Problem 2-08

The following information is available concerning the historical risk and return relationships in the U.S. capital markets:

1. Explain why the geometric and arithmetic mean returns are not equal and whether one or the other may be more useful for investment decision making.

   The arithmetic average assumes -Select-compounding or interest-on-interest; the presence of simple interest Item 1 , while the geometric average assumes -Select-compounding or interest-on-interest; the presence of simple interest Item 2 .

2. For the time period indicated, rank these investments on a relative basis using the coefficient of variation from most to least desirable. Do not round intermediate calculations. Round your answers to two decimal places.

   Rank	Investment Category	Сoefficient of variation, %
   1	-Select-Common Stocks, Long-term corporate bonds, Long-term government bonds, Real estate, Treasury bills Item 3
   2	-Select-Common Stocks, Long-term corporate bonds, Long-term government bonds, Real estate, Treasury bills Item 5
   3	-Select-Common Stocks, Long-term corporate bonds, Long-term government bonds, Real estate, Treasury bills Item 7
   4	-Select-Common Stocks, Long-term corporate bonds, Long-term government bonds, Real estate, Treasury bills Item 9
   5	-Select-Common Stocks, Long-term corporate bonds, Long-term government bonds, Real estate, Treasury bills Item 11

3. Assume the arithmetic mean returns in these series are normally distributed. Calculate the range of returns that an investor would have expected to achieve 95 percent of the time from holding long-term government bonds. Do not round intermediate calculations. Round your answers to two decimal places. Use a minus sign to enter negative values, if any.

   Arithmetic: from   % to    %

Below is a list of prices for $1,000-par zero-coupon Treasury securities of various maturities. An 11% coupon $100 par bond pays an semi-annual coupon and will mature in 1.5 years. What should be the YTM on the bond? Assume semi-annual interest compounding for this question. Maturity (periods) Price of $1,000 par bond

1 943.4

2 873.52

3 770

Equipment maintenance costs for manufacturing explosion-proof pressure switches are projected to be $125,000 in year one and increase by 2.5% each year through year five. What is the equivalent annual worth of the maintenance costs at an interest rate of 10% per year, compounded MONTHLY?

Please do not use excel and show formulas.

Nicki​ Johnson, a sophomore mechanical engineering​ student, receives a call from an insurance​ agent, who believes that Nicki is an older woman ready to retire from teaching. He talks to her about several annuities that she could buy that would guarantee her an annual fixed income. The annuities are as follows in the popup​ window: If Nicki could earn 9 percent on her money by placing it in a savings​ account, should she place it instead in any of the​ annuities? Which​ ones, if​ any? Why?

What rate of return could Nicki earn on her money if she place it in annuity A with $6,500 payment per year and 16 years duration?

Suppose you have access to the following bond data.

One year zero coupon bond, priced at 98, face value 100. Two year coupon bond, priced at 97. Annual coupons are $2, delivered at end of year. Three year coupon bond, priced at 96. Annual coupons are $3, delivered at the end of the year.

1. What is the coupon rate on the two-year coupon bond?

2. What is the current yield on the three-year coupon bond?

3. What is the yield-to-maturity of the three-year coupon bond?

4. Extract one year, two year, and three year spot rates from the bond data.

5. Using the spot rates, calculate the present value of $35 received in one year and $35 received in two years.

6. Using the spot rates, calculate the rate I should be able to lock in for a one year loan starting one year from now. Suppose now that you are a life insurance company projecting to pay benefits of $40 per year for the next 10 years to your policyholders. You are operating in an economy where the term structure of interest rates is completely flat at 4%, so that all spot rates are 4%.

7. Calculate the present value of your benefit obligations.

8. Calculate the duration of your benefit obligations.

9. Given your calculation above, if you were choosing a single type of bond from 1-year, 2-year, 3-year, 4-year, 5-year, 6-year, 7-year, 8-year, 9-year, and 10-year zero coupon bonds, which would serve you best from the perspective of asset-liability matching? In other words, if interest rates were to change, which bond’s price would move most closely with the present value of your obligations?

10. Calculate the percentage change in the value of your obligations if the interest rate were to drop from 4.0% to 3.9%.

11. Calculate the percentage change in the value of the bond you identified in (9) if the interest rate were to drop from 4.0% to 3.9%.

12. Calculate the percentage change in the value of a 1-year zero coupon bond if the interest rate were to drop from 4.0% to 3.9%.

13. (EXTRA CREDIT) If you were allowed to invest in more than one type of bond, could you provide a better match to your benefit obligations than you found in (9)? Propose a mix of bonds that would provide a better match, and verify that the percentage change in the value of the mix would more closely match the percentage change in obligation value in the interest rate scenario used in (10) through (12).

Bill has been adding funds to his investment account each year for the past 3 years. He started with an initial investment of $1,000. After earning a 10% return the first year, he added $3,000 to his portfolio. In this year his investments lost 5%. Undeterred, Bill added $2,000 the next year and earned a 2% return. Last year, discouraged by the recent results, he only added $500 to his portfolio, but in this final year his investments earned 8%. What was Bill's dollar-weighted average return for his investments?

You’ve just opened a margin account with $16,000 at your local brokerage firm. You instruct your broker to purchase 1,200 shares of Landon Golf stock, which currently sells for $28 per share. Suppose the call money rate is 7 percent and your broker charges you a spread of 1 percent over this rate. You hold the stock for 6 months and sell at a price of $35 per share. The company paid a dividend of $0.47 per share the day before you sold your stock. 1. What is your total dollar return from this investment? 2. What is your effective annual rate of return?

1. You started your investment with an opening deposit of $1,000.  Your portfolio grew as follows:

1. Calculate the average return and geometric return for eachyear.  
2. What is the arithmetic average of your returns?

What is your long-term geometric average?  (the average at end of year 10

please show me how you calculated using excel

Which costs are relevant to Brad's decision to purchase a new, larger boat? If Brad decides to purchase a larger boat, what costs will be affected by this decision? Will they increase or decrease? Identify any unavoidable costs associated with the operation of Fishing Unlimited. Calculate the revenue generated by a 6-hour trip with the old boat (6 guests) and the new boat (8 guests) and compare the two figures. Identify the costs that changed. What conclusion can you draw based on your analysis? Brad Winston is the owner and operator of Fishing Unlimited, a charter fishing business operated out of Oregon Inlet, NC. Brad has been taking groups of guests offshore to fish for tuna and marlin for over 15 years. He purchased his current fishing boat when he started the business but now believes that a larger and better-outfitted vessel would allow him to increase the rate he charges per charter. Currently, he can carry a maximum of 6 guests while the larger boat will carry up to 8. The larger boat would also require him to take 2 deckhands on each outing, providing better service to his customers. Cost data for Brad's business is shown in the table below.

Fishing Unlimited Annual straight-line depreciation on boat$ 8,300

($175,000 original cost - $90,000 estimated resale value/20 years)

Fuel Cost (per hour)$ 50 Insurance Premium (annual)$ 1,900

Maintenance and Repairs (annual)$ 3,500

Fishing Tackle and Gear (original cost)$ 7,000

Tackle and Bait (per guest)$ 20

Deck Hand wages (per hour)$ 20

Dock Fees (annual)$ 2,400

Captain's License (annual)$ 200

Food and Beverages (per guest)$ 25

Professional Fees (per year)$ 750

Dock Utilities (annual)$ 1,200 

Brad has someone interested in purchasing his existing boat for $80,000. He could use this cash as a deposit on the new boat which will cost him $225,000. His banker estimates the payments on the new boat will be about $1,500. The new boat is more fuel efficient and he believes he can cut his fuel costs by 10% but the more expensive boat will increase his insurance premium by 12%. He is also concerned that he will have to change to a larger boat slip which would increase his dock fees by 5%. The good thing about the new boat is that he should save on maintenance and repairs, at least for the first 3 years. The only other expense Brad would incur with the new boat is adding some additional fishing tackle and gear to accommodate larger parties that he estimates would cost him about $1,500.

His fees for both the old and the new boat are as follows: Old Boat 4 hours$ 550 6 hours$ 650 Full Day (9 hours)$ 1,100 New Boat 4 hours $ 600 6 hours $ 700 Full Day (9 hours) $1,200

Matta manufacturing is trying to decide between two different conveyor belt systems. System A costs $264,000, has a four year-life, and requires $81,000 in pretax annual operating costs. System B costs $372,000, has a six year life, and requires $75,000 in pretax annual operating costs. Both systems are to be depreciated straight-line to zero over their lives and will have zero salvage value. Whichever system is chosen, it will not be replaced when it wears out. The tax rate is 34 percent and the discount rate is 8 percent.

A/ Calculate the NPV for both conveyor belt systems

B/ Which conveyor belt system should the firm choose?

annual cash flow,

-500,000
125,000
150,000
175,000
200,000
250,000

What is the Modified IRR (MIRR), with a reinvestment rate equal to the WACC of 8%?

annual cash flow,

-500,000
125,000
150,000
175,000
200,000
250,000

What is the IRR of the investment

A borrower is offered a 30 year, fully amortizing ARM with an initial rate of 3.35%. After the first year, the interest rate will adjust each year, using 1 yr LIBOR as the index, plus a margin of 175bp. The price of the property is $8,000,000 and the loan will have an initial LTV ratio of 75% At the first reset date, 1 year LIBOR is at 3%. What is the borrower s payment during the 2nd year of the loan