**Question 22** NPV, perpetuity with growth, effective rate, effective rate conversion

What is the NPV of the following series of cash flows when the discount rate is 10% given as an effective annual rate?

The first payment of $90 is in 3 years, followed by payments every 6 months in perpetuity after that which shrink by 3% every 6 months. That is, the growth rate every 6 months is actually negative 3%, given as an effective 6 month rate. So the payment at ## t=3.5 ## years will be ## 90(1-0.03)^1=87.3 ##, and so on.

**Question 31** DDM, perpetuity with growth, effective rate conversion

What is the NPV of the following series of cash flows when the discount rate is **5**% given as an effective **annual** rate?

The first payment of $10 is in 4 years, followed by payments every 6 months forever after that which shrink by 2% every 6 months. That is, the growth rate every 6 months is actually **negative 2%**, given as an effective **6 month** rate. So the payment at ## t=4.5 ## years will be ## 10(1-0.02)^1=9.80 ##, and so on.

**Question 155** inflation, real and nominal returns and cash flows, Loan, effective rate conversion

You are a banker about to grant a 2 year loan to a customer. The loan's principal and interest will be repaid in a single payment at maturity, sometimes called a zero-coupon loan, discount loan or bullet loan.

You require a **real** return of **6**% pa over the two years, given as an effective annual rate. Inflation is expected to be **2**% this year and **4**% next year, both given as effective annual rates.

You judge that the customer can afford to pay back $**1,000,000** in **2** years, given as a **nominal** cash flow. How much should you lend to her right now?

**Question 215** equivalent annual cash flow, effective rate conversion

You're about to buy a car. These are the cash flows of the two different cars that you can buy:

- You can buy an old car for $5,000 now, for which you will have to buy $90 of fuel at the end of each week from the date of purchase. The old car will last for 3 years, at which point you will sell the old car for $500.
- Or you can buy a new car for $14,000 now for which you will have to buy $50 of fuel at the end of each week from the date of purchase. The new car will last for 4 years, at which point you will sell the new car for $1,000.

Bank interest rates are 10% pa, given as an effective annual rate. Assume that there are exactly 52 weeks in a year. Ignore taxes and environmental and pollution factors.

Should you buy the or the ?

**Question 249** equivalent annual cash flow, effective rate conversion

Details of two different types of desserts or edible treats are given below:

- High-sugar treats like candy, chocolate and ice cream make a person very happy. High sugar treats are cheap at only $2 per day.
- Low-sugar treats like nuts, cheese and fruit make a person equally happy if these foods are of high quality. Low sugar treats are more expensive at $4 per day.

The advantage of low-sugar treats is that a person only needs to pay the dentist $2,000 for fillings and root canal therapy once every 15 years. Whereas with high-sugar treats, that treatment needs to be done every 5 years.

The real discount rate is 10%, given as an effective annual rate. Assume that there are 365 days in every year and that all cash flows are real. The inflation rate is 3% given as an effective annual rate.

Find the equivalent annual cash flow (EAC) of the high-sugar treats and low-sugar treats, including dental costs. The below choices are listed in that order.

Ignore the pain of dental therapy, personal preferences and other factors.

You own an apartment which you rent out as an investment property.

What is the price of the apartment using discounted cash flow (DCF, same as NPV) valuation?

Assume that:

- You just signed a contract to rent the apartment out to a tenant for the next 12 months at $2,000 per month, payable in advance (at the start of the month, t=0). The tenant is just about to pay you the first $2,000 payment.
- The contract states that monthly rental payments are fixed for 12 months. After the contract ends, you plan to sign another contract but with rental payment increases of 3%. You intend to do this every year.

So rental payments will increase at the start of the 13th month (t=12) to be $2,060 (=2,000(1+0.03)), and then they will be constant for the next 12 months.

Rental payments will increase again at the start of the 25th month (t=24) to be $2,121.80 (=2,000(1+0.03)^{2}), and then they will be constant for the next 12 months until the next year, and so on. - The required return of the apartment is 8.732% pa, given as an effective annual rate.
- Ignore all taxes, maintenance, real estate agent, council and strata fees, periods of vacancy and other costs. Assume that the apartment will last forever and so will the rental payments.

A home loan company advertises an interest rate of 6% pa, payable monthly. Which of the following statements about the interest rate is **NOT** correct? All rates are given to four decimal places.

A credit card company advertises an interest rate of 18% pa, payable monthly. Which of the following statements about the interest rate is **NOT** correct? All rates are given to four decimal places.

A semi-annual coupon bond has a yield of 3% pa. Which of the following statements about the yield is **NOT** correct? All rates are given to four decimal places.

**Question 659** APR, effective rate, effective rate conversion, no explanation

A home loan company advertises an interest rate of 9% pa, payable monthly. Which of the following statements about the interest rate is **NOT** correct? All rates are given with an accuracy of 4 decimal places.

**Question 662** APR, effective rate, effective rate conversion, no explanation

Which of the following interest rate labels does **NOT** make sense?

An effective **monthly** return of 1% ##(r_\text{eff monthly})## is equivalent to an effective **annual** return ##(r_\text{eff annual})## of:

An effective **semi-annual** return of 5% ##(r_\text{eff 6mth})## is equivalent to an effective **annual** return ##(r_\text{eff annual})## of: