**Question 49** inflation, real and nominal returns and cash flows, APR, effective rate

In Australia, nominal yields on **semi**-annual coupon paying Government Bonds with 2 years until maturity are currently **2.83**% pa.

The inflation rate is currently **2.2**% pa, given as an APR compounding per **quarter**. The inflation rate is not expected to change over the next 2 years.

What is the real yield on these bonds, given as an APR compounding every 6 months?

**Question 50** DDM, stock pricing, inflation, real and nominal returns and cash flows

Most listed Australian companies pay dividends twice per year, the 'interim' and 'final' dividends, which are roughly 6 months apart.

You are an equities analyst trying to value the company BHP. You decide to use the Dividend Discount Model (DDM) as a starting point, so you study BHP's dividend history and you find that BHP tends to pay the same interim and final dividend each year, and that both grow by the same rate.

You expect BHP will pay a $0.55 interim dividend in six months and a $0.55 final dividend in one year. You expect each to grow by 4% next year and forever, so the interim and final dividends next year will be $0.572 each, and so on in perpetuity.

Assume BHP's cost of equity is 8% pa. All rates are quoted as nominal effective rates. The dividends are nominal cash flows and the inflation rate is 2.5% pa.

What is the current price of a BHP share?

**Question 58** NPV, inflation, real and nominal returns and cash flows, Annuity

A project to build a toll bridge will take two years to complete, costing three payments of $100 million at the start of each year for the next three years, that is at t=0, 1 and 2.

After completion, the toll bridge will yield a constant $50 million at the end of each year for the next 10 years. So the first payment will be at t=3 and the last at t=12. After the last payment at t=12, the bridge will be given to the government.

The required return of the project is 21% pa given as an effective annual **nominal** rate.

All cash flows are **real** and the expected inflation rate is 10% pa given as an effective annual rate. Ignore taxes.

The Net Present Value is:

**Question 64** inflation, real and nominal returns and cash flows, APR, effective rate

In Germany, nominal yields on **semi**-annual coupon paying Government Bonds with 2 years until maturity are currently **0.04**% pa.

The inflation rate is currently **1.4**% pa, given as an APR compounding per **quarter**. The inflation rate is not expected to change over the next 2 years.

What is the real yield on these bonds, given as an APR compounding every 6 months?

**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 180** equivalent annual cash flow, inflation, real and nominal returns and cash flows

Details of two different types of light bulbs are given below:

- Low-energy light bulbs cost $3.50, have a life of nine years, and use about $1.60 of electricity a year, paid at the end of each year.
- Conventional light bulbs cost only $0.50, but last only about a year and use about $6.60 of energy a year, paid at the end of each year.

The real discount rate is 5%, given as an effective annual rate. Assume that all cash flows are real. The inflation rate is 3% given as an effective annual rate.

Find the Equivalent Annual Cost (EAC) of the low-energy and conventional light bulbs. The below choices are listed in that order.

**Question 210** real estate, inflation, real and nominal returns and cash flows, income and capital returns

Assume that the Gordon Growth Model (same as the dividend discount model or perpetuity with growth formula) is an appropriate method to value real estate.

The rule of thumb in the real estate industry is that properties should yield a **5**% pa rental return. Many investors also regard property to be as risky as the stock market, therefore property is thought to have a required **total** return of **9**% pa which is the average total return on the stock market including dividends.

Assume that all returns are effective annual rates and they are **nominal** (not reduced by inflation). Inflation is expected to be **2**% pa.

You're considering purchasing an investment property which has a rental yield of 5% pa and you expect it to have the same risk as the stock market. Select the most correct statement about this property.

**Question 239** income and capital returns, inflation, real and nominal returns and cash flows, interest only loan

A bank grants a borrower an **interest-only** residential mortgage loan with a very large 50% deposit and a **nominal** interest rate of **6%** that is not expected to change. Assume that inflation is expected to be a **constant 2%** pa over the life of the loan. Ignore credit risk.

From the bank's point of view, what is the long term expected **nominal capital** return of the loan asset?

**Question 278** inflation, real and nominal returns and cash flows

Imagine that the interest rate on your savings account was 1% per year and inflation was 2% per year.

**Question 295** inflation, real and nominal returns and cash flows, NPV

When valuing assets using discounted cash flow (net present value) methods, it is important to consider inflation. To properly deal with inflation:

(I) Discount nominal cash flows by nominal discount rates.

(II) Discount nominal cash flows by real discount rates.

(III) Discount real cash flows by nominal discount rates.

(IV) Discount real cash flows by real discount rates.

Which of the above statements is or are correct?

**Question 337** capital structure, interest tax shield, leverage, real and nominal returns and cash flows, multi stage growth model

A fast-growing firm is suitable for valuation using a multi-stage growth model.

It's **nominal** unlevered cash flow from assets (##CFFA_U##) at the end of this year (**t=1**) is expected to be $**1** million. After that it is expected to grow at a rate of:

**12**% pa for the next two years (from t=1 to 3),**5**% over the fourth year (from t=3 to 4), and**-1**% forever after that (from t=4 onwards). Note that this is a negative one percent growth rate.

Assume that:

- The nominal WACC
**after**tax is**9.5**% pa and is not expected to change. - The nominal WACC
**before**tax is**10**% pa and is not expected to change. - The firm has a target debt-to-
**equity**ratio that it plans to maintain. - The inflation rate is
**3**% pa. - All rates are given as
**nominal**effective annual rates.

What is the levered value of this fast growing firm's assets?

**Question 353** income and capital returns, inflation, real and nominal returns and cash flows, real estate

A residential investment property has an expected **nominal** total return of **6**% pa and nominal capital return of **3**% pa.

Inflation is expected to be **2**% pa. All rates are given as effective annual rates.

What are the property's expected **real** total, capital and income returns? The answer choices below are given in the same order.

**Question 363** income and capital returns, inflation, real and nominal returns and cash flows, real estate

A residential investment property has an expected **nominal** total return of **8**% pa and nominal capital return of **3**% pa.

Inflation is expected to be **2**% pa. All rates are given as effective annual rates.

What are the property's expected **real** total, capital and income returns? The answer choices below are given in the same order.

**Question 407** income and capital returns, inflation, real and nominal returns and cash flows

A stock has a **real** expected total return of **7**% pa and a real expected capital return of **2**% pa.

Inflation is expected to be **2**% pa. All rates are given as effective annual rates.

What is the **nominal** expected total return, capital return and dividend yield? The answers below are given in the same order.

**Question 522** income and capital returns, real and nominal returns and cash flows, inflation, real estate

A residential investment property has an expected nominal total return of **6**% pa and nominal capital return of **2.5**% pa. Inflation is expected to be **2.5**% pa.

All of the above are effective **nominal** rates and investors believe that they will stay the same in perpetuity.

What are the property's expected **real** total, capital and income returns?

The answer choices below are given in the same order.

**Question 523** income and capital returns, real and nominal returns and cash flows, inflation

A low-growth mature stock has an expected nominal total return of **6**% pa and nominal capital return of **2**% pa. Inflation is expected to be **3**% pa.

All of the above are effective **nominal** rates and investors believe that they will stay the same in perpetuity.

What are the stock's expected **real** total, capital and income returns?

The answer choices below are given in the same order.

**Question 525** income and capital returns, real and nominal returns and cash flows, inflation

Which of the following statements about cash in the form of notes and coins is **NOT** correct? Assume that inflation is positive.

Notes and coins:

**Question 526** real and nominal returns and cash flows, inflation, no explanation

How can a **nominal** cash flow be precisely converted into a **real** cash flow?

**Question 529** DDM, real and nominal returns and cash flows, inflation, real estate, no explanation

If housing rents are constrained from growing more than the maximum target inflation rate, and houses can be priced as a perpetuity of growing net rental cash flows, then what is the implication for house prices, all things remaining equal? Select the **most correct** answer.

*Background:* Since 1990, many central banks across the world have become 'inflation targeters'. They have adopted a policy of trying to keep inflation in a predictable narrow range, with the hope of encouraging long-term lending to fund more investment and maintain higher GDP growth.

Australia's central bank, the Reserve Bank of Australia (RBA), has specifically stated their inflation target range is between 2 and 3% pa.

Some Australian residential property market commentators suggest that because rental costs comprise a large part of the Australian consumer price index (CPI), rent costs across the nation cannot significantly exceed the maximum inflation target range of 3% pa without the prices of other goods growing by less than the target range for long periods, which is unlikely.

**Question 535** DDM, real and nominal returns and cash flows, stock pricing

You are an equities analyst trying to value the equity of the Australian telecoms company Telstra, with ticker TLS. In Australia, listed companies like Telstra tend to pay dividends every **6** months. The payment around August is called the final dividend and the payment around February is called the interim dividend. Both occur annually.

- Today is mid-
**March 2015**. - TLS's last interim dividend of $
**0.15**was one month ago in mid-**February 2015**. - TLS's last final dividend of $
**0.15**was seven months ago in mid-**August 2014**.

Judging by TLS's dividend history and prospects, you estimate that the nominal dividend growth rate will be **1**% pa. Assume that TLS's total nominal cost of equity is **6**% pa. The dividends are nominal cash flows and the inflation rate is **2.5**% pa. All rates are quoted as nominal effective annual rates. Assume that each month is exactly one twelfth (1/12) of a year, so you can ignore the number of days in each month.

Calculate the current TLS share price.

**Question 554** inflation, real and nominal returns and cash flows

On his 20th birthday, a man makes a resolution. He will put $**30** cash under his bed at the **end** of every month starting from today. His birthday today is the first day of the month. So the first addition to his cash stash will be in one month. He will write in his will that when he dies the cash under the bed should be given to charity.

If the man lives for another **60** years, how much money will be under his bed if he dies just after making his last (720th) addition?

Also, what will be the **real** value of that cash in today's prices if inflation is expected to **2.5%** pa? Assume that the inflation rate is an effective annual rate and is not expected to change.

The answers are given in the same order, the amount of money under his bed in 60 years, and the real value of that money in today's prices.

**Question 574** inflation, real and nominal returns and cash flows, NPV

What is the present value of a **nominal** payment of $100 in 5 years? The **real** discount rate is 10% pa and the inflation rate is 3% pa.

**Question 575** inflation, real and nominal returns and cash flows

You expect a **nominal** payment of $100 in 5 years. The **real** discount rate is 10% pa and the inflation rate is 3% pa. Which of the following statements is **NOT** correct?

**Question 576** inflation, real and nominal returns and cash flows

What is the present value of a **nominal** payment of $1,000 in 4 years? The **nominal** discount rate is 8% pa and the inflation rate is 2% pa.

**Question 577** inflation, real and nominal returns and cash flows

What is the present value of a **real** payment of $500 in 2 years? The **nominal** discount rate is 7% pa and the inflation rate is 4% pa.

**Question 578** inflation, real and nominal returns and cash flows

Which of the following statements about inflation is **NOT** correct?

**Question 604** inflation, real and nominal returns and cash flows

Apples and oranges currently cost $**1** each. Inflation is **5**% pa, and apples and oranges are equally affected by this inflation rate. Note that when payments are not specified as real, as in this question, they're conventionally assumed to be nominal.

Which of the following statements is **NOT** correct?

**Question 664** real and nominal returns and cash flows, inflation, no explanation

What is the present value of **real** payments of $100 every year forever, with the first payment in one year? The **nominal** discount rate is 7% pa and the inflation rate is 4% pa.

**Question 727** inflation, real and nominal returns and cash flows

The Australian Federal Government lends money to domestic students to pay for their university education. This is known as the Higher Education Contribution Scheme (HECS). The nominal interest rate on the HECS loan is set equal to the consumer price index (CPI) inflation rate. The interest is capitalised every year, which means that the interest is added to the principal. The interest and principal does not need to be repaid by students until they finish study and begin working.

Which of the following statements about HECS loans is **NOT** correct?

**Question 728** inflation, real and nominal returns and cash flows, income and capital returns, no explanation

Which of the following statements about gold is **NOT** correct? Assume that the gold price increases by inflation. Gold:

**Question 732** real and nominal returns and cash flows, inflation, income and capital returns

An investor bought a bond for $**100** (at t=0) and one year later it paid its annual coupon of $**1** (at t=1). Just after the coupon was paid, the bond price was $**100.50** (at t=1). Inflation over the past year (from t=0 to t=1) was **3**% pa, given as an effective annual rate.

Which of the following statements is **NOT** correct? The bond investment produced a:

**Question 734** real and nominal returns and cash flows, inflation, DDM, no explanation

An equities analyst is using the dividend discount model to price a company's shares. The company operates domestically and has no plans to expand overseas. It is part of a mature industry with stable positive growth prospects.

The analyst has estimated the **real** required return (r) of the stock and the value of the dividend that the stock **just paid** a moment before ##(C_\text{0 before})##.

What is the highest perpetual **real** growth rate of dividends (g) that can be justified? Select the most correct statement from the following choices. The highest perpetual real expected growth rate of dividends that can be justified is the country's expected:

**Question 739** real and nominal returns and cash flows, inflation

There are a number of different formulas involving real and nominal returns and cash flows. Which one of the following formulas is **NOT** correct? All returns are effective annual rates. Note that the symbol ##\approx## means 'approximately equal to'.

**Question 740** real and nominal returns and cash flows, DDM, inflation

Taking inflation into account when using the DDM can be hard. Which of the following formulas will **NOT** give a company's current stock price ##(P_0)##? Assume that the annual dividend was just paid ##(C_0)##, and the next dividend will be paid in one year ##(C_1)##.

**Question 744** income and capital returns, real and nominal returns and cash flows, inflation

If someone says "my shares rose by 10% last year", what do you assume that they mean?

**Question 745** real and nominal returns and cash flows, inflation, income and capital returns

If the nominal gold price is expected to increase at the same rate as inflation which is 3% pa, which of the following statements is **NOT** correct?