Chapter 5 Flashcards
How do we determine the appropriate discount rate from an interest rate
We need to understand the ways interest rates are quotes:
Interest rates can be quoted for different time intervals:
- Monthly , semi annually,etc
(To see which is the best interest rate we have to adjust the interest rate to a time period that matches that of our cash flows
How are interest rates often stated as
The effective annual rate
What is the effective annual rate (EAR)?
It indicates the ‘total’ amount of interest that will be earned at the end of ‘1’ year.
This is method so far in the text book we have learnt.
Example: For example, with an EAR of 5%, a $100,000 investment grows to the following:
100,000*(1+5%) = 105k
What do we have to do to the rate factor first?
We have to adjust the rate factor depending on the length of the period.
Essentially were trying to find the equivalent effective interest rate for different periods
How can we find an equivalent interest rate to an EAR in a different period
(1+R) ^ n -1
Example:
Suppose your bank account pays interest monthly with an EAR of 6%. What amount of interest will you earn each month? If you have no money in the bank today, how much will you need to save at the end of each month to accumulate $100,000 in 10 year
See 5.1
How does banks usually quote their intrest rates?
Annual Percentage Rate (APR)
What is the annual percentage rate?
Its the amount of simple interest earned in one year without the effect of compounding even though compounding may occur.
How do we compute the actual amount of interest we earn in one year using the APR?
The APR must be converted EAR
How to convert APR to EAR
r = APR/k
How do we convert the APR to the implied effective rate and then to EAR
(APR/Compounding periods)
(1+r) ^ k - 1
How can we find the APR if we want to find it?
APR = r*K
Rate = Implied or effective rate were looking for originally
For example, a quoted rate of 100% per decade compounded semiannually can be converted into a rate quoted as a rate per six months compounded monthly as follows.
In text :
100%/(2*1) = 5%
(1+5%) ^2/12 *6
For instance, a Canadian mortgage quote will give an APR with semiannual compounding; in order to work with the monthly annuity payments of a mortgage, we must use the effective monthly rate. Eq. 5.3 is not useful in this case; however, we could still use the two steps shown above but with a modification to step 2. Consider a Canadian mortgage quote of 8% APR with semiannual compounding.
Look in the textbook
Example:You want to save for a special vacation that you will take in six years. Given a rate of 6% per year with monthly compounding for your savings account at Scotiabank, you wish to know what will be the future value of an annuity of deposits you will make to your account. This information will help you decide the best way to save. You are considering the following annuities over a six-year time frame:
Equal monthly deposits of $100 each
Equal semiannual deposits of $600 each
Equal annual deposits of $1200 each
Equal biannual deposits (every two years) of $2400 each
End of 5.1
How do we calculate a loan payment?
1st : Compute the discount rate from the quoted intrest rate from the loan
2nd: We match the outstanding loan balance with the present value of the loan payments
Loan balance = Pv of loan payments
What are amortizing loans?
These are loan where each month we pay interest on the loan + some portion of the loan balance
Are monthly payments equal every month?
Yes
How to find the cash payment for an annuity formula.
Use the regular PV (annuity) formula and isolate C
What do we call this thing, where we borrow money in order to buy a house?
A mortgage
What is a mortgage?
A mortgage is a loan where the borrow borrows money to buy a house and the property is the collateral to the lender.
Who usually gives out mortgages
Banks
with APR compounding
What is the oustanding balance on a loan
Its the outstanding principal left to pay which is equal to the PV of the remaining future loan payments.
How can we calculate the outstanding loan balance?
The PV of the remaining loan payments using the loan rate as the discount rate
How are interest rates determined?
They are determined in the market and its based on the individuals willingness to borrow and lend
Who creates nominal interest rates?
these are interest rates that are quoted by banks and other financial institutions.
We have used these for discounting cash flows
What are nominal interest rates?
This the rate at which your money will grow if invested for a certain period but it doesnt take into consideration of inflation
What is inflation
Its when prices of things go up over time
How do we adjust out nominal interest rate to include inflation
Use the real interest rate
What is the real interest rate?
it shows how much your money will grow if you invest it after adjusting for inflation
How to calculate the real interest rate?
Rr = Rate minus inflation / 1+ inflation
What does interest rates affect?
It affects individuals ability to save money but also how much businesses want to borrow money or invest.
What happens if the interest rate rises?
The NPV (benefit) received from an investment falls making it less profitable.
Higher interest rate = Profit is less and vise versa
What does businesses do when interest rates are higher?
They are less likely to invest because future return is smaller and vise versa
What does the interest rates the bank offer are dependent on what factors?
- Horizon
- Term of the invetsment or loan
What is a term structure?
This is the relationship between the investment term and the interest rate
What is a yield curve
Its when we plot the relationship of investment term and the interest rate (in this case)
How can we compute the risk-free cash flows over different horizons ?
Present value or future value
What is the spot rate of interest?
The spot rate is just the specific interest rate for a given time period. For example, the one-year spot rate is the interest rate for one year, and the 18-year spot rate is for 18 years.
When there are multiple risk-free cash flows that have different horizons do we calculate the PV of it the same
YES
Whats a common mistake when computing the annuity (PV) when the interest rates vary?
Trying to compute it when there are multiple interest rates
What a person should do is find the PV of the annuity and after that find the rate, by isolating for the R, however we cannot do that by hand so have to use the RATE in excel
How does the bank of canada determine the very short term interest rates
Through its inlfuence on overnight rates
What are overnight rates?
Overnight rates is the rate at which banks can borrow cash reserves on an overnight basis
What does the yield curve show?
Relatuonship between short and long term interest rates
What happens if the yield curve is steep or inverted?
The yield curve shows the relationship between short-term and long-term interest rates.
If the yield curve is steep (long-term rates are much higher than short-term rates), it usually means people expect interest rates to rise in the future.
If the yield curve is inverted (long-term rates are lower than short-term rates), it suggests people expect interest rates to fall, which often signals a slowing economy or even a recession
What are two other factors we have to look at when evalauting interest rates?
Risk
Taxes
How does interest rates vary?
With investment horizons but also the identity of the borrower
What is the lowest interest rate paid on what?
Bonds
- As there is no risk that the government will fail to pay the interest on these bonds so their considered risk-free interest rates.
When looking at investments other than government investments what added factor do they all have?
Some risk of default
- The stated interest rate is the max amount the receivers will recieve
- Investors may receive less if the borrower has financial difficulties and is unable to fully repay the loan.
What do investors ask for to compensate for the risk?
To compensate for the risk that they will receive less if the firm defaults, investors demand a higher interest rate than the rate on Government of Canada bonds.
What does the after tax interest rate mean?
Tax effectively reduced cash flow, so the after tax interest rate is the amount after tax is reduced from the interest investors would keep
How to calculate the after-tax interest rate
R = r*(1-t)
What is the opportunity cost of capital
Its the return the investor forgoes when the investor takes on a new project.
For example, if a business wants to start a new project and needs to borrow money, it has to offer a return that’s as good as what investors could earn from other options with the same risk and time frame.
What does the opportunity cost of capital act as what?
The opportunity cost of capital acts as a benchmark. If a business wants to invest in a new project, it should only do so if the project’s return is better than what investors could get elsewhere.
