Finance401Examen1

The following table gives the available projects (in $millions) for a firm. ABCDEFG 5.04.05.01.02.07.08.0Initial investment1.5−0.51.00.50.51.01.0NPV The firm has only $20 million to invest. What is the maximum NPV that the company can obtain?

4.5 A + C + D + E + F = 4.5; Total investment = 5 + 5 + 1 + 2 + 7 = $20 million.

You buy a 12-year 10 percent annual coupon bond at par value, $1,000. You sell the bond three years later for $1,100. What is your rate of return over this three-year period?

40 percent Rate of return = (coupon income + price change)/investment. Rate of return = (300+100)/1,000 = 40%.

If the nominal interest rate per year is 10 percent and the inflation rate is 4 percent, what is the real rate of interest?

5.8 percent Using Irving Fisher's equation, 1 + rreal = (1 + r nominal)/(1 + r inflation) = 1.1/1.04 = 1.058; rreal = 5.8%.

Company Y does not plow back any earnings and is expected to produce a level dividend stream of $6.2 a share. If the current stock price is $41.2, what is the market capitalization rate? (Enter your answer as a percent rounded to 2 decimal place.)

15.05% r = DIV1 / P0 r = $6.2 / $41.2 r = 0.1505, or 15.05%

If the cash flows for Project M are C0 = -1,000; C1 = +200; C2 = +700; and C3 = +698, calculate the IRR for the project.

23 percent -1,000 + [200/(1 + IRR)] + [700/(1 + IRR)^2] + [698/(1 + IRR)^3] = 0; IRR = 23%. In Excel: In , arrange cash flows in order starting with -1,000 in cell A1 and ending with +698 in cell A4, then "= IRR(A1:A4)".

Company Z's earnings and dividends per share are expected to grow indefinitely by 4% a year. Assume next year's dividend per share is $17 and next year's EPS is $5. The market capitalization rate is 14%. If Company Z were to distribute all of its earnings, it could maintain a level dividend stream of $5 a share. How much is the market actually paying per share for growth opportunities? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

$134.29 P0 = DIV1 / (r − g) P0 = $17 / (0.14 − 0.04) P0 = $170.00 P0 = EPS1 / r + PVGO PVGO = $170.00 − $5 / 0.14 PVGO = $134.29

If the present value of $1 received n years from today at an interest rate of r is 0.3855, then what is the future value of $1 invested today at an interest rate of r percent for n years?

$2,594 FV = 1/(0.3855) = 2.594.

What is the present value of a six-year, $5,000 per year annuity at a discount rate of 10 percent?

$21,776.30 PV = [(1/0.10) - (1/((0.10)(1.10^6)))] × 5,000 = 21,776.30.

John House has taken a 20-year, $250,000 mortgage on his house at an interest rate of 6 percent per year. What is the remaining balance (or value) of the mortgage after the payment of the fifth annual installment?

$211,689.53 Step 1: I = 6%; N = 20; PV = 250,000; FV = 0. Compute PMT = 21,796.14. Step 2: I = 6%; N = 15; PMT = 21,796.14. Compute PV = 211,689. 53.

Mr. Hopper expects to retire in 30 years, and he wishes to accumulate $1,000,000 in his retirement fund by that time. If the interest rate is 12 percent per year, how much should Mr. Hopper put into his retirement fund at the end of each year in order to achieve this goal?

$4,143.66 Future value annuity factor = [(1.12^30 - 1]/(0.12) = 241.3327; payment = 1,000,000/241.3327 = 4143.66.

Company Z's earnings and dividends per share are expected to grow indefinitely by 4% a year. If next year's dividend is $4 and the market capitalization rate is 12%, what is the current stock price?

$50.00 P0 = DIV1 / (r − g) P0 = $4 / (0.12 − 0.04) P0 = $50.00

Mr. Free has $100 income this year and zero income next year. The market interest rate is 10 percent per year. If Mr. Free consumes $30 this year and invests the rest in the market, what will be his consumption next year?

$77 (100 − 30) × (1.1) = 77.

Mr. Thomas has $100 income this year and zero income next year. The market interest rate is 10 percent per year. Mr. Thomas also has an investment opportunity in which he can invest $50 this year and receive $80 next year. Suppose Mr. Thomas consumes $50 this year and invests in the project. What will be his consumption next year?

$80 (100 - 50 - 50) × 1.1 + 80 = 80

The present value of $100,000 expected at the end of one year, at a discount rate of 25 percent per year, is:

$80,000. PV = (100,000)/(1 + 0.25) = 80,000.

After retirement, you expect to live for 25 years. You would like to have $75,000 income each year. How much should you have saved in your retirement account to receive this income, if the annual interest rate is 9 percent per year? (Assume that the payments start on the day of your retirement.)

$802,995.88 PV = [[(1/0.09) - (1/((0.09)(1.09^25)))] × 75,000] × (1.09) = 802,995.88. Alternatively, [(75,000/.09) × [1 - (1/(1.09^25)]] × (1.09) = 802,995.88.

A three-year bond has an 8.0 percent coupon rate and a $1,000 face value. If the yield to maturity on the bond is 10 percent, calculate the price of the bond assuming that the bond makes semiannual coupon payments.

$949.24 PV = (40/1.05) + (40/(1.05^2)) + . . . + (1040/(1.05^6)) = $949.24. Alternatively, the semiannual payment = (1,000) × (0.08/2) = $40.The semiannual yield = (10%)/2 = 5%.Using a financial calculator, PMT = 40; FV = 1,000; N = (3 × 2); I = 5,Compute PV = 949.24.

Monte Carlo simulation involves the following steps: I) Step 1: Modeling the project; II) Step 2: Specifying probabilities; III) Step 3: Simulating cash flows; IV) Step 4: Calculating present value

1,2,3,4

A bond has a face value of $1,000, an annual coupon rate of 7 percent, yield to maturity of 10 percent, and 20 years to maturity. The bond's duration is

10.0 years Step 1: N = 20; PMT = 70; FV = 1,000; I = 10. Compute PV = 744.59. Step 2: Duration = [((1)(70)/1.1) + ((2)(70)/1.1^2) + . . . + ((20)(1070)/1.1^20)]/744.59 = 10 years.

A bond has a face value of $1,000, a coupon rate of 0 percent, yield to maturity of 9 percent, and 10 years to maturity. This bond's duration is

10.0 years.

A bond has a face value of $1,000, a coupon rate of 0 percent, yield to maturity of 9 percent, and 10 years to maturity. This bond's duration is

10.0 years. Duration is equal to maturity for zero-coupon bonds.

Consider a bond with a face value of $1,000, an annual coupon rate of 6 percent, a yield to maturity of 8 percent, and 10 years to maturity. This bond's duration is

7.6 years Step 1: N = 10; PMT = 60; FV = 1,000; I = 8. Compute PV = 865.80. Step 2: Duration = [1(55.56) + 2(51.44) + 3(47.63) + 4(44.10) + 5(40.83) + 6(37.81) + 7(35) + 8(32.42) + 9(30.01) + 10(490.99)]/(865.80) = 7.6 years.

The survey of CFOs indicates that the NPV method is always, or almost always, used for evaluating investment projects by approximately

75 percent of firms

Consider the following cash flows: Cash Flows ($)C0C1C2−8,5506,30021,600 a. Calculate the net present value of the above project for discount rates of 0, 50, and 100%. b. What is the IRR of the project?

@0: 19350 @50: 5,250 @100: 0 b. 100% a. NPV = −$8,550 + $6,300 / (1 + 0) + $21,600 / (1 + 0)2 = $19,350 NPV = −$8,550 + $6,300 / (1 + 0.50) + $21,600 / (1 + 0.50)2 = $5,250 NPV = −$8,550 + $6,300 / (1 + 1) + $21,600 / (1 + 1)2 = $0 b.100%; NPV = 0 when the discount rate is 100 percent.

Which bond is more sensitive to an interest rate change of 0.75 percent? Bond A: YTM = 4.00%, maturity = 8 years, coupon = 6% or $60, par value = $1,000. Bond B: YTM = 3.50%, maturity = 5 years, coupon = 7% or $70, par value = $1,000.

Bond A Volatility increases with duration. A relatively longer maturity or a relatively smaller coupon are both features that extend a bond's duration. The price of bond A decreases from 1,134 to 1,108. Bond B decreases in price from 1,158 to 1,121. Bond A drops by 4.67 percent while Bond B drops by 3.15 percent.

The yield to maturity on a bond is really its internal rate of return.

True

A project's "book value" represents, essentially, the market valuation of the project.

False

In the United States, most bonds make coupon payments annually.

False

In the case of a loan project (borrowing), one should accept the project if the IRR is more than the cost of capital.

False

Short-term and long-term interest rates always move in parallel.

False

The discounted payback method calculates the payback period and then discounts the payback period at the opportunity cost of capital.

False

The duration of any bond is the same as its maturity.

False

Treasury bills typically provide higher average returns, both in nominal terms and in real terms, than long-term government bonds.

False

Which of the following statements most appropriately describes scenario analysis?

It looks at different but consistent combinations of variables.

How does modified internal rate of return (MIRR) differ from IRR?

MIRR reduces the number of sign changes in a cash flow sequence.

We can imagine the financial manager doing several things on behalf of the firm's stockholders. But in well-functioning capital markets, shareholders will vote for only one of these goals. Which one?

Make shareholders as wealthy as possible by investing in real assets.

You have the chance to participate in a project that produces the following cash flows: Cash Flows ($)C0C1C2-4,7004,300-10,900 a. The internal rate of return is 13.26%. If the opportunity cost of capital is 10%, what is the NPV of the project? b. Would you accept the offer?

NPV: -9,799..17 b: No

In the principal-agent framework

Shareholders are the principals and managers are the agents

Two bonds have the same maturity, risk rating, and face value, but have different coupon rates. The bond with a lower coupon rate will have a longer duration.

True

Which of the following does not represent an option to abandon a project?

Your friend builds a custom-made home.

Which of the following portfolios has the least risk?

a portfolio of Treasury bills

Which of the following statements is true? The process of discounting is the inverse of the process of compounding. Ending balances using simple interest are always greater than ending balances using compound interest at positive interest rates. The present value of an annuity due is always less than the present value of an equivalent ordinary annuity at positive interest rates. The future value of an annuity due is always less than the present value of an equivalent ordinary annuity at positive interest rates.

The process of discounting is the inverse of the process of compounding.

Which of the following statements about the relationship between interest rates and bond prices is true?

There is an inverse relationship between bond prices and interest rates, and the price of long-term bonds fluctuates more than the price of short-term bonds for a given change in interest rates (assuming that the coupon rate is the same for both).

A corporation has a legal existence of its own and is based on "articles of incorporation."

True

A risk premium generated by comparing stocks to 10-year U.S. Treasury bonds will be smaller than a risk premium generated by comparing stocks to U.S. Treasury bills.

True

If the term structure of interest rates is flat, then the 9-year spot interest rate equals the 10-year spot interest rate.

True

Long-term spot rates are usually higher than short-term spot rates.

True

Present values have the value additivity property.

True

The U.S. Treasury issues inflation-indexed bonds known as TIPS.

True

The board of directors is ultimately responsible for all large investment decisions.

True

The payback rule ignores all cash flows after the cut-off date.

True

The profitability index of a positive NPV project is always positive.

True

Costs associated with the conflicts of interest between the managers and the shareholders of a corporation are called:

agency costs

Disadvantages of the corporate form include...

agency costs double taxation cost of managing the corporation *all of the options*

The rate of return is also called the...

discount rate, hurdle rate, opportunity cost of capital

Suppose a firm has $100 million in excess cash. It could

do all of the options: invest the funds in projects with positive NPVs. pay high dividends to the shareholders. buy another firm.

The volatility of a bond is given by

duration/(1 + yield) and slope of the curve relating the bond price to the interest rate only.

If a bond pays interest semiannually, then it pays interest

every six months

The sale of financial assets by a corporation is also referred to as the...

financing decision

What has been the average annual rate of return in real terms for a portfolio of U.S. common stocks between 1900 and 2017?

greater than 8%

As CFO of your corporation, you would prefer (all else equal) to see the price of your corporation's bonds

increase, indicating that bond investors view your firm as less risky.

If a bond's volatility is 10.00 percent and the interest rate goes down by 0.75 percent (points), then the price of the bond

increases by 7.50 percent Percentage change in bond price = -(volatility) × (change in interest rates) = -10 × (-0.75) = +7.5%

What has been the average annual real rate of interest on Treasury bills over the past 117 years (from 1900 to 2017)?

less than 2%

Which of the following is an important function of financial markets?

providing financing, providing liquidity, reducing risk, and providing information

The IRR is defined as

the discount rate that makes a project's NPV equal to zero

If the cash flows for project A are C0 = −1,000; C1 = +600; C2 = +400; and C3 = +1,500, calculate the payback period.

two years Initial investment: 1,000 = CF1 + CF2 = 600 + 400; payback period = 2 years.