FIN 300 Lecture 4: Chapters 5 & 6

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31 Oct 2016

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Example: borrow today, return in 10 years yes or no, in 10 years, in 20 years, in 30 years (given 4% annual interest rate) Future value: future value is the amount to which an investment will grow after earning interest. Interest can be of two types: simple interest: interest is earned only on the original investment, compound interest: interest is earned on the interest. You invest in an account paying simple interest at the rate of 6% per year. Fv = x (1 + 5 x 6%) You invest in an account paying compound interest at the rate of 6% per year. How much will the account be worth in 5 years: answers: Interest earned in year 1 = x 6% Interest earned in year 2 = x 6% Interest earned in year 3 = . 36 x 6% Interest earned in year 4 = . 10 x 6%

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QUESTION 1 The time value of money refers to the issue of: A. what the value of the stream of future cash flows is today. B. why a dollar received tomorrow is worth more than a dollar received today. C. what the time required to double an amount of money. D. why people prefer to consume things at some time in the future rather than today.

QUESTION 2 The process of converting an amount given at the present time into a future value is called: A. annualizing. B. discounting. C. compounding. D. capital budgeting. 2 points

QUESTION 3 Juan Vinson is planning to buy a house in five years. He is looking to invest $25,000 today in an index mutual fund that will provide him a return of 12 percent annually. How much will he have at the end of five years? (Round to the nearest dollar.) A. $45,000 B. $28,000 C. $44,059 D. $28,530 2 points

QUESTION 4 Which of the following statements is true with respect to the present value of a future amount? A. The higher the discount rate, the higher the present value of a single sum for a given time period. B. The relation between present value and time is exponential. C. The greater the time period, the higher the present value of a single sum for a given interest rate. D. The lower the discount rate, the lower the present value of a single sum for a given time period. 2 points

QUESTION 5 Which of the following statements is true of the rule of 72? A. It can be used to determine the amount of time it takes to double an investment. B. It is fairly accurate for interest rates between 25 and 50 percent. C. It states that the time to double your money (TDM) approximately equals 72/i, where i represents the years it takes to double your investment. D. It can be used to estimate approximate compound interest earned for a period of 72 days. 2 points

QUESTION 6 The present value of future cash flows are computed by multiplying future value with the: A. discounting factor. B. compound factor. C. interest rate. D. number of periods. 2 points

QUESTION 7 The present value of multiple cash flows is: A. greater than the sum of the cash flows. B. equal to the sum of all the cash flows. C. less than the sum of the cash flows. D. higher or lower than the cash flows depending on the interest rate. 2 points

QUESTION 8 Cash flows associated with annuities are considered to be: A. an uneven cash flow stream. B. a constant cash flow stream. C. a mix of constant and uneven cash flow streams. D. a cash flow stream with decreasing trend. 2 points

QUESTION 9 The annuity transformation method is used to transform: A. a present value annuity to a future value annuity. B. a present value annuity to an annuity due. C. an ordinary annuity to an annuity due. D. a perpetuity to an annuity. 2 points

QUESTION 10 The true cost of borrowing is the: A. annual percentage rate. B. effective annual rate. C. quoted interest rate. D. periodic rate.

8. You have saved $250,000 for a cash down payment to buy a house. You are currently prepared to
pay up to $3,000 per month for a 20-year mortgage, and your bank is currently charging 4% p.a.
interest, compounded monthly. What amount is closest to the maximum you can pay for a house?
A) $633,453
B) $745,066
C) $824,204
D) $1,205,365
E) None of the above
9. You have just accepted a job offer, which came with a signing bonus of $5,000 to be paid today
in your retirement account. Your employer will also contribute an extra $10,000 at the end of
each full year (you start work tomorrow!). If this account is expected to earn 10% p.a.
compounded semi-annually, which number is closest to the amount of money will you have in
that account after five years? (including the payment for that year).
A) $59,500
B) $65,500
C) $69,500
D) $72,500
E) None of the above
10. Which of the following is/are an advantage of being a publicly listed company?
A) Access to capital markets
B) Limited liability
C) Unlimited life
D) All of the above
E) None of the above
11. A bond with 15 years to maturity is paying 6% coupons semi-annually, and the last coupon has
just been paid. The face value is $1,000 and the yield to maturity is 8% p.a.
What is the price today closest to:
A) $827.08
B) $932.95
C) $1,000.00
D) $1,324.32
E) None of the above
12. Company HDE is expected to pay an interim dividend of $1.00 six months from now and a final
dividend of $2.10 one year from now. HDE is then expected to repeat the same pattern every year
for the foreseeable future with no growth in dividends. Given that the appropriate effective
discount rate is 7.0% p.a., what is the stock price of HDE closest to today?
A) $30
B) $35
C) $40
D) $45
E) None of the above
13. Which of the following statements is FALSE?
A) The process of moving a value or cash flow forward in time is known as compounding.
B) The effect of earning interest on interest is known as compound interest.
C) It is only possible to compare or combine values at the same point in time.
D) A dollar in the future is worth more than a dollar today.
E) Interest paid only on the principal is simple interest.
14. Consider the following four alternatives:
1. $132 received in two years.
2. $160 received in five years.
3. $200 received in eight years.
4. $220 received in ten years.
The ranking of the four alternatives from most valuable to least valuable if the interest rate is
7% per year would be:
A) 1, 2, 3, 4
B) 4, 3, 2, 1
C) 3, 4, 2, 1
D) 3, 1, 2, 4
E) 3, 1 = 2, 4

Assume that you are nearing graduation and that you have appliedfor a job with a local bank. As part of the bankâs evaluationprocess, you have been asked to take an examination that coversseveral financial analysis techniques. The first section of thetest addresses time value of money analysis. See how you would doby answering the following questions:

a. Drawcash flow time lines for (1) a $100 lump-sum cash flow at the endof Year 2, (2) an ordinary annuity of $100 per year for threeyears, (3) an uneven cash flow stream of $50, $100, $75, and $50 atthe end of Years 0 through 3.

b. (1)What is the future value of an initial $100 after three years if itis invested in an account paying 10%annual interest?

(2) What is the present value of $100 to bereceived in three years if the appropriate interest rate is10%?

c. Wesometimes need to find how long it will take a sum of money (oranything else) to grow to some specified amount. For example, if acompanyâs sales are growing at a rate of 20%per year, approximatelyhow long will it take sales to triple?

d. Whatis the difference between an ordinary annuity and an annuity due?What type of annuity is shown in the following cash flow time line?How would you change it to the other type of annuity?

0 1 2 3

100 100 100

e. (1)What is the future value of a 3-year ordinary annuity of $100 ifthe appropriate interest rate is 10%?

(2) What is the present value of the annuity?

(3) What would the future and present values be ifthe annuity were an annuity due?

f. What is the present value of the following uneven cash flow stream?The appropriate interest rate is 10%, compounded annually.

0 1 2 3 4

100 300 300 150

g. Whatannual interest rate will cause $100 to grow to $125.97 in 3years?

h. (1)Will the future value be larger or smaller if we compound aninitial amount more often than annuallyâfor example, every 6months, or semiannuallyâholding the stated interest rateconstant? Why?

(2) Define the stated, or quoted, or simple, rate,(r_SIMPLE), annual percentage rate (APR), the periodicrate (r_PER), and the effective annual rate(r_EAR).

(3) What is the effective annual rate for a simplerate of 10%, compounded semiannually? Compounded quarterly?Compounded daily?

(4) What is the future value of $100 after threeyears under 10%semiannual compounding? Quarterly compounding?

i. Will the effective annual rate ever be equal to the simple (quoted)rate? Explain.

j. (1) What is the value at the end of Year 3 of thefollowing cash flow stream if the quoted interest rate is 10%,compounded semiannually?

0 1 2 3

100 100 100

(2) What is the PV of the same stream?

(3) Is the stream an annuity?

(4) An important rule is that you should nevershow a simple rate on a time line or use it in calculations unlesswhat condition holds? (Hint: Think of annual compounding,when r_SIMPLE = r_EAR = r_PER.) Whatwould be wrong with your answer to parts (1) and (2) if you usedthe simple rate 10%rather than the periodic rater_SIMPLE/2 = 10%/2 = 5%?

k. (1)Construct an amortization schedule for a $1,000 loan that has a10%annual interest rate that is repaid in three equalinstallments.

(2) What is the annual interest expense for theborrower, and the annual interest income for the lender, duringYear 2?

l. Suppose on January 1 you deposit $100 in an account that pays asimple, or quoted, interest rate of 11.33463%, with interest added(compounded) daily. How much will you have in your account onOctober 1, or after 9 months?

m. Now suppose youleave your money in the bank for 21 months. Thus, on January 1 youdeposit $100 in an account that pays a 11.33463%compounded daily.How much will be in your account on October 1 of the followingyear?

n. Suppose someone offered to sell you a note that calls for a $1,000payment 15 months from today. The person offers to sell the notefor $850. You have $850 in a bank time deposit (savings instrument)that pays a 6.76649%simple rate with daily compounding, which is a7%effective annual interest rate; and you plan to leave this moneyin the bank unless you buy the note. The note is not riskyâthat is,you are sure it will be paid on schedule. Should you buy the note?Check the decision in three ways: (1) by comparing your futurevalue if you buy the note versus leaving your money in the bank,(2) by comparing the PV of the note with your current bankinvestment, and (3) by comparing the r_EAR on the notewith that of the bank investment.

o. Suppose the note discussed in part n, above, costs $850, but callsfor five quarterly payments of $190 each, with the first paymentdue in 3 months rather than $1,000 at the end of 15 months. Wouldit be a good investment?

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FIN 300 Lecture 4: Chapters 5 & 6

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