Principles of Finance ACST603
Tutorial 2, Week 2 Time value of money and interest rates
Homework questions.
You are a depositor giving cash at the start, therefore you are lending to the bank. The bank is borrowing from you.
You are a depositor giving cash at the start, therefore you are buying debt from the bank. The bank has sold their debt to you. You've bought the bank's promise to pay you back, which is a contract on a piece of paper.
You are a depositor giving cash at the start, therefore you are investing in the debt asset issued by the bank. In return for you investment, the bank issued you the piece of paper debt contract promising to pay you back the principal plus interest.
The deposit account at the bank is your debt asset since it will give you a future benefit. On the other side of the coin, the deposit account is the bank's debt liability since they owe it to you.
Borrowers owe money to their lenders.
Lenders are owed money by their borrowers who owe them. Strangely, 'owed' is not the past tense of 'owe'. They have completely opposite meanings which doesn't make sense.
Owners of debt assets must be lenders since they are owed money, they expect a positive benefit in the future when they're paid back.
You received cash from the bank at the start using the home loan, therefore you sold the home loan debt.
You received cash at the start using the home loan and in return you issued the piece of paper debt contract promising to pay back the principal plus interest to the bank.
Which of the following statements is NOT correct? Borrowers:
Borrowers sell debt. This is because borrowers receive cash at the start for selling the debt contract to the lender. Note that selling debt can also be called being 'shorting' debt.
Which of the following statements is NOT correct? Lenders:
Lenders are owed money by borrowers. Confusingly, lenders' debt is actually an asset, not a liability. Lenders own the asset class debt.
Which of the following statements is NOT correct? Bond investors:
A bond investor buys bonds, which is lending. But a debtor sells bonds, which is borrowing.
Which of the following statements is NOT correct? Lenders:
Writing debt is selling debt or borrowing, not lending. The borrower writes the contract promising to pay the lender back the principal and interest and then sells it to the lender.
You deposit money into a bank. Which of the following statements is NOT correct? You:
When you deposit money at the bank, you have not issued debt, the bank has issued the debt contract to you. You have invested in the bank's debt.
The bank would have given you a piece of paper receipt when you deposited the money. This is a sort of debt contract that the bank issued to you in which they promise to pay you interest and eventually the principal when you choose to withdraw the cash.
You bought a house, primarily funded using a home loan from a bank. Which of the following statements is NOT correct?
The home loan is a debt asset to the bank since they're the lender. The home loan is a debt liability to you since you're the borrower.
Question 771 debt terminology, interest expense, interest tax shield, credit risk, no explanation
You deposit money into a bank account. Which of the following statements about this deposit is NOT correct?
No explanation provided.
By convention, money market securities' yields are always quoted as:
Money market securities' yields are always quoted as simple interest rates:
###P_0 = \dfrac{F_d}{(1+r_\text{simple} \times d/365)}###However, yields on bonds are generally quoted as annualised percentage rates compounding semi-annually.
Which of the following is NOT a money market security?
BAB's, CD's, PN's and Treasury notes are all money market securities. Money market securities tend to have short maturities of less than one year, pay no coupons, are priced using simple interest rates and are highly liquid, low risk and low yield.
Which of the following is also known as 'commercial paper'?
Promissory notes are also known as commercial paper. Promissory notes are issued directly by corporations without the involvement of banks. Banks do not issue PN's and do not accept (guarantee) them against default for other companies.
Confusingly, commercial paper and commercial bills are not the same. Bank accepted bills are a type of 'commercial bill'. Promissory notes are sometimes called 'commercial paper'.
Which of the following statements is NOT correct? Money market securities are:
Money market securities do not pay coupons. They are purchased by the lender at the start and pay back the face value at maturity. There are no cash flows in between. The interest can be calculated as the face value at maturity less the price at the start.
Note that money market securities can be sold prior to maturity, but this payment on sale is not a coupon.
A 180-day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 8% pa and there are 365 days in the year. What is its price now?
###\begin{aligned} P_\text{0, bill} =& \frac{F_d}{1 + r_\text{simple} \times \frac{d}{365}} \\ =& \frac{1,000,000}{1 + 0.08 \times \frac{180}{365}} \\ =& 962,045.33 \\ \end{aligned} ###
A 90-day Bank Accepted Bill (BAB) has a face value of $1,000,000. The simple interest rate is 10% pa and there are 365 days in the year. What is its price now?
###\begin{aligned} P_\text{0, bill} =& \frac{F_d}{1 + r_\text{simple} \times \frac{d}{365}} \\ =& \frac{1,000,000}{1 + 0.1 \times \frac{90}{365}} \\ =& 975,935.8289 \\ \end{aligned} ###
Question 327 bill pricing, simple interest rate, no explanation
On 27/09/13, three month Swiss government bills traded at a yield of -0.2%, given as a simple annual yield. That is, interest rates were negative.
If the face value of one of these 90 day bills is CHF1,000,000 (CHF represents Swiss Francs, the Swiss currency), what is the price of one of these bills?
No explanation provided.
A bank bill was bought for $99,000 and sold for $100,000 thirty (30) days later. There are 365 days in the year. Which of the following formulas gives the simple interest rate per annum over those 30 days?
Note: To help you identify which is the correct answer without doing any calculations yourself, the formulas used to calculate the numbers are given.
The bill pricing formula can be re-arranged to make the simple interest rate the subject:
###P_0 = \dfrac{F_d}{(1+r_\text{simple} \times d/365)} ### ###\begin{aligned} r_\text{simple} &= \left( \dfrac{F_d}{P_0} -1 \right) \times \dfrac{365}{d} \\ &= \left( \dfrac{100,000}{99,000} -1 \right) \times \dfrac{365}{30} \\ &= 0.1228956229 \\ &= 12.28956229 \% \text{ pa}\\ \end{aligned}###A 90 day bank bill has a face value of $100,000.
Investor A bought the bill when it was first issued at a simple yield to maturity of 3% pa and sold it 20 days later to Investor B who expected to earn a simple yield to maturity of 5% pa. Investor B held it until maturity.
Which of the following statements is NOT correct?
Bank bills are money market securities so the simple interest formula should be be used to price them. On day 20 the bank bill will only have 70 (=90-20) days left until maturity.
###P_\text{0, bill} = \frac{F_d}{(1 + r_\text{simple} \times d/365)} ### ###\begin{aligned} P_\text{20, bill} &= \frac{F_{90}}{(1 + r_\text{simple} \times (90-20)/365)} \\ &= \frac{100,000}{(1 + 0.05 \times (90-20)/365)} \\ &= 99,050.20353 \\ \end{aligned}###The initial price of the bank bill is:
###\begin{aligned} P_\text{0, bill} &= \frac{F_{90}}{(1 + r_\text{simple} \times 90/365)} \\ &= \frac{100,000}{(1 + 0.03 \times 90/365)} \\ &= 99,265.70574 \\ \end{aligned}###To find the historical yield from day zero to 20 as a simple annual rate:
###P_\text{0, bill} = \frac{P_{20}}{(1 + r_{0 \rightarrow 20} \times (20)/365)}### ###99,265.70574 = \frac{99,050.20353}{(1 + r_{0 \rightarrow 20} \times 20/365)} ### ###\begin{aligned} r_{0 \rightarrow 20} &= \left( \frac{99,050.20353}{99,265.70574} - 1 \right) \times \frac{365}{20} \\ &= -0.002170963 \times \frac{365}{20} \\ &= -0.039620081 \\ &= -3.9620081 \%\text{ pa} \\ \end{aligned}###The historical simple return was -3.9620081% pa over the 20 days before Investor B bought the bond. Note that the historical (past) return was negative since the bill price fell when the yield to maturity (future expected return) rose from 3% to 5% pa.