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AcF100 > Week 14 - Loan and Interest Rates, Bond Valuation > Flashcards

Week 14 - Loan and Interest Rates, Bond Valuation Flashcards

1
Q

What is the result of quotation of interest rates?

A

tradition, legislation, or unfortunately quoted in deliberately deceptive ways to mislead borrowers and investors

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2
Q

What is interest rate per period

A

most straightforward but NOT on an annual basis

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3
Q

What is a stated annual interest rate/ quoted rate?

A

most available rate with periodic compounding

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4
Q

What is effective interest rate?

A

most informative rate

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5
Q

What is the stated annual interest rate known as in the US?

A

annual percentage rate (APR)

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6
Q

What is APR

A

annual percentage rate/ stated annual rate

the interest charged per period x the number of periods per year

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7
Q

How is the APR normally quoted?

A

In many countries, legal rules require APRs to be quoted

In the US and UK, certain laws require the lender to disclose the APR on all consumer loans

Normally, the APR is the quoted interest rate in financial news or newspapers

However, the APR’s calculations vary internationally

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8
Q

What is the APR if the monthly rate is 0.5%?

A

0.5 x 12 = 6%

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8
Q

What is the APR if the semi-annual rate is 0.5%?

A

0.5 x 2 = 1%

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9
Q

What is the monthly rate of the APR is 12% with monthly compounding?

A

12%/12 = 1%

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10
Q

What is the frequency of compounding?

A

some investments pay interest more than once a year (eg semi-annual interest rate that compounds twice a year)

Normally financial institutions will use the quoted annual interest rate (r_s) to standardise the comparison between different products

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11
Q

How can the same quoted APR correspond to many different compounding frequencies per year?

A

10% compounded semi-annually 10%/2 = 5% every 6 months

10% compounded quarterly 10%/4 = 2.5% every 3 months

10% compounded monthly 10%/12 = 0.83% every month

10% compounded daily 10%/365 = 0.02739% every day

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12
Q

How can the future value formula be expressed to do with the frequency of compouding?

A

FV = PV (1 + r_s/m)^mN

PV_A = C_m/ r_s/m (1 - 1/(1+r_s/m)^mN)

FV_A = C_m [(1+r_s/m)^mN - 1]/ r_s/m

r_s is the quoted annual interest rate

m is the number of compounding periods

N is the number of years

the periodic rate r_s/m, and the number of compounding periods, mN, must be compatible

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13
Q

For a £1 investment with 10% quoted rate

A

annually: £1×(1+0.10) = £1.10

semi-annually (𝑟_𝑠∕𝑚 = 0.10∕2 =0.05) £1×(1+0.05)^2=£1.1025

quarterly (𝑟_𝑠∕𝑚 = 0.10∕4 = 0.025) £1×(1+0.025)^4=£1.1038

monthly (𝑟_𝑠∕𝑚 = 0.10∕12 = 0.0083)£1×(1+0.0083)^12=£1.1042

daily (𝑟_𝑠∕𝑚= 0.10∕365 = 0.0002739)£1×(1+0.0002739)^365=£1.1051

continuous compounding: £1×𝑒^(0.10×1) = £1.105171
continuous compounding: 𝐹𝑉_𝑁=𝑃𝑉×𝑒^(𝑟_𝑠 𝑁)

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14
Q

What is the effective annual rate (EAR)

A

the actual rate paid (or received) after accounting for compounding that occurs during the year

the interest rate expressed as if it were compounded once per year

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15
Q

What is the EAR of a 10% quoted rate?

A

given the same APR, is the compounding periods per year increase, then the EAR will increase too

used to compare two alternative investments with different compounding periods

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16
Q

What is the EAR formula?

A

EAR = (1+ quoted rate/m)^m - 1
m is the number of times interest is compounded for year

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17
Q

What is the effective annual rate of 14.9% compounded monthly?

A

m = 12
EAR = 1+ 0.149/12)^12 - 1
EAR = 0.1596 or 15.96%

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18
Q

A bank is offering 12% compounded quarterly. You put £100 in an account, what is the EAR?

And how much will you have at the end of 2 years?

A

EAR = (1+ 0.12/4)^4 - 1 = 0.1255

Pt2 Method 1
£100 x (1 + 0.12/4)^8 = 126.68
Method 2
£100 x (1 + 0.1255)^2 = 126.68

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19
Q

If you have an effective rate, how can you compute the APR?

A

Rearrange the EAR equation

APR = m x [(1+EAR)^1/m -1]

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20
Q

What do you always need to make sure matches?

A

interest rate and the time period match

monthly cash flow periods -> monthly rate

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21
Q

What do you do if you have an APR based on monthly compounding and there is a mismatch with the frequency of cash flows (say, these are annual)?

A

you have to adjust the interest rate accordingly

annual cash flow periods -> effective annual rate rather than APR

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22
Q

Suppose you want to buy a new computer. The store is willing to allow you to make monthly payments. The entire computer system costs £3,500. The loan period is for 2 years. The interest rate is 16.9% with monthly compounding.

What is your monthly payment?

A

Monthly rate = 0.169/12 = 0.0141

Number of months = 2 x 12 = 24

3500 = C/0.0141 x [ 1 - 1/(1+ 0.0141)^24]

C = 172.88

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23
Q

What are the 3 basic types of loans?

A
  1. Pure discount loans
  2. Interest-only loans/ bullet bonds
  3. Amortised loans (fully or partially)
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24
Q

What is a pure discount loan?

A

the borrower receives money today and repays a single lump sum at the end of the loan (without any (other) interest payments)

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25
Q

What are 2 examples of pure discount loans?

A
  1. US government treasury bills
  2. Zero-coupon bonds

the principal amount is repaid at some future date without any periodic interest payments

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26
Q

Suppose your firm borrows £6,805,832 today from a bank and will pay back £10,000,000 in 5 years. What is the interest (rate) cost of the loan?

A

PV = £6,805,832
FV = £10,000,000

10,000,000 = 6,805,832 x (1+r)^5

r = 8%

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27
Q

What are interest only loans

A

they require payment of interest each period and the repayment of the principal at a later date

the principal is repaid all at once

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28
Q

What are two types of amortised loans?

A
  1. Fixed principal
  2. Fixed payments (more common)
29
Q

What are amortised loans?

A

the principal is repaid over time
- the amount of the principal is decreasing overtime
ie the principal will be progressively reduced to zero
- as part of the principal get repaid, interest is calculated only on the remainder of the principal

Periodic payments = interest + repayment of a portion of the principal
Eg housing loans (mortgages, car loans etc)

30
Q

What is amortisation schedule?

A

a table that describes the periodic payments as well as the interest and principal balance after each payment

31
Q

Amortisation schedule example: A company borrows £4,000 using a 4 year loan at 8% interest from the bank. What is the amortisation schedule for?

A

Fixed principal: principal reduction is constant each year
periodic payment = £1000 + interest

Fixed payment: periodic payment is constant each year
annuity
given PV, r and t, what is C (periodic payment)?
answer £1,207.68

32
Q

Fixed principal looks like (table)

A

Columns:
Year, Beginning Balance, Periodic Payment, Interest Paid, Principal Paid, Ending Balance

33
Q

How is the principal balance reduced?

A

By the same (fixed) amount each period
At the end of the last period, the principal is reduced to zero

The periodic payment is different each year
The periodic payment is reduced each year
Interest paid is decreasing over time

34
Q

What is the periodic payment C is in the form of?

A

an ordinary annuity

35
Q

How do corporations raise capital to use for long term investments?

A

3 sources:
1. Cheapest is through using retained earning
2. Borrow money
3. Issue equity (last resort)

36
Q

What are bonds?

A

a debt instrument that requires the issuer to repay to the investors the amount borrowed plus interest over a specified period of time

37
Q

What parties are involved in bonds?

A
  1. Issuers
  2. Investors
  3. Other parties
38
Q

What do issuers do in terms of bonds?

A

the parties (government or corporations) that borrow money and issue debt securities

such as debtors and borrowers

39
Q

What do investors do in terms of bonds?

A

the parties (persons, government or corporations that borrow money and issue debt securities)

such as creditors, lenders, bondholders

40
Q

What do other parties do in terms of bonds?

A

underwriters: investment banking firms that act as agents to distribute bonds to investors. They will charge a fee for the service.

41
Q

What is the face value F (par value) of the bond?

A

the amount the issuer agrees to repay the bondholder at maturity (end of the loan)

most the time it isnt equal to the bond price

42
Q

How does the borrower usually pay back a loan?

A

a bond is normally an interest only loan
the borrower will pay the interest every period, but none of the principal will be paid until the end of the loan

43
Q

What are coupons C?

A

the periodic payments that issuers promise to make

44
Q

How are coupons C usually expressed?

A

as a percentage of the par value, it is usually constant and determined upon issue

45
Q

What is the coupon payment calculation?

A

Coupon payment = Coupon rate (c) x Par value (F) / Number of coupon payments per year

coupon rate isnt the discount rate for discounting

46
Q

What is maturity?

A

the number of years until the face value is paid

46
Q

What is the current yield or CY formula?

A

CY = Annual coupon payment/ market price

47
Q

What does the maturity date of a bond refer to?

A

refers to the date when the debt will cease to exist

48
Q

Can there be more than one coupon payment in a calendar year?

A

yes there may be more than one coupon payment and can correspond to many compounding periods

49
Q

What count as short term bonds?

A

1-5 years

50
Q

What count as intermediate bonds?

A

5-12 years

51
Q

What counts as a long term bond?

A

12+ years

52
Q

What is the yield to maturity?

A

the interest rate investors want to ear on a bond

53
Q

What is the yield to maturity also called?

A

the market interest rate

54
Q

How is yield to maturity reflected on the bond?

A

it is the implicit rate of interest or the time value of money that is reflected in the bond price and that bondholders receive

this is the appropriate discount rate for bond valuation

55
Q

What does the yield depend on to change over time?

A

depending on the investors’ risk attitudes and investment opportunities

56
Q

The yield to maturity is the rate of return on the bond to an investor given 3 critical assumptions. What are they?

A
  1. The investor holds the bond to maturity
  2. The issuer makes all of the coupon and principal payments in full on the scheduled dates (the issuer doesnt default on any of the payments)
  3. The investor is able to reinvest coupon payments at the same yield
57
Q

How to calculate bond price as the present value of cash flows?

A

Bond price = TΣt=1 C/(1+r)^t + F/(1+r)^T =
PV(Coupons) + PV(Face value) = C x [1- 1/(1+r)^t] /r + F x 1/(1+r)^T

where C = c x F
(c stands for coupon rate)

58
Q

What is the implicit rate of interest investors earn? formula

A

(c x F)/r x [1- 1/(1+r)^t] + F x 1/(1+r)^T

59
Q

What is the relationship between price and yield to maturity?

A

x axis yield to maturity %
y axis Price

downward sloping, inverse relationship

60
Q

What is the relationship between par value and bond price if the yield-to-maturity = coupon rate?

A

if YTM = coupon rate
then par value = bond price

61
Q

What is the relationship between par value and bond price if the yield-to-maturity > coupon rate?

A

if YTM > coupon rate
then par value > bond price

selling at a discount, called a discount bond

62
Q

What is the relationship between par value and bond price if the yield-to-maturity < coupon rate?

A

if YTM < coupon rate
then par value < bond price

selling at a premium, called a premium bond

63
Q

What is a consol bond?

A

a fixed-income security with no maturity date

64
Q

What are 2 causes of bond price movements?

A
  1. the passage of time
  2. changes in interest rates (YTM)
65
Q

How does the passage of time cause bond price movements?

A

the price of a bond changes as the bond approaches its maturity date

66
Q

How does the change in interest rates (YTM) cause bond price movements?

A

for a standard, option free bond, the cash flows will not change during the bond’s life

as a result, any changes in market interest rates will be reflected in the bond’s price

67
Q

Who will care about the price change of the bond?

A

investors and issuers

68
Q

A bonds value can differ substantially from its par value prior to maturity. Where will the price converge towards?

A

Regardless of its required yield, the price will converge toward par value as maturity approaches

AcF100 (13 decks)

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