# Estimating rates of return

If the P/E ratio on the S&P 500 is 10, given historical earnings growth patterns, what would be a reasonable estimate of long-run future expected rates of return on the stock market? Assume a long-run inflation rate of 2.5% per annum.

Note: Please explain question in detail so I can better understand.

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#### Solution Preview

Here is a simple definition of the P/E ratio:

The price-to-earnings ratio, or P-E ratio, or P/E ratio, is an equity valuation multiple. It is defined as market price per share divided by annual earnings per share.

In the case above, this multiple is 10; that is, for every dollar of earnings per share, the stock has a value of 10 cents. Now, assuming this ratio remains the same, then it is logical to conclude that the value of the stock will increase IN PROPORTION to the increase in earnings by a multiple of 10, ADJUSTED for the inflation rate of 2.5% (inflation represents the amount by which prices increase versus the ability to consume --- meaning that if prices increase by 2.5% inflated, then consumption ability has generally decreased by that ...

#### Solution Summary

A discussion of real versus expected investment returns based upon historical growth patterns of the stock market.

Multiple choice, please show the work if you can

Multiple Choice

Identify the letter of the choice that best completes the statement or answers the question.

____ 1. You are given the following data:

r* = real risk-free rate = 4%

Constant inflation premium = 7%

Maturity risk premium = 1%

Default risk premium for AAA bonds = 3%

Liquidity premium for long-term T-bonds = 2%

Assume that a highly liquid market does not exist for long-term T-bonds, and the expected rate of inflation is a constant. Given these conditions, the nominal risk-free rate for T-bills is __________, and the rate on long-term Treasury bonds is __________.

a. 4%; 14%

b. 4%; 15%

c. 11%; 14%

d. 11%; 15%

e. 11%; 17%

____ 2. The real risk-free rate is expected to remain at 3 percent. Inflation is expected to be 3 percent this year, and 4 percent next year. The maturity risk premium is estimated to be equal to 0.1%(t - 1), where t = the maturity of a bond (in years). All Treasury securities are highly liquid, and therefore have no liquidity premium. Three-year Treasury bonds yield 0.5 percentage points (0.005) more than two-year Treasury bonds (that is, two-year bond yield plus 0.5%). What is the expected level of inflation in Year 3?

a. 4.5%

b. 4.7%

c. 5.0%

d. 5.6%

e. 6.3%

____ 3. The Florida Boosters Association has decided to build new bleachers for the football field. Total costs are estimated to be $1 million, and financing will be through a bond issue of the same amount. The bond will have a maturity of 20 years, a coupon rate of 8 percent, and has annual payments. In addition, the Association must set up a reserve to pay off the loan by making 20 equal annual payments into an account which pays 8 percent, annual compounding. The interest-accumulated amount in the reserve will be used to retire the entire issue at its maturity 20 years hence. The Association plans to meet the payment requirements by selling season tickets at a $10 net profit per ticket. How many tickets must be sold each year to service the debt, i.e., to meet the interest and principal repayment requirements?

a. 5,372

b. 10,186

c. 15,000

d. 20,459

e. 25,000

____ 4. Suppose you put $100 into a savings account today, the account pays a nominal annual interest rate of 6 percent, but compounded semiannually, and you withdraw $100 after 6 months. What would your ending balance be 20 years after the initial $100 deposit was made?

a. $226.20

b. $115.35

c. $62.91

d. $9.50

e. $3.00

____ 5. Terry Austin is 30 years old and is saving for her retirement. She is planning on making 36 contributions to her retirement account at the beginning of each of the next 36 years. The first contribution will be made today (t = 0) and the final contribution will be made 35 years from today (t = 35). The retirement account will earn a return of 10 percent a year. If each contribution she makes is $3,000, how much will be in the retirement account 35 years from now (t = 35)?

a. $894,380

b. $813,073

c. $897,380

d. $987,118

e. $978,688

____ 6. You have just taken out a 10-year, $12,000 loan to purchase a new car. This loan is to be repaid in 120 equal end-of-month installments. If each of the monthly installments is $150, what is the effective annual interest rate on this car loan?

a. 6.5431%

b. 7.8942%

c. 8.6892%

d. 8.8869%

e. 9.0438%

____ 7. John and Barbara Roberts are starting to save for their daughter's college education.

? Assume that today's date is September 1.

? College costs are currently $10,000 a year and are expected to increase at a rate equal to 6 percent per year for the foreseeable future. All college payments are due at the beginning of the year. (So for example, college will cost $10,000 if you start now, and $10,600 if you start next September 1).

? Their daughter will enter college 15 years from now. She will be enrolled for four years. Therefore the Roberts will need to make four tuition payments. The first payment will be made on September 1 of the year she enters college (Year 15). The final payment will be made on September 1 of her last year in college (Year 18). Notice that because of rising tuition costs, the tuition payments will increase each year.

? The Roberts would also like to give their daughter a lump-sum payment of $50,000 on the September 1 after she graduates (i.e., at Year 19) in order to help with a down payment on a home, or to assist with graduate school tuition.

? The Roberts currently have $10,000 in their college account. They anticipate making 15 equal contributions to the account at the end of each of the next 15 years. (The first contribution would be made on September 1 one year from now (i.e., at Year 1) and the final contribution will be made on September 1 when she enters college (i.e., Year 15).

? All current and future investments are assumed to earn an 8 percent return. (Ignore taxes.)

How much should the Roberts contribute each year in order to reach their goal?

a. $3,156.69

b. $3,618.95

c. $4,554.83

d. $5,955.54

e. $6,279.54

____ 8. Bates Motors has the following information for the previous year: Net income = $200; Net operating profit after taxes (NOPAT) = $300; Total assets = $1,000; and Total net operating capital = $800. The information for the current year is: Net income = $500; Net operating profit after taxes (NOPAT) = $400; Total assets = $1,300; and Total net operating capital = $900. What is the free cash flow for the current year?

a. $100

b. $200

c. $300

d. $400

e. $500

____ 9. Casey Motors recently reported the following information:

? Net income = $600,000.

? Tax rate = 40%.

? Interest expense = $200,000.

? Operating capital = $9 million.

? After-tax cost of capital = 10%.

What is the company's EVA?

a. ($300,000)

b. ($180,000)

c. $0

d. $200,000

e. $400,000

____ 10. You have been scouring The Wall Street Journal looking for stocks that are "good values" and have calculated the expected returns for five stocks. Assume the risk-free rate (rRF) is 7 percent and the market risk premium (rM - rRF) is 2 percent. Which security would be the best investment? (Assume you must choose just one.)

Expected Return Beta

a. 9.01% 1.70

b. 7.06% 0.00

c. 5.04% -0.67

d. 8.74% 0.87

e. 11.50% 2.50

____ 11. A money manager is managing the account of a large investor. The investor holds the following stocks:

Stock Amount Invested Estimated Beta

A $2,000,000 0.80

B 5,000,000 1.10

C 3,000,000 1.40

D 5,000,000 ???

The portfolio's required rate of return is 17 percent. The risk-free rate, rRF, is 7 percent and the return on the market, rM, is 14 percent. What is Stock D's estimated beta?

a. 1.256

b. 1.389

c. 1.429

d. 2.026

e. 2.154

____ 12. You are holding a stock which has a beta of 2.0 and is currently in equilibrium. The required return on the stock is 15 percent, and the return on an average stock is 10 percent. What would be the percentage change in the return on the stock, if the return on an average stock increased by 30 percent while the risk-free rate remained unchanged?

a. +20%

b. +30%

c. +40%

d. +50%

e. +60%

____ 13. Allison Engines Corporation has established a target capital structure of 40 percent debt and 60 percent common equity. The firm expects to earn $600 in after-tax income during the coming year, and it will retain 40 percent of those earnings. The current market price of the firm's stock is P0 = $28; its last dividend was D0 = $2.20, and its expected growth rate is 6 percent. Allison can issue new common stock at a 15 percent flotation cost. What will Allison's marginal cost of equity capital (not the WACC) be if it must fund a capital budget requiring $600 in total new capital?

a. 15.8%

b. 13.9%

c. 7.9%

d. 14.3%

e. 9.7%

____ 14. Hilliard Corp. wants to calculate its weighted average cost of capital (WACC). The company's CFO has collected the following information:

? The company's long-term bonds currently offer a yield to maturity of 8 percent.

? The company's stock price is $32 per share (P0 = $32).

? The company recently paid a dividend of $2 per share (D0 = $2.00).

? The dividend is expected to grow at a constant rate of 6 percent a year (g = 6%).

? The company pays a 10 percent flotation cost whenever it issues new common stock (F = 10%).

? The company's target capital structure is 75 percent equity and 25 percent debt.

? The company's tax rate is 40 percent.

? The company anticipates issuing new common stock during the upcoming year.

What is the company's WACC?

a. 10.67%

b. 11.22%

c. 11.47%

d. 12.02%

e. 12.56%

____ 15. A stock analyst has obtained the following information about J-Mart, a large retail chain:

(1) The company has noncallable bonds with 20 years maturity remaining and a maturity value of $1,000. The bonds have a 12 percent annual coupon and currently sell at a price of $1,273.8564.

(2) Over the past four years, the returns on the market and on J-Mart were as follows:

Year Market J-Mart

2001 12.0% 14.5%

2002 17.2 22.2

2003 -3.8 -7.5

2004 20.0 24.0

(3) The current risk-free rate is 6.35 percent, and the expected return on the market is 11.35 percent. The company's tax rate is 35 percent.

The company anticipates that its proposed investment projects will be financed with 70 percent debt and 30 percent equity. What is the company's estimated weighted average cost of capital (WACC)?

a. 8.04%

b. 9.00%

c. 10.25%

d. 12.33%

e. 13.14%

____ 16. Vanderheiden Inc. is considering two average-risk alternative ways of producing its patented polo shirts. Process S has a cost of $8,000 and will produce net cash flows of $5,000 per year for 2 years. Process L will cost $11,500 and will produce cash flows of $4,000 per year for 4 years. The company has a contract that requires it to produce the shirts for 4 years, but the patent will expire after 4 years, so the shirts will not be produced after 4 years. Inflation is expected to be zero during the next 4 years. If cash inflows occur at the end of each year, and if Vanderheiden's cost of capital is 10 percent, by what amount will the better project increase Vanderheiden's value?

a. $677.69

b. $1,098.89

c. $1,179.46

d. $1,237.76

e. $1,312.31

____ 17. A company is analyzing two mutually exclusive projects, S and L, whose cash flows are shown below:

Years 0 1 2 3 4

S -1,100 900 350 50 10

L -1,100 0 300 500 850

The company's cost of capital is 12 percent, and it can get an unlimited amount of capital at that cost. What is the regular IRR (not MIRR) of the better project? (Hint: Note that the better project may or may not be the one with the higher IRR.)

a. 13.09%

b. 12.00%

c. 17.46%

d. 13.88%

e. 12.53%

____ 18. Mooradian Corporation estimates that its cost of capital is 11 percent. The company is considering two mutually exclusive projects whose after-tax cash flows are as follows:

Project S Project L

Year Cash Flow Cash Flow

0 -$3,000 -$9,000

1 2,500 -1,000

2 1,500 5,000

3 1,500 5,000

4 -500 5,000

What is the modified internal rate of return (MIRR) of the project with the highest NPV?

a. 11.89%

b. 13.66%

c. 16.01%

d. 18.25%

e. 20.12%

____ 19. Simmons Shoes is considering a project with the following cash flows:

Project

Year Cash Flow

0 -$700

1 400

2 -200

3 600

4 500

Simmons' WACC is 10 percent. What is the project's modified internal rate of return (MIRR)?

a. 17.10%

b. 18.26%

c. 25.28%

d. 28.93%

e. 29.52%

____ 20. Cannon Company has enjoyed a rapid increase in sales in recent years, following a decision to sell on credit. However, the firm has noticed a recent increase in its collection period. Last year, total sales were $1 million, and $250,000 of these sales were on credit. During the year, the accounts receivable account averaged $41,096. It is expected that sales will increase in the forthcoming year by 50 percent, and, while credit sales should continue to be the same proportion of total sales, it is expected that the days sales outstanding will also increase by 50 percent (assume a 365-day year). If the resulting increase in accounts receivable must be financed by external funds, how much external funding will Cannon need?

a. $41,664

b. $51,370

c. $47,359

d. $106,471

e. $93,750

____ 21. The Meryl Corporation's common stock is currently selling at $100 per share, which represents a P/E ratio of 10. If the firm has 100 shares of common stock outstanding, a return on equity of 20 percent, and a debt ratio of 60 percent, what is its return on total assets (ROA)?

a. 8.0%

b. 10.0%

c. 12.0%

d. 16.7%

e. 20.0%