Accounting Mathematical Assistant

9/20/23, 9:18 PM Assignment Print View

8. Award: 4.76 points

The appropriate annual discount rate for the following cash flows is 7 percent compounded quarterly.

HINT: even though there is a series of cash flows, we can't use the annuity equation since the cash flows aren't constant (or growing at a constant rate). Instead you must value the cash flows using the chapter 5 formula for single cash flow, and then add them all together.

The twist here is that the compounding of interest is not annual, but the cash flows are. So when you use the

chapter 5 formula PV = FV / (1+r)t , you must first convert the APR into an EAR. Alternatively, you could simply change t to represent the number of compounding periods (4 in each year) and use the true quarterly discount rate as r, which in this case is APR/4.

Year Cash Flow  1        $600  2          800  3       0  4  1,100

Required:

What is the present value of the cash flows?

$756.56

$2,089.28

$2,047.49

$2,131.07

$2,098.68

References

Multiple Choice Difficulty: Basic Learning Objective: 06-1

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9/20/23, 9:19 PM Assignment Print View

9. Award: 4.76 points

You took out a loan with an effective annual interest rate of 9 percent.

What is the equivalent 18-month interest rate on this loan? Note: I don't want the APR, I want the EPR (the actual interest rate charged over 18 months).

(Click to select)

rev: 09_17_2012

References

Worksheet Learning Objective: 06-04 How interest rates are quoted (and misquoted).

Difficulty: Intermediate Section: 6.3 Comparing Rates: The Effect of Compounding

9/20/23, 9:19 PM Assignment Print View

10. Award: 4.76 points

You took out a loan with an effective annual interest rate of 7 percent.

What is the equivalent quarterly (3 month) interest rate on this loan? Note: I don't want the APR, I want the EPR (the actual 3-month interest rate).

(Click to select) 09_17_2012

References

Worksheet Learning Objective: 06-04 How interest rates are quoted (and misquoted).

Difficulty: Intermediate Section: 6.3 Comparing Rates: The Effect of Compounding

9/20/23, 9:19 PM Assignment Print View

11. Award: 4.76 points

Your mother retired today and has the option of purchasing an annuity. If she exchanges $39,000 of her savings today for a 6.80 percent, 17-year annuity, what will her annual cash flow be? (Unless stated otherwise, always assume the first payment is received at the end of the period, not the start).

NOTE: You are exchanging cash today for a series of cash flows. This is an annuity problem (chapter 6), where we the value of the annuity is defined at the START of all the cash flows, so use the present value of

an annuity equation . You already know what the annuity is worth today (PVA), the

number of payments (t), as well as the discount rate (r). You only need to calculate C, the size of the cash flow.

$4,218.68

$10,104.00

$3,939.42

$3,668.99

$2,294.12

References

Multiple Choice Difficulty: Basic Learning Objective: 06-1

P = CVA

1−(1+r)−N

r

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9/20/23, 9:19 PM Assignment Print View

12. Award: 4.76 points

You want to have $45,000 in your savings account 3 years from now, and you're prepared to make equal annual deposits into the account at the end of each year. If the account pays 7.5 percent interest each year, what amount must you deposit each year?

NOTE: You are exchanging cash today for a series of cash flows. This is an annuity problem (chapter 6) where we the value of the annuity is defined at the END of all the cash flows, so use the future value of an annuity

equation, . You already know what the annuity is targeted to be worth in the future (FVA),

the number of payments (N), as well as the discount rate (r). You only need to calculate C, the size of the cash flow.

$3,374.95

$3,375.04

$13,929.19

$15,000.00

$16,973.69

References

Multiple Choice Difficulty: Basic Learning Objective: 06-1

F = CVA

−1(1+r)N

r

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9/20/23, 9:20 PM Assignment Print View

13. Award: 4.76 points

Suppose you are going to receive $23,000 per year for 10 years. The appropriate interest rate is 7 percent per year.

Requirement 1: (a)What is the present value of the payments if they are in the form of an ordinary annuity (cash flow starts

at the end of the first compounding period)?

(Click to select)

(b)What is the present value if the payments are an annuity due (cash flow starts at the beginning of the first compounding period)?

(Click to select)

Requirement 2: (a)Suppose you plan to invest the payments for 10 years, what is the future value if the payments are an

ordinary annuity?

(Click to select)

(b)Suppose you plan to invest the payments for 10 years, what is the future value if the payments are an annuity due?

(Click to select)

References

Worksheet Difficulty: Intermediate Learning Objective: 06-1

9/20/23, 9:20 PM Assignment Print View

14. Award: 4.76 points

Staal Corporation will pay a $2.98 per share dividend next year. The company pledges to increase its dividend by 5 percent per year indefinitely. If you require a return of 14 percent on your investment, how much will you pay today for one share of the company’s stock? (Round your answer to 2 decimal places. (e.g., 32.16))

NOTE: Dividends are payments made to shareholders. In general the payments are assumed to be quarterly unless otherwise stated (as in this problem). In this problem the dividend is annual and grows at a constant rate in perpetuity.

Stock price $

References

Worksheet Difficulty: Basic Learning Objective: 08-01 How stock prices depend on future dividends and dividend growth.

9/20/23, 9:21 PM Assignment Print View

15. Award: 4.76 points

Given an interest rate of 8.5 percent per year, what is the value at date t = 9 of a perpetual stream of $700 payments that begins at date t = 17?

NOTE: Valuing a perpetuity is easy: PVp = C/r. This equation gives you the value one period before the cash

flows start. But in this problem the cash flows don't start in one period, so when you use the present value equation you are actually calculating the value of the perpetuity at time t = 16, or one period before the cash flows begin. 

$4,652.33

$8,235.29

$4,287.87

$4,559.29

$4,745.38

References

Multiple Choice Difficulty: Intermediate Learning Objective: 06-1

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9/20/23, 9:21 PM Assignment Print View

16. Award: 4.76 points

You grandfather won a lottery years ago. The value of his winnings at the time was $50,000. He invested this money such that it will provide annual payments of $2,400 a year to his heirs forever. What is the rate of return?

4.75 percent

4.80 percent

5.00 percent

5.10 percent

5.15 percent

References

Multiple Choice Learning Objective: 06-2

Difficulty: Basic Section: 6.2

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9/20/23, 9:21 PM Assignment Print View

17. Award: 4.76 points

Lane, Inc., has an issue of preferred stock that pays a $3.55 dividend every quarter in perpetuity. If this stock currently sells for $91, what is the effective annual required return? (Round your answer to 2 decimal places and report as a percent. (e.g., 32.16%)) HINT: Don't forget to use an annual effective interest rate, not a quarterly rate or an APR.

Required return %

References

Worksheet Difficulty: Basic Learning Objective: 08-01 How stock prices depend on future dividends and dividend growth.

9/20/23, 9:21 PM Assignment Print View

18. Award: 4.76 points

Atlas Insurance wants to sell you an annuity which will pay you $600 per quarter for 30 years. You want to earn a minimum annual rate of return of 5.0 percent with quarterly compounding. What is the most you are willing to pay as a lump sum today to buy this annuity?

$32,868.16

$32,411.57

$37,189.71

$31,207.66

$36,893.88

References

Multiple Choice Learning Objective: 06-2

Difficulty: Basic Section: 6.2

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9/20/23, 9:22 PM Assignment Print View

19. Award: 4.76 points

Your car dealer is willing to lease you a new car for $299 a month for 60 months. Payments are due on the first day of each month starting with the day you sign the lease contract. If your annual interest rate is 4.9 percent with monthly compounding, what is the current value of the lease?

$15,947.61

$16,246.61

$16,181.75

$15,915.18

$15,882.75

References

Multiple Choice Learning Objective: 06-2

Difficulty: Basic Section: 6.2

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9/20/23, 9:22 PM Assignment Print View

20. Award: 4.76 points

Grohl Co. issued 14-year bonds at a coupon rate of 9 percent. The bonds make semiannual payments. If the yield to maturity on these bonds is 7 percent, what is the current bond price?

Reminder from undergraduate class: Coupon bonds pay interest (called the coupon) on the face value (amount originally borrowed and to be re-paid at maturity). The discount rate implicit in the bond's price is called the yield to maturity, or simply the yield. The bond's face value should be assumed to be $1,000 and the annual coupon is paid in two installments, unless otherwise stated. Note that bond yields and coupons are always quoted as APRs. So if the problem quotes a 10% coupon bond that matures in 5 years, the bond actually pays $50 (or 5% of $1,000) every 6 months (which is 10% of face value over one year), and there would be 10 coupons to be paid (2 each year for 5 years).

We value all assets by calculating the present value of future cash flows generated by the asset. Coupon bonds have two types of cash flow: the coupons (interest payments) which are paid every six month, and the repayment of the face value (which is the original amount borrowed). So to value a coupon bond you use the yield to maturity to value the coupons as an annuity, and then add the present value of the payment of $1,000 (the face value, which is re-paid at maturity).

$1,622.35

$1,176.67

$639.27

$1,120.17

$1,186.67

References

Multiple Choice Difficulty: Basic Learning Objective: 07-02 Bond values and yields and why they fluctuate.

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9/20/23, 9:22 PM Assignment Print View

21. Award: 4.80 points

The Pocatello Pokeys have just hired a new team manager. The contract requires  $26,000,000 be paid to the manager after she completes 9 years of service. The team wants to set aside an equal amount of money each year to cover this payment. If the team earns 8 percent on their investments, how much must the team set aside each year? Assume they set aside the first payment at the end of the year. 

$2,292,092.43

$2,016,695.36

$2,082,072.44

$2,011,281.98

$2,080,000.00

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9/20/23, 9:17 PM Assignment Print View

3. Award: 4.76 points

Big Dom's Pawn Shop charges an interest rate of 17 percent per month on loans to its customers. Like all lenders, Big Dom must report an APR to consumers.

Required : (a) What rate should the shop report (APR)?

(Click to select)

(b) What is the actual effective annual rate (EAR)?

(Click to select)

References

Worksheet Difficulty: Basic Learning Objective: 06-4