Agricultural Economics 330



Agricultural Finance

Problems: Introduction and the Time Value of Money

Instructor: Dr. David J. Leatham

Definitions

1. A single period profit maximization objective function is not sufficient for a financial manager because it ignores and .

2. : The yield of an investment, i.e., the rate that makes the present value of the cash inflows equal to the present value of the cash outflows.

3. : A series of payments of a fixed amount for a specified number of periods.

4. : The present value of future (remaining) payments of any contract discounted at the market rate.

5. : A period of time that principal accrues interest before interest is added to principal.

True or False. Circle the most correct answer. If False, justify your answer.

T F A risk averse individual is someone that is not willing to take risk.

T F Most individuals don't like to take risk (risk averse) but are willing to invest in risky projects if they are compensated for taking risk.

T F Usually an investment with a higher expected profit also has a higher risk when compared to other similar investments.

T F The yield on an investment is always equal to the discount rate.

T F Suppose that you purchase a bond that matures in 10 years for $875.38. The bond has a par value of $1,000, and pays a coupon of eight percent semiannually (8% is an annual rate). If you plan to sell the bond at the end of five years and you expect that the bond will have a market rate of 12% when you sell it, the annual yield on this five year investment would be less than eight percent. Justify your answer.

T F The market value of a contract will increase as interest rates increase, holding everything else constant.

T F The yield on an investment increases as the purchase price of the investment goes up, holding everything else constant.

T F The process of converting a single sum of money today to an equivalent amount in some future time period is called discounting.

T F The book value of a contract will increase as interest rates decrease, holding everything else constant.

T F Suppose you are asked to find the present value of a future sum of money. The present value will be greater than the future sum of money if the discount rate is positive.

T F The present value of an annuity can be calculated by finding the present value of each sum of money in the annuity and adding the respective present values together.

T F Interest rates are considered an exchange price between present and future dollars.

T F If only the time value of money is considered (e.g., ignore risk & inflation), $100 today is equivalent to $259.37 10 years from today if interest rates are 10% compounded annually. Show work.

T F If you have already purchased bonds, you want interest rates (market rates) on bonds to increase, holding everything else constant.

T F The uniform series future value factor [USFVr,N] is based on beginning of period cash flows.

T F Holding everything else constant, if the yield on bonds go up, the price of bonds will also go up. Explain.

T F Principal is a tax deductible expense.

T F The book value (tax basis) of an asset is always less than its market value.

Problems

1. There are two investments available. Investment A has an expected profit of $100 and a standard deviation of $70. Investment B has a probability distribution of profit as follows:

|Profit |Probability |

|$ 10 |0.25 |

|$100 |0.50 |

|$210 |0.25 |

A. Calculate the expected value, variance, standard deviation, and coefficient of variation for investment B (show all your work).

B. Which investment is the best for a risk averse individual? Show graphically and explain. Use back of paper if needed.

2. Suppose you want to purchase a Ford Mustang five years from today.

A. If you expect the Mustang will cost $30,000, how much money will you need to deposit in your bank account quarterly starting three months from today in order to pay cash for the car in five years? Assume that the last payment will be made in five years from today and that the bank pays 4% interest (compounded quarterly).

B. If you deposit $24,586.33 in your bank account today, how many years will you have to wait before you have $30,000 in your account? Assume that the bank pays 4% interest (compounded quarterly).

3. An investment promises to pay the following sums of money in the designated time periods and the market yield on such investments is 10%:

|0 |1 |2 |3 |4 |5 |6 |7 |

|$0 |$400 |$400 |$400 |$400 |$400 |$400 |$1,000 |

A. Calculate its Market Value.

B. Calculate its Value at the end of the 7th year.

C. Explain why the annuity given above and the values obtained in 1.A and 1.B are equivalent.

4. If a bond is listed at 8s April 18, 2000 (par value = $1,000) and is sold for $883.10, what is the semiannual and annual yield on this bond? [SHOW TIME LINE AND FACTORS]

5. If you had $18,115.62 to deposit today in Citizens Savings Bank at 8 percent (compounded quarterly), how many years would you have to wait before you could pay $40,000 in cash for a new Mercedes?

6. Five years ago you incurred a 15-year term loan that required annual payments of $2,000 per year. You have made four payments in previous years and the fifth payment is due today. The note holder proposes that you buy back this note today for $15,000. Would it pay you to borrow the money at the bank at 10% interest rate and buy back this note (hint: calculate the market value of the loan and compare with the price for which the bank is willing to sell you the note)?

7. Assume that you have a chance to buy a bond that matures in 6 years, has a par value of $100,000, pays a coupon of 8 percent semiannually , and has a market rate of 6% (remember that the 8% and 6% are annual rates, respectively). Answer parts a-d even if some parts of the problem are wrong. Partial credit will be given.

A. Calculate the market value of the bond described above.

B. Calculate the market value of the bond described above at the end of three years from today if the market rate (yield) on comparable bonds increases to 12%.

C. Calculate the net present value of this bond investment if you plan to buy the bond described in part a and plan to sell the bond in three years at the price calculated in part b. Assume that you require a 5% rate of return on capital (convert this to a semiannual rate).

D. The annual yield (internal rate of return) on the investment presented in part c is (Show your work, and circle the correct answer)

(1) less than 2%, or

(2) greater than 2%.

8. Suppose you deposit $3,500 today in a savings account at 4.0% interest compounded annually. Assuming no withdrawal, how much would you have at the end of 10 years?

9. Suppose you deposit $100 today in a savings account paying 5% interest compounded annually. How many years would you need to leave it in the bank before you had $121.55 in your bank account?

10. Given the following information, calculate the gross ratio for a farm firm (show your work):

Beginning Farm Assets $490,000

Ending Farm Assets 510,000

Beginning Farm Liabilities 200,000

Ending Farm liabilities 200,000

Net Income from farm operations (before taxes) 34,000

Nonfarm Income 20,000

Total farm expenses 220,000

Net Income after-tax 39,000

Interest on Farm loans (cash) 15,000

Change in Accrued Interest 1,000

Taxes 15,000

11. Suppose you have an opportunity to buy an annuity that promises to pay $400 at the end of the year for the next six years (there will be six $400 payments):

A. How much should you pay for the annuity if you have other comparable investment opportunities that have a 6% rate of return?

B. Based on the price you pay for the annuity in 3.A, how much interest would you earn over the six years if you buy the annuity?

Essay

1. Define the turnover ratio:

Multiple Choice

1. A risk averse decision maker will

A. not take any risk;

B. take some risk if compensated;

C. likes to gamble;

D. choose the investment with the highest expected profit.

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