8% per year (annually). How much
money will you have in the account when you sell
the investment?
Examples
• Present Value of an Annuity Example :
– You will receive $5,000 per year over the next 30
years as equity income from a ground lease you wish
to purchase. Investors require an 8% return for
similar investments If you wish to buy this property,
how much should you offer (in one lump sum) for
the investment today?
Examples
• Sinking Fund Payment Example:
– You wish to buy a house in 5 years. The down
payment on a house, like you hope to purchase, will
be $7,500. How much must you save every year to
afford this down payment, given that you can invest
the savings with the bank at 8%?
Examples
• Mortgage Payment Example:
– You have negotiated the purchase of a condominium
for $70,000. You will need a loan of $60,000, which
the local bank has offered based on a 30 year term
at 6% interest (annually). How much will your
annual payment be for the condo?
– Since nearly all mortgages are calculated on a
monthly basis what is the monthly payment for the
loan?
Net Present Value (NPV)
• Difference between how much an investment
costs and how much it is worth to an investor
• NPV Decision Rule
– If the NPV is equal to or greater than zero,
we choose to invest
Net Present Value (NPV)
• PV inflows – PV outflows
– NPV Formula:
FV
 (1  i)n  CF0
Internal Rate of Return (IRR)
• The discount rate that makes the NPV equal
to zero - the rate of return on the investment
• IRR Decision Rule
– If the IRR is greater than or equal to our
required rate of return, we choose to invest
Calculating Uneven Cash Flows
• Initial Cash Flow is the Cost of the
Investment
– Initial Cash Flow is Zero (0) if solving for PV
• Use the Nj Key for Repeating Sequential Cash
Flows