Week 14 - Loan and Interest Rates, Bond Valuation Flashcards

Question

What is the effective annual rate (EAR)

Answer 1

the true annual interest rate, the actual return (for investments) or cost (for loans), considering the effects of compounding that occurs during the year the interest rate expressed as if it were compounded once per year

Answer 2

If the APR (quoted annual rate) remains the same, increasing the number of compounding periods per year (m) will always increase the Effective Annual Rate (EAR). This happens because interest is applied more frequently, leading to more growth over time Since different investments may have different compounding periods, we use EAR to make a fair comparison. The investment with the higher EAR is the better choice (assuming everything else is equal)

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

Rearrange the EAR equation APR = m x [(1+EAR)^1/m -1] APR = Quoted Annual Interest Rate EAR = Effective Annual Rate m = Number of compounding periods per year

Answer 7

Ensuring that the interest rate and the time period match If there is a mismatch between the compounding frequency and the frequency of cash flows, adjustments are necessary to ensure consistency in calculations

Answer 8

Monthly Cash Flows → Monthly Rate If you're working with monthly cash flows, you must use a monthly rate, not the annual rate. If you have an APR based on monthly compounding, you can convert it to the monthly rate by dividing the APR by 12 (for monthly compounding)

Answer 9

Annual Cash Flows → Effective Annual Rate (EAR) If the cash flows are annual (meaning one payment per year), you should use the Effective Annual Rate (EAR), not the APR. The APR is typically for periods shorter than one year (monthly, quarterly, etc.), but the EAR takes into account all the effects of compounding over a year

Answer 10

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

Answer 11

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

Answer 12

the borrower receives money today (the principal amount) and repays a single lump sum at the end of the loan (maturity date) instead of paying interest over the life of the loan, the borrower repays the full principal at the end, along with the interest built into the principal amount. The interest is implicitly included in the loan's face value, and it is not paid periodically

Answer 13

Loan Amount: £10,000 Maturity Period: 5 years The loan will mature to £15,000 (representing the interest and principal). Borrower receives £10,000 now, but must repay £15,000 at the end of 5 years.

Answer 14

1. US government treasury bills 2. Zero-coupon bonds the principal amount is repaid at some future date without any periodic interest payments

Answer 15

PV = £6,805,832 FV = £10,000,000 10,000,000 = 6,805,832 x (1+r)^5 r = 8%

Answer 16

they require payment of interest each period and the repayment of the principal at the end of the loan term

Answer 17

Suppose you take out an interest-only mortgage with the following terms: Loan Amount: £100,000 Interest Rate: 5% per year Loan Term: 10 years Interest-Only Period: 5 years Principal Repayment: At the end of 10 years Monthly payments are based only on the interest: Monthly Interest Payment = (5% x 100000)/12 =£416.67 The borrower only makes these monthly payments during the first 5 years, without reducing the principal. After the Interest-Only Period (Years 6-10): Once the interest-only period ends, the borrower starts repaying the principal, either as a lump sum or with new monthly payments that include both interest and principal. For example, if the remaining term is 5 years, the new monthly payments would include principal amortization based on the £100,000 loan and the interest rate.

Answer 18

1. Fixed principal 2. Fixed payments (more common)

Answer 19

loan where the borrower repays the principal in instalments over time, with each instalment consisting of both an interest payment and a principal repayment. As the loan progresses, the amount of principal outstanding decreases, and the interest payments also decrease accordingly 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)

Answer 20

a table that describes the periodic payments, interest and principal balance after each payment It helps the borrower understand how much of their payment is going towards interest and how much is going towards reducing the loan principal

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

it means the payments are made at the end of each period.

Answer 25

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

Answer 26

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

Answer 27

1. Issuers 2. Investors 3. Other parties

Answer 28

the parties (government or corporations) that borrow money and issue debt securities such as debtors and borrowers

Answer 29

Issuers raise capital by selling bonds to investors. In exchange, they agree to pay back the principal (face value) of the bond at maturity along with periodic interest payments (coupon payments)

Answer 30

the parties (persons, government or corporations that borrow money and issue debt securities) such as creditors, lenders, bondholders

Answer 31

Investors provide the capital to issuers by purchasing bonds. In return, investors receive interest payments over the life of the bond and the face value (principal) of the bond at maturity

Answer 32

Another term for investors holding bonds. They earn periodic interest (coupons) and are repaid the principal when the bond matures

Answer 33

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

Answer 34

Underwriters act as intermediaries in bond issuance. They may take on some risk by guaranteeing to sell a certain amount of bonds and can charge a fee for the service. The underwriting fee is typically a percentage of the total amount raised in the bond offering

Answer 35

as an interest-only loan, meaning the issuer (borrower) makes periodic interest payments to the bondholder (investor) but does not repay the principal (face value) until maturity

Answer 36

the amount the issuer agrees to repay the bondholder at maturity (end of the loan) it is typically £1,000, $1,000, or €1,000, but it can vary It is a fixed amount agreed upon at issuance most the time it isnt equal to the bond price

Answer 37

the periodic payments that issuers promise to make and bondholder receives

Answer 38

Example: If a bond has a 5% coupon rate and a £1,000 face value, it pays £50 per year in interest (or £25 semi-annually if paid twice a year)

Answer 39

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

Answer 40

Coupon payment = (Coupon rate (c) x Par value (F)) / Number of coupon payments per year coupon rate isnt the discount rate for discounting

Answer 41

No The coupon rate is fixed when the bond is issued and determines the periodic coupon payment. The discount rate (or yield to maturity, YTM) is the market rate used to price the bond

Answer 42

the number of years till the date when the issuer repays the face value to the bondholder

Answer 43

measures the bond's return based on its current market price (P) rather than its face value

Answer 44

CY = Annual coupon payment/ market price

Answer 45

A bond with a 6% coupon rate, £1,000 face value, and a market price of £950 has: CY = (0.06x1000)/950 =6.32% Note: Current yield does not account for capital gains or losses if the bond is sold before maturity.

Answer 46

refers to the date when the principal (face value) is repaid, and the bond contract ends Until maturity, the issuer makes periodic coupon payments (if applicable)

Answer 47

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

Answer 48

5-12 years

Answer 49

the annual return an investor will earn if they hold a bond until maturity. It is the discount rate that equates the present value (PV) of the bond’s future cash flows to its current market price (P)

Answer 50

the market interest rate, implicit rate of interest, required rate of return

Answer 51

Reflects the bondholder’s return based on current market conditions Changes over time as investor risk preferences and market conditions shift Used to price bonds and compare investment opportunities

Answer 52

depending on the investors' risk attitudes and investment opportunities

Answer 53

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

Answer 54

YTM assumes that the investor does not sell the bond before maturity. If the investor sells the bond early, the actual return may be higher or lower than the YTM due to price fluctuations in the bond marke

Answer 55

The bond issuer must pay all interest (coupons) and principal as scheduled. If the issuer defaults, investors do not receive full payments, leading to lower actual returns than YTM suggests. Credit risk is a factor here—higher-rated bonds (AAA) have a lower risk of default than lower-rated bonds (junk bonds)

Answer 56

YTM assumes that every coupon payment is reinvested at the same YTM rate. In reality, interest rates fluctuate over time, and the investor may not find reinvestment opportunities at the same YTM rate. This is known as reinvestment risk: If interest rates fall, future coupon payments earn less than expected. If interest rates rise, future coupons could be reinvested at a higher return than YTM

Answer 57

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) P = Market price of the bond C = Coupon payment per period (C=c×F) c = Coupon rate F = Face value of the bond r = Yield to Maturity (YTM) T = Number of periods to maturity usually bond price = 1000 same as Face value

Answer 58

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

Answer 59

x axis yield to maturity % y axis Price downward sloping, inverse relationship

Answer 60

if YTM = coupon rate then par value = bond price The bond is selling at par (i.e., at its face value). Investors are willing to pay exactly the face value because the coupon payments provide a return equal to the market rate

Answer 61

if YTM > coupon rate then par value > bond price selling at a discount, called a discount bond Investors require a higher return than what the bond’s coupon offers, so they pay less than the face value.

Answer 62

If a bond pays a 5% coupon but the market interest rate is 7%, investors will only buy it if it is priced below face value to compensate for the lower coupon rate

Answer 63

if YTM < coupon rate then par value < bond price selling at a premium, called a premium bond Investors are willing to pay more than the face value because the coupon payments are higher than the market-required return

Answer 64

If a bond pays a 7% coupon but the market rate is only 5%, investors will bid up the bond’s price above face value to earn the higher fixed payments

Answer 65

a fixed-income security with no maturity date, meaning it pays coupons forever without repaying the principal

Answer 66

P = C/r P = Price of the bond C = Annual coupon payment r = Yield to Maturity (YTM) (required return by investors)

Answer 67

Face Value (F) = 1,000 Coupon Rate = 8% Annual Coupon Payment (C) = 8% × 1,000 = 80 Yield to Maturity (r) = 10% = 0.10 Time to Maturity = ∞ (Perpetual Bond) P = 80/0.10 = 800 the price of the consol bond is $800

Answer 68

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

Answer 69

As a bond approaches maturity, its price gradually moves toward its face value (par). If a bond is trading at a discount, its price will rise toward par. If a bond is trading at a premium, its price will decline toward par. This happens because, at maturity, the investor receives only the face value, regardless of whether they bought the bond at a premium or discount

Answer 70

Bond prices are inversely related to market interest rates (YTM). When interest rates (YTM) rise → bond prices fall When interest rates (YTM) fall → bond prices rise This happens because investors always compare a bond’s fixed coupon rate to newly available market rates

Answer 71

investors (bondholders) and issuers (companies and government)

Answer 72

If interest rates drop, existing bonds with higher coupon rates become more valuable (price increases). If interest rates rise, existing bonds with lower coupon rates become less valuable (price decreases). Investors who plan to sell bonds before maturity care about these price movements.

Answer 73

If bond prices fall (because interest rates increase), issuers may need to offer higher yields to attract investors for new bond issues. If bond prices rise (because interest rates drop), issuers might refinance debt at lower costs by issuing new bonds at lower interest rates

Answer 74

Before maturity, a bond’s market price can be above or below its par value. However, as the bond approaches its maturity date, its price gradually converges to its par value (face value)