Chapter 5

Question 1

how can we compute an equivalent effective interest rate for a longer time period

Answer 1

by raising the interest rate factor (1+r) to the appropriate power

Question 2

what’s the formula to finding the equivalent n-period effective rate

Answer 2

[(1+r)^n] -1 for effective rate over more than 1 period

or (1+r)^n for EAR over a fraction of a period

Question 3

what’s APR

Answer 3

amount of simple interest earned in 1 year - amount of interest earned without the effect of compounding even though compounding may occur

must convert APR to EAR for a lot of calculations

because the APR does not reflect the true amount you will earn over one year, the APR itself cannot be used as a discount rate and it is not an effective annual rate. Instead, the APR with compounding periods is a way of indirectly quoting the effective interest rate, r, earned each compounding period.

Question 4

what’s an implied effective rate

Answer 4

shows the actual interest earned over the compounding period

Question 5

how to convert APR to its implied effective interest rate

Answer 5

1. rate = APR/k compounding periods per year
2. then 1 + EAR = (1+r)^k

or 1 + EAR = (1 + [APR/k])^k

Question 6

why does EAR increase with the frequency of compounding

Answer 6

bc of ability to earn interest on interest sooner

Question 7

define continuous compounding

Answer 7

compounding of interest every instant - an infinite times in a year

Question 8

does compounding more frequently have a large impact

Answer 8

no it has a negligible impact on EAR and is rarely observed

Question 9

whats The three-step method just shown can be applied to any interest rate quote

Answer 9

Step 1: Divide by the compounding frequency to get the implied effective rate per compounding period.

Step 2: Convert the effective six-month rate into a rate per month as the final rate quote has monthly compounding.

Convert the effective monthly rate into a rate quoted per six months compounded monthly by multiplying by 6.

Question 10

define amortizing loans

Answer 10

a loan where the borrower makes monthly payments that include interest on loan plus some part of the loan balance

Question 11

how to calculate a loan payment

Answer 11

we first compute the discount rate from the quoted interest rate of the loan, and then equate the outstanding loan balance with the present value of the loan payments and solve for the loan payment.

Question 12

what’s the outstanding loan balance and how to calculate it

Answer 12

outstanding balance on a loan, also called the outstanding principal, is equal to the present value of the remaining future loan payments, again evaluated using the loan interest rate. We calculate the outstanding loan balance by determining the present value of the remaining loan payments using the loan rate as the discount rate.

Question 13

define nominal interest rate

Answer 13

interest rate quoted by banks and other financial institutions that indicate the rate at which money will grow if invested for certain period of time

Question 14

define real interest rate

Answer 14

the rate of growth of purchasing power after adjusting for inflation

Question 15

what’s the growth of purchasing power formula

Answer 15

growth of money/growth of prices = (1+r)/(1+i)

Question 16

what’s the formula for the real interest raet

Answer 16

(r-i)/(1+i) = r-i approx

Question 17

how does interest rate affect individual and firms

Answer 17

Interest rates affect not only individuals’ propensity to save but also firms’ incentive to raise capital and invest.

increases cost of borrowing

an increase in interest rate will decrease the investment’s NPV

Question 18

define term structure

Answer 18

the relationship between the investment term and the interest rate

Question 19

define yield curve

Answer 19

a plot of bond yields as a function of the bonds’ maturity date

Question 20

when was the long term and short term interest rates difference especially pronounced

Answer 20

in 2010

Question 21

what happened to interest rates in 2016

Answer 21

were low across the entire term structure

Question 22

define the spot rate of interest

Answer 22

current interest rates for different terms to maturity determined from default-free zero coupon bond yields

Question 23

how to find the single interest rate to value an annuity when there’s multiple discount rates

Answer 23

first compute the present value of the annuity and then solve for its IRR - the IRR of the annuity is always between the highest and lowest discount rates

Question 24

define the overnight rate

Answer 24

the overnight loan rate charged by banks with excess reserves at the bank of canada to banks that need additional funds to meet reserve requirements.

the federal funds rate is influenced by bank of canada’s monetary policy and itself influences other interest rates in the market

Question 25

what happen if interest rates are expected to rise/

Answer 25

long term spot rates will tend to be higher than short term spot rates so as to attract investors as investors usually don’t want to make long term investments as they invest on a short term basis and then reinvest it

Question 26

what happens if interest rates are expected to fall

Answer 26

long-term spot rates will tend to be lower than short-term spot rates so as to attract borrowers.

this is bc borrowers would not wish to borrow at long-term rates that are equal to short-term rates. They would do better by borrowing on a short-term basis, and then taking out a new loan after rates fall.

Question 27

is the shape of the yield curve influenced by interest rate expectations

Answer 27

yes it’s strongly influenced by interest rate expectations + risk

Question 28

what does a sharply increasing yield curve vs decreasing yield curve indicate

Answer 28

A sharply increasing (steep) yield curve, with long-term rates much higher than short-term rates, generally indicates that interest rates are expected to rise in the future. A decreasing (inverted) yield curve, with long-term rates lower than short-term rates, generally signals an expected decline in future interest rates.

Question 29

steeping vs declining yield curve in economy

Answer 29

Because interest rates tend to drop in response to a slowdown in the economy, an inverted yield curve is often interpreted as a negative forecast for economic growth. Conversely, the yield curve tends to be steep as the economy comes out of a recession and interest rates are expected to rise.

Question 30

what did central banks do following the 2008 financial crisis

Answer 30

central banks not only used their power to set short-term rates but also exerted significant influence on long-term rates by purchasing longer-term bonds so as to bid up their price and consequently reduce the long-term interest rates. Under such unusual influence by central banks, the information conveyed by the term structure may be less meaningful in terms of expectations for future interest rates.

Question 31

why do interest rates vary so widely

Answer 31

due to risk

Question 32

why is the interest rate paid on government of cand bonds the lowest

Answer 32

These bonds are widely regarded to be risk free because there is virtually no chance the government will fail to pay the interest and default on these bonds. Thus, when we refer to the “risk-free interest rate,” we mean the rate on Government of Canada bonds (for shorter terms, we also look at Government of Canada treasury bills).

Question 33

why is there a higher interest rate on securities other than the Gov’t bonds

Answer 33

All other borrowers have some risk of default. For these loans, the stated interest rate is the maximum amount that investors will receive. Investors may receive less if the company has financial difficulties and is unable to fully repay the loan. 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. The difference between the interest rate of the loan and the Government of Canada bond rate will depend on investors’ assessment of the likelihood that the firm will default.

Question 34

what’s should we make note of when discounting future cash flows

Answer 34

it is important to use a discount rate that matches both the horizon and the risk of the cash flows. Specifically, the right discount rate for a cash flow is the rate of return available in the market on other investments of comparable risk and term.

Question 35

define the after tax interest rate and what’s the formula

Answer 35

reflects the amount of interest an investor can keep after taxes have been deducted

interest rate * (1-tax rate) = interest rate - (tax rate * interest rate)

Question 36

what does the ability to deduct interest expense due on the effective after tax interest rate

Answer 36

the ability to deduct the interest expense lowers the effective after-tax interest rate paid on the loan; this is an important consideration when we compare various forms of investing and financing rates

Question 37

what is the cost of paying interest on a loan offset by?

Answer 37

by the benefit of the tax deduction.

Question 38

define the opportunity cost of capital

Answer 38

the best available expected return offered in the market on an investment of comparable risk and term to the cash flow being discounted.

Question 39

define cost of capital

Answer 39

the expected return available on securities with equivalent risk and term to a particular investment