*Corporate Finance, 4e ***(Berk / DeMarzo)**

**Chapter 5 Interest Rates**

** **

5.1 Interest Rate Quotes and Adjustments

1) Which of the following statements is FALSE?

- A) Because interest rates may be quoted for different time intervals, it is often necessary to adjust the interest rate to a time period that matches that of our cash flows.
- B) The effective annual rate indicates the amount of interest that will be earned at the end of one year.
- C) The annual percentage rate indicates the amount of simple interest earned in one year.
- D) The annual percentage rate indicates the amount of interest including the effect of compounding.

Answer: D

Diff: 1

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Conceptual

2) Which of the following equations is INCORRECT?

- A) – 1=
*APR* - B) Equivalent
*n*-Period Discount Rate = (1 +*r*)*n*– 1 - C) 1 +
*EAR*= - D) Interest Rate per Compounding Period =

Answer: A

Diff: 2

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Conceptual

3) The effective annual rate (EAR) for a loan with a stated APR of 8% compounded monthly is closest to:

- A) 7.72%
- B) 8.00%
- C) 8.30%
- D) 8.66%

Answer: C

Explanation: C) *EAR* = (1 + *APR/k*)*k* – 1 = (1 + .08/12)12 – 1 = .083 or 8.3%

Diff: 1

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

4) The effective annual rate (EAR) for a loan with a stated APR of 10% compounded quarterly is closest to:

- A) 9.65%
- B) 10.00%
- C) 10.38%
- D) 12.50%

Answer: C

Explanation: C) *EAR* = (1 + *APR/k*)*k* – 1 = (1 + .10/4)4 – 1 = .1038 or 10.38%

Diff: 1

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

5) The effective annual rate (EAR) for a savings account with a stated APR of 4% compounded daily (use 365 day year) is closest to:

- A) 3.92%
- B) 4.00%
- C) 4.08%
- D) 14.60%

Answer: C

Explanation: C) *EAR* = (1 + *APR/k*)*k* – 1 = (1 + .04/365)365 – 1 = .04088 or 4 .08%

Diff: 1

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

*Use the table for the question(s) below.*

Consider the following investment alternatives:

Investment |
Rate |
Compounding |

A | 6.25% | Annual |

B | 6.10% | Daily |

C | 6.125 | Quarterly |

D | 6.120 | Monthly |

6) Which alternative offers you the highest effective rate of return?

- A) Investment A
- B) Investment B
- C) Investment C
- D) Investment D

Answer: D

Explanation: D) *EAR* (A) = (1 + *APR/k*)*k* – 1 = (1 + .0625/1)1 – 1 = .0625 or 6.250%

*EAR* (B) = (1 + *APR/k*)*k* – 1 = (1 + .0610/365)365 – 1 = .06289 or 6.289%

*EAR* (C) = (1 + *APR/k*)*k* – 1 = (1 + .06125/4)4 – 1 = .06267 or 6.267%

*EAR* (D) = (1 + *APR/k*)*k* – 1 = (1 + .0612/12)12 – 1 = .06295 or 6.300%

Diff: 2

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

7) Which alternative offers you the lowest effective rate of return?

- A) Investment A
- B) Investment B
- C) Investment C
- D) Investment D

Answer: A

Explanation: A) *EAR* (A) = (1 + *APR/k*)*k* – 1 = (1 + .0625/1)1 – 1 = .0625 or 6.250%

*EAR* (B) = (1 + *APR/k*)*k* – 1 = (1 + .0610/365)365 – 1 = .06289 or 6.289%

*EAR* (C) = (1 + *APR/k*)*k* – 1 = (1 + .06125/4)4 – 1 = .06267 or 6.267%

*EAR* (D) = (1 + *APR/k*)*k* – 1 = (1 + .0612/12)12 – 1 = .06295 or 6.300%

Diff: 2

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

8) The highest effective rate of return you could earn on any of these investments is closest to:

- A) 6.250%
- B) 6.267%
- C) 6.295%
- D) 6.310%

Answer: C

Explanation: C) *EAR* (A) = (1 + *APR/k*)*k* – 1 = (1 + .0625/1)1 – 1 = .0625 or 6.250%

*EAR* (B) = (1 + *APR/k*)*k* – 1 = (1 + .0610/365)365 – 1 = .06289 or 6.289%

*EAR* (C) = (1 + *APR/k*)*k* – 1 = (1 + .06125/4)4 – 1 = .06267 or 6.267%

*EAR* (D) = (1 + *APR/k*)*k* – 1 = (1 + .0612/12)12 – 1 = .06295 or 6.300%

Diff: 2

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

9) The lowest effective rate of return you could earn on any of these investments is closest to:

- A) 6.150%
- B) 6.250%
- C) 6.289%
- D) 6.300%

Answer: B

Explanation: B) *EAR* (A) = (1 + *APR/k*)*k* – 1 = (1 + .0625/1)1 – 1 = .0625 or 6.250%

*EAR* (B) = (1 + *APR/k*)*k* – 1 = (1 + .0610/365)365 – 1 = .06289 or 6.289%

*EAR* (C) = (1 + *APR/k*)*k* – 1 = (1 + .06125/4)4 – 1 = .06267 or 6.267%

*EAR* (D) = (1 + *APR/k*)*k* – 1 = (1 + .0612/12)12 – 1 = .06295 or 6.300%

Diff: 2

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

* *

*Use the information for the question(s) below.*

Your firm needs to invest in a new delivery truck. The life expectancy of the delivery truck is five years. You can purchase a new delivery truck for an upfront cost of $200,000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of $4000 (paid at the end of each month). Your firm can borrow at 6% APR with quarterly compounding.

10) The effective annual rate on your firm’s borrowings is closest to:

- A) 6.00%
- B) 6.14%
- C) 6.25%
- D) 6.30%

Answer: B

Explanation: B) *EAR* = (1 + *APR/k*)*k* – 1 = (1 + .06/4)4 – 1 = .06136 or 6.14%

Diff: 1

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

11) The effective annual rate for a credit card that charges a 19.9% APR compounded daily is closest to:

- A) 18.15%
- B) 19.9%
- C) 22.0%
- D) 24.2%

Answer: C

Explanation: C) EAR = (1 + .199/365)365 – 1 = .220116

Diff: 1

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

12) The effective annual rate for a certificate of deposit that pays 3.9% APR compounded monthly is closest to:

- A) 3.83%
- B) 3.90%
- C) 3.97%
- D) 4.04%

Answer: C

Explanation: C) EAR = (1 + .039/12)12 – 1 = .039705

Diff: 1

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

13) Wesley Mouch’s auto loan requires monthly payments and has an effective annual rate of 6.43%. The APR on this auto loan is closest to:

- A) 6.00%
- B) 6.25%
- C) 6.50%
- D) 6.62%

Answer: B

Explanation: B) APR = ( – 1) × 12 = .062479

Diff: 2

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

14) Interest on James Taggart’s credit card balances are compounded daily at an effect annual rate of 14.91%. The APR on his credit card is closest to:

- A) 13.90%
- B) 13.95%
- C) 14.91%
- D) 16.08%

Answer: A

Explanation: A) APR = ( – 1) × 365 = .139006

Diff: 2

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

15) Suppose the interest rate is 9% APR with monthly compounding. Then the present value of an annuity that pays $250 every three months for the next five years is closest to:

- A) $2280
- B) $3985
- C) $3990
- D) $3995

Answer: B

Explanation: B) EAR = (1 + .09/12)12 – 1 = .093807

APR = ( – 1) × 4 = .090677

PVA = PMT = 250 = $3,984.49

Diff: 3

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

16) Floyd Ferris invested $3000 into an account five years ago. Today his account has grown to have a balance of $3927.50. Given that his account offered monthly compounding of interest, the APR on this account is closest to:

- A) 5.00%
- B) 5.25%
- C) 5.40%
- D) 5.54%

Answer: C

Explanation: C) APR = ( × 12 = .054

Diff: 3

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

*Use the information for the question(s) below.*

Your firm needs to invest in a new delivery truck. The life expectancy of the delivery truck is five years. You can purchase a new delivery truck for an upfront cost of $200,000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of $4000 (paid at the end of each month). Your firm can borrow at 6% APR with quarterly compounding.

17) The effective monthly discount rate that you should use to evaluate the truck lease is closest to:

- A) 0.487%
- B) 0.498%
- C) 1.500%
- D) 1.535%

Answer: B

Explanation: B) *EAR* = (1 + *APR/k*)*k* – 1 = (1 + .06/4)4 – 1 = .06136 or 6.14%

Monthly rate = (1 + *EAR*)(1/12) – 1 = (1.06136)(1/12) – 1 = .004975 = 0.498%

Diff: 2

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

18) The present value of the lease payments for the delivery truck is closest to:

- A) $206,900
- B) $207,050
- C) $207,680
- D) $198,420

Answer: B

Explanation: B) First we need to calculate the monthly discount rate for the lease arrangement.

*EAR* = (1 + *APR/k*)*k* – 1 = (1 + .06/4)4 – 1 = .06136 or 6.14%

Monthly rate = (1 + *EAR*)(1/12) – 1 = (1.06136)(1/12) – 1 = .004975 = 0.4975%

PV = 4000 × (1/0.004975) × (1 – 1/(1.00497560)) = 207,051.61

Diff: 3

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

19) You are considering purchasing a new automobile that will cost you $28,000. The dealer offers you 4.9% APR financing for 60 months (with payments made at the end of the month). Assuming you finance the entire $28,000 and finance through the dealer, your monthly payments will be closest to:

- A) $1454
- B) $527
- C) $467
- D) $457

Answer: B

Explanation: B) First we need the monthly interest rate = *APR/k* = .049/12 = .004083 or .4083%.

28,000 = PMT × (1/0.004083) × (1 – 1/(1.00408360))

PMT = $527.11

Diff: 2

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

20) You are considering purchasing a new truck that will cost you $34,000. The dealer offers you 1.9% APR financing for 48 months (with payments made at the end of the month). Assuming you finance the entire $34,000 and finance through the dealer, your monthly payments will be closest to:

- A) $708
- B) $725
- C) $736
- D) $1086

Answer: C

Explanation: C) First we need the monthly interest rate = *APR/k* = .019/12 = .001583 or .1583%.

34,000 = PMT × (1/0.001583) × (1 – 1/(1.00158348))

PMT = $736.15

Diff: 2

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

* *

*Use the information for the question(s) below.*

You are in the process of purchasing a new automobile that will cost you $27,500. The dealership is offering you either a $2500 rebate (applied toward the purchase price) or 1.9% financing for 48 months (with payments made at the end of the month). You have been pre-approved for an auto loan through your local credit union at an interest rate of 6.5% for 48 months.

21) If you take the $2500 rebate and finance your new car through your credit union your monthly payments will be closest to:

- A) $520
- B) $573
- C) $593
- D) $799

Answer: C

Explanation: C) First we need the monthly interest rate = *APR/k* = .065/12 = .005417 or .5417%.

25,000 = PMT × (1/0.005417) × (1 – 1/(1.00541748))

PMT = $592.87

Diff: 2

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

22) If you forgo the $2500 rebate and finance your new car through the dealership your monthly payments (with payments made at the end of the month) will be closest to:

- A) $520
- B) $573
- C) $595
- D) $799

Answer: C

Explanation: C) First we need the monthly interest rate = *APR/k* = .019/12 = .001583 or .1583%.

27,500 = PMT × (1/0.001583) × (1 – 1/(1.00158348))

PMT = $595.41

Diff: 2

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

* *

*Use the information for the question(s) below.*

You are purchasing a new home and need to borrow $250,000 from a mortgage lender. The mortgage lender quotes you a rate of 6.25% APR for a 30-year fixed rate mortgage. The mortgage lender also tells you that if you are willing to pay 2 points, they can offer you a lower rate of 6.0% APR for a 30-year fixed rate mortgage. One point is equal to 1% of the loan value. So if you take the lower rate and pay the points you will need to borrow an additional $5000 to cover points you are paying the lender.

23) Assuming you don’t pay the points and borrow from the mortgage lender at 6.25%, then your monthly mortgage payment (with payments made at the end of the month) will be closest to:

- A) $694
- B) $708
- C) $1540
- D) $1600

Answer: C

Explanation: C) First we need the monthly interest rate = *APR/k* = .0625/12 = .005208 or .5208%.

250,000 = PMT × (1/0.005208) × (1 – 1/(1.005208360))

PMT = $1539.29

Diff: 2

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

24) Assuming you pay the points and borrow from the mortgage lender at 6.00%, then your monthly mortgage payment (with payments made at the end of the month) will be closest to:

- A) $708
- B) $1530
- C) $1540
- D) $1600

Answer: B

Explanation: B) First we need the monthly interest rate = *APR/k* = .0600/12 = .005000 or 0.50%.

255,000 = PMT × (1/0.005) × (1 – 1/(1.005360))

PMT = $1528.85

Diff: 2

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

* *

*Use the information for the question(s) below.*

Two years ago you purchased a new SUV. You financed your SUV for 60 months (with payments made at the end of the month) with a loan at 5.9% APR. You monthly payments are $617.16 and you have just made your 24th monthly payment on your SUV.

25) The amount of your original loan is closest to:

- A) $14,808
- B) $22,212
- C) $32,000
- D) $37,020

Answer: C

Explanation: C) First we need the monthly interest rate = *APR/k* = .059/12 = .004917 or 0.4917%.

PV = 617.16 × (1/0.004917) × (1 – 1/(1.00491760)) = $31,999.86

Diff: 2

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

26) Assuming that you have made all of the first 24 payments on time, then the outstanding principal balance on your SUV loan is closest to:

- A) $14,808
- B) $20,300
- C) $22,212
- D) $32,000

Answer: B

Explanation: B) First we need the monthly interest rate = *APR/k* = .059/12 = .004917 or 0.4917%.

PV = 617.16 × (1/0.004917) × (1 – 1/(1.00491736)) = $20,316.92

Remember:

*N* = 36 (remaining payments 60 – 24 = 36)

Diff: 2

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

* *

*Use the information for the question(s) below.*

Your firm needs to invest in a new delivery truck. The life expectancy of the delivery truck is five years. You can purchase a new delivery truck for an upfront cost of $200,000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of $4000 (paid at the end of each month). Your firm can borrow at 6% APR with quarterly compounding.

27) Should you purchase the delivery truck or lease it? Why?

Answer: First we need to calculate the monthly discount rate for the lease arrangement.

EAR = (1 + *APR/k*)*k* – 1 = (1 + .06/4)4 – 1 = .06136 or 6.14%

Monthly rate = (1 + *EAR*)(1/12) – 1 = (1.06136)(1/12) – 1 = .004975 = 0.4975%

PV = 4000 × (1/0.004975) × (1 – 1/(1.00497560)) = $207,051.61

So leasing the truck will cost us 207051.61 – 200,000 = 7051.61 more than purchasing. Therefore, we are better off purchasing the truck.

Diff: 3

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

28) You are in the process of purchasing a new automobile that will cost you $25,000. The dealership is offering you either a $1000 rebate (applied toward the purchase price) or 3.9% financing for 60 months (with payments made at the end of the month). You have been pre-approved for an auto loan through your local credit union at an interest rate of 7.5% for 60 months. Should you take the $2000 rebate and finance through your credit union or forgo the rebate and finance through the dealership at the lower 3.9% APR?

Answer: Take the rebate!

Credit Union:

First we need the monthly interest rate = *APR/k* = .075/12 = .00625 or .625%.

Now:

*PV* = 24,000 (rebate 25,000 – 1,000)

*I* = .625

*FV* = 0

*N* = 60

Compute *PMT* = $480.91

Dealership:

First we need the monthly interest rate = *APR/k* = .039/12 = .00325 or .325%.

Now:

*PV* = 25,000 (no rebate)

*I* = .325

*FV* = 0

*N* = 60

Compute *PMT* = $459.29

Since 459.29 < 480.91, go with the dealership and forgo the rebate.

Diff: 3

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

29) You are purchasing a new home and need to borrow $325,000 from a mortgage lender. The mortgage lender quotes you a rate of 6. 5% APR for a 30-year fixed rate mortgage (with payments made at the end of each month). The mortgage lender also tells you that if you are willing to pay 1 point, they can offer you a lower rate of 6.25% APR for a 30-year fixed rate mortgage. One point is equal to 1% of the loan value. So if you take the lower rate and pay the points, you will need to borrow an additional $3250 to cover points you are paying the lender. Assuming that you do not intend to prepay your mortgage (pay off your mortgage early), are you better off paying the 1 point and borrowing at 6.25% APR or just taking out the loan at 6.5% without any points?

Answer: Pay the points!

Points (6.25% APR)

First we need the monthly interest rate = *APR/k* = .0625/12 = .00520833 or .5208%.

Now:

*PV* = 328,250 ( 325,000 + 1 point)

*I* = .5208

*FV* = 0

*N* = 360 (30 years × 12 months)

Compute *PMT* = $2021.01

No Points

First we need the monthly interest rate = *APR/k* = .065/12 = .005417 or .5417%.

Now:

*PV* = 325,000 (no points)

*I* = .5417

*FV* = 0

*N* = 360 (30 years × 12 months)

Compute *PMT* = $2054.22

Since $2021.01 < $2054.22, pay the points!

Diff: 3

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

* *

*Use the information for the question(s) below.*

Two years ago you purchased a new SUV. You financed your SUV for 60 months (with payments made at the end of the month) with a loan at 5.9% APR. You monthly payments are $617.16 and you have just made your 24th monthly payment on your SUV.

30) Assuming that you have made all of the first 24 payments on time, then how much interest have you paid over the first two years of your loan?

Answer: $3129.09

First figure out the outstanding balance:

We need the monthly interest rate = *APR/k* = .059/12 = .004917 or 0.4917%.

Now

*I* = .4917

*FV* = 0

*N* = 36 (remaining payments = 60 – 24 = 36)

*PMT* = 617.16

Compute *PV* = $20,316,80

Next figure out the original loan amount:

First we need the monthly interest rate = *APR/k* = .059/12 = .004917 or 0.4917%.

Now

*I* = .4917

*FV* = 0

*N* = 60 (original number of payments)

*PMT* = 617.16

Compute *PV* = $31,999.55

So the amount of principal paid = 31,999.55 – 20,316.80 = 11,682.75.

You have paid a total of 24 × 617.16 = $14,811.84.

So amount of Interest = 14,811.84 – 11,682.75 = 3129.09.

Diff: 3

Section: 5.1 Interest Rate Quotes and Adjustments

Skill: Analytical

5.2 Application: Discount Rates and Loans

1) Hugh Akston took out a 30-year mortgage with an EAR of 5.9%. If Hugh borrowed $300,000 to buy his home, then his monthly payment will be closest to:

- A) $835
- B) $1750
- C) $1780
- D) $10,240

Answer: B

Explanation: B) APR = ( – 1) × 12 = .057462

*PMT* = = 1750.00

Diff: 3

Section: 5.2 Application: Discount Rates and Loans

Skill: Analytical

*Use the following information to answer the question(s) below.*

Dagny Taggart has just purchased a home and taken out a $400,000 mortgage. The mortgage has a 30-year term with monthly payments and has an APR of 5.4%.

2) Dagny’s monthly payments are closest to:

- A) $1110
- B) $1800
- C) $2215
- D) $2245

Answer: D

Explanation: D) *PMT* = = 2246.12

Diff: 2

Section: 5.2 Application: Discount Rates and Loans

Skill: Analytical

3) The total amount of interest that Dagny will pay during the first month of her mortgage is closest to:

- A) $1110
- B) $1785
- C) $1800
- D) $2245

Answer: C

Explanation: C) *PMT* = = 2246.12

First Month’s Interest = $400,000 × .054/12 = $1800

First Month’s Principal = $2246.12 – $1800 = $446.12

Diff: 1

Section: 5.2 Application: Discount Rates and Loans

Skill: Analytical

4) The total amount of principal that Dagny will pay during the first month of her mortgage is closest to:

- A) $246
- B) $446
- C) $1800
- D) $2245

Answer: B

Explanation: B) *PMT* = = 2246.12

First Month’s Interest = $400,000 × .054/12 = $1800

First Month’s Principal = $2246.12 – $1800 = $446.12

Diff: 2

Section: 5.2 Application: Discount Rates and Loans

Skill: Analytical

5) The total amount of interest that Dagny will pay during the first three months of her mortgage is closest to:

- A) $1345
- B) $5380
- C) $5395
- D) $6740

Answer: C

Explanation: C) *PMT* = = 2246.12

First Month’s Interest = $400,000 × .054/12 = $1800

First Month’s Principal = $2246.12 – $1800 = $446.12

Second Month’s Interest = ($400,000 – 446.12) × .054/12 = $1797.99

Second Month’s Principal = $2246.12 – $1797.99 = $448.13

Third Month’s Interest = (400,000 – 446.12 – 448.13) × .054/12 = $1795.98

Third Month’s Principal = $2246.12 – $1795.98 = $450.14

Total Interest = $1800 + $1797.99 + $1795.98 = $5393.97

Total Principal = $446.12 + $448.13 + $450.14 = $1344.39

Diff: 3

Section: 5.2 Application: Discount Rates and Loans

Skill: Analytical

6) The total amount of principal that Dagny will pay during the first three months of her mortgage is closest to:

- A) $1340
- B) $1345
- C) $5395
- D) $6740

Answer: B

Explanation: B) *PMT* = = 2246.12

First Month’s Interest = $400,000 × .054/12 = $1800

First Month’s Principal = $2246.12 – $1800 = $446.12

Second Month’s Interest = ($400,000 – 446.12) × .054/12 = $1797.99

Second Month’s Principal = $2246.12 – $1797.99 = $448.13

Third Month’s Interest = (400,000 – 446.12 – 448.13) × .054/12 = $1795.98

Third Month’s Principal = $2246.12 – $1795.98 = $450.14

Total Interest = $1800 + $1797.99 + $1795.98 = $5393.97

Total Principal = $446.12 + $448.13 + $450.14 = $1344.39

Diff: 3

Section: 5.2 Application: Discount Rates and Loans

Skill: Analytical

5.3 The Determinants of Interest Rates

1) Which of the following statements is FALSE?

- A) The interest rates that banks offer on investments or charge on loans depends on the horizon of the investment or loan.
- B) The Federal Reserve determines very short-term interest rates through its influence on the federal funds rate.
- C) The interest rates that are quoted by banks and other financial institutions are nominal interest rates.
- D) Fundamentally, interest rates are determined by the Federal Reserve.

Answer: D

Diff: 1

Section: 5.3 The Determinants of Interest Rates

Skill: Conceptual

2) Which of the following statements is FALSE?

- A) The relationship between the investment term and the interest rate is called the term structure of interest rates.
- B) Real interest rates indicate the rate at which your money will grow if invested for a certain period.
- C) The yield curve is a potential leading indicator of future economic growth.
- D) The shape of the yield curve will be strongly influenced by interest rate expectations.

Answer: B

Diff: 1

Section: 5.3 The Determinants of Interest Rates

Skill: Conceptual

3) Which of the following statements is FALSE?

- A) The yield curve changes over time.
- B) The formulas for computing present values of annuities and perpetuities cannot be used in situations in which cash flows need to be discounted at different rates.
- C) We can use the term structure to compute the present and future values of a risk-free cash flow over different investment horizons.
- D) The yield curve tends to be inverted as the economy comes out of a recession.

Answer: D

Diff: 2

Section: 5.3 The Determinants of Interest Rates

Skill: Conceptual

4) Which of the following statements is FALSE?

- A) The plot of the relationship between the investment risk and the interest rate is call the yield curve.
- B) Each of the last six recessions in the United States was preceded by a period with an inverted yield curve.
- C) The nominal interest rate does not represent the increase in purchasing power that will result from investing.
- D) A risk-free cash flow received in two years should be discounted at the two-year interest rate.

Answer: A

Diff: 1

Section: 5.3 The Determinants of Interest Rates

Skill: Conceptual

5) Which of the following statements is FALSE?

- A) An inverted yield curve generally signals an expected decline in future interest rates.
- B) An inverted yield curve is often interpreted as a positive forecast for economic growth.
- C) All the formulas for computing present values of annuities and perpetuities are based upon discounting all of the cash flows at the same rate.
- D) The rate of growth of your purchasing power is determined by the real interest rate.

Answer: B

Diff: 2

Section: 5.3 The Determinants of Interest Rates

Skill: Conceptual

6) Which of the following formulas is INCORRECT?

- A)
*i*= – 1 - B) 1 +
*rr*= - C)
*rr*≈*i*–*r* - D)
*rr*=

Answer: C

Diff: 2

Section: 5.3 The Determinants of Interest Rates

Skill: Conceptual

7) If the current inflation rate is 4.2% and you are earning a real rate of return on an investment of 3.8%, then the nominal rate on this investment is closest to:

- A) 3.8%
- B) 4.2%
- C) 8.0%
- D) 8.2%

Answer: D

Explanation: D) (1 + real)(1 + inf) = (1 + nom) → (1.038)(1.042) – 1 = .081596

Diff: 1

Section: 5.3 The Determinants of Interest Rates

Skill: Analytical

8) If an investment providing a nominal return of 12.25% only offers a real rate of return of 5.70%, then the inflation rate is closest to:

- A) 5.70%
- B) 6.20%
- C) 6.55%
- D) 12.25%

Answer: B

Explanation: B) (1 + nom)/(1 + real) = (1 + inf) → (1.1225)/(1.0570) – 1 = .061968

Diff: 1

Section: 5.3 The Determinants of Interest Rates

Skill: Analytical

9) If the current inflation rate is 5%, then the nominal rate necessary for you to earn an 8% real interest rate on your investment is closest to:

- A) 13.0%
- B) 13.4%
- C) 4.9%
- D) 3.0%

Answer: B

Explanation: B) *nominal* = (1 + *inflation*)(1 + *real*) – 1 = (1.05)(1.08) – 1 = .134 or 13.4%

Diff: 1

Section: 5.3 The Determinants of Interest Rates

Skill: Analytical

10) If the current inflation rate is 4% and you have an investment opportunity that pays 10%, then the real rate of interest on your investment is closest to:

- A) 10.0%
- B) 14.0%
- C) 6.0%
- D) 5.8%

Answer: D

Explanation: D) 1 + *nominal* = (1 + *inflation*)(1 + *real*)

real interest rate = – 1 = .057692 or 5.77%

Diff: 1

Section: 5.3 The Determinants of Interest Rates

Skill: Analytical

*Use the table for the question(s) below.*

Suppose the term structure of interest rates is shown below:

Term |
1 year |
2 years |
3 years |
5 years |
10 years |
20 years |

Rate (EAR%) | 5.00% | 4.80% | 4.60% | 4.50% | 4.25% | 4.15% |

11) What is the shape of the yield curve and what expectations are investors likely to have about future interest rates?

- A) Inverted; Higher
- B) Normal; Higher
- C) Inverted; Lower
- D) Normal; Lower

Answer: C

Diff: 2

Section: 5.3 The Determinants of Interest Rates

Skill: Conceptual

12) The present value of receiving $1000 per year with certainty at the end of the next three years is closest to:

- A) $2737
- B) $2723
- C) $2733
- D) $2744

Answer: A

Explanation: A) = 1000/(1.05) + 1000/(1.048)2 + 1000/(1.046)3 = 2737

Diff: 2

Section: 5.3 The Determinants of Interest Rates

Skill: Analytical

13) Consider an investment that pays $1000 certain at the end of each of the next four years. If the investment costs $3500 and has an NPV of $74.26, then the four year risk-free interest rate is closest to:

- A) 4.50%
- B) 4.58%
- C) 4.55%
- D) 4.53%

Answer: D

Explanation: D) *NPV* = 74.26 = -3500 + 1000/(1.05)1 + 1000/(1.048)2 + 1000/(1.046)3 + 1000/(1 + x)4

3574.26 – 1000/(1.05)1 + 1000/(1.048)2 + 1000/(1.046)3 = 1000/(1 + x)4

837.60 = 1000/(1 + *X*)4 → (1 + *X*)4 = 1000/837.60 → *X* = .0453 or 4.53%

Diff: 3

Section: 5.3 The Determinants of Interest Rates

Skill: Analytical

14) The NPV of an investment that costs $2700 and pays $1000 certain at the end of one, three, and five years is closest to:

- A) 21.47
- B) $1665.62
- C) -100.26
- D) -71.38

Answer: D

Explanation: D) *NPV* = -2700 + 1000/(1.05)1 + 1000/(1.046)3 + 1000/(1.045)5 = -71.38

Diff: 2

Section: 5.3 The Determinants of Interest Rates

Skill: Analytical

15) Should the nominal interest rate ever be negative? Can the real interest rate ever be negative? Explain.

Answer: The nominal interest rate should never be negative since by just holding your money you are earning a 0% return (no negative) on your money. The real rate, however, can be negative anytime that the inflation rate exceeds the nominal rate.

Diff: 1

Section: 5.3 The Determinants of Interest Rates

Skill: Conceptual

* *

*Use the table for the question(s) below.*

Suppose the term structure of interest rates is shown below:

Term |
1 year |
2 years |
3 years |
5 years |
10 years |
20 years |

Rate (EAR%) | 5.00% | 4.80% | 4.60% | 4.50% | 4.25% | 4.15% |

16) What is the NPV of an investment that costs $2500 and pays $1000 certain at the end of one, three, and five years?

Answer: *NPV* = -2500 + 1000/(1.05)1 + 1000/(1.046)3 + 1000/(1.045)5 = 128.62

Diff: 2

Section: 5.3 The Determinants of Interest Rates

Skill: Analytical

5.4 Risk and Taxes

1) Which of the following statements is FALSE?

- A) When we refer to the “risk-free interest rate,” we mean the rate on U.S. Treasuries.
- B) Interest rates vary with the investment horizon.
- C) All borrowers, besides the U.S. Treasury, have some risk of default.
- D) When interest on a loan is tax deductible, the effective after-tax interest rate is
*τ*× (1 –*r*).

Answer: D

Diff: 2

Section: 5.4 Risk and Taxes

Skill: Conceptual

2) Which of the following statements is FALSE?

- A) The equivalent after-tax interest rate is
*r*– (*τ*×*r*). - B) Interest rates vary based on the identity of the borrower.
- C) The ability to deduct the interest expense increases the effective after-tax interest rate paid on the loan.
- D) For loans to borrowers other than the U.S. Treasury, the stated interest rate is the maximum amount that investors will receive.

Answer: C

Diff: 2

Section: 5.4 Risk and Taxes

Skill: Conceptual

3) Which of the following statements is FALSE?

- A) U.S. Treasury securities are widely regarded to be risk-free because there is virtually no chance the government will default on these bonds.
- B) In general, if the interest rate is
*r*and the tax rate is*τ*, then for each $1 invested you will earn interest equal to*r*and owe taxes of*τ*×*r*on the interest. - C) Investors may receive less than the stated interest rate if the borrowing company has financial difficulties and is unable to fully repay the loan.
- D) Taxes reduce the amount of interest the investor can keep, and we refer to this reduced amount as the tax effective interest rate.

Answer: D

Diff: 2

Section: 5.4 Risk and Taxes

Skill: Conceptual

4) Which of the following statements is FALSE?

- A) The actual cash flow that the investor will get to keep will be reduced by the amount of any tax payments.
- B) The equivalent after-tax interest rate is
*r*(1 –*τ*). - C) The right discount rate for a cash flow is the rate of return available in the market on other investments of comparable risk and term.
- D) To compensate for the risk that they will receive less than promised if the firm defaults, investors demand a lower interest rate than the rate on U.S. Treasuries.

Answer: D

Diff: 1

Section: 5.4 Risk and Taxes

Skill: Conceptual

5) Assume that you presently have a monthly home mortgage with a stated interest rate of 7% APR. If your income tax rate is 20%, then the after tax EAR for your home mortgage is closest to:

- A) 5.6%
- B) 7.2%
- C) 5.8%
- D) 7.0%

Answer: C

Explanation: C) Step #1 find the EAR

*EAR* = (1 + .07/12)12 – 1 = 7.2%

Step #2 find the after tax cost

*aftertax* = *before tax *(1 – *T*) = .072 (1 – .2) = .0578 or approximately 5.8%

Diff: 2

Section: 5.4 Risk and Taxes

Skill: Analytical

* *

*Use the following information to answer the question(s) below:*

Suppose the term structure of risk-free interest rates is given as:

Term 1 year 2 years 3 years 5 years 10 years

Rate 2.25% 2.80% 3.20% 4.10% 6.30%

6) The present value of an investment that pays $2000 in one year and $3000 in three years for certain is closest to:

- A) $4707
- B) $4685
- C) $4729
- D) $5000

Answer: B

Explanation: B) PV = 2000/(1.0225)1 + 3000/(1.032)3 = 4685.48

Diff: 2

Section: 5.4 Risk and Taxes

Skill: Analytical

7) The present value of an investment that pays $1000 in two years and $5000 in ten years for certain is closest to:

- A) $3660
- B) $3687
- C) $3707
- D) $4292

Answer: A

Explanation: A) PV = 1000/(1.028)^2 + 5000/(1.063)^10 = 3660.44

Diff: 2

Section: 5.4 Risk and Taxes

Skill: Analytical

* *

*Use the table for the question(s) below.*

Suppose you have the following Loans/Investments

Credit Card | 14.90% APR (Monthly Compounding) |

Automobile Loan | 5.90% APR (Monthly Compounding) |

Home Equity Loan | 8.25% APR (Monthly Compounding) |

Money Market Fund | 5.10% EAR |

8) If your income tax rate is 30%, then the after-tax EAR for your home equity loan is closest to:

- A) 6.0%
- B) 5.9%
- C) 8.6%
- D) 5.8%

Answer: A

Explanation: A) Step #1 find the EAR

*EAR* = (1 + .0825/12)12 – 1 = 8.569%

Step #2 find the after tax cost

*aftertax* = *before tax *(1 – *T*) = .08569 (1 – .3) = .0599 or approximately 6.0%

Diff: 2

Section: 5.4 Risk and Taxes

Skill: Analytical

9) If your income tax rate is 30%, then the after-tax return you receive on your money market fund is closest to:

- A) 3.7%
- B) 5.1%
- C) 3.6%
- D) 4.2%

Answer: C

Explanation: C) This is already stated as an EAR, so *aftertax* = *before tax* (1 – *T*) = .051 (1 – .3) = .0357 or approximately 3.6%

Diff: 2

Section: 5.4 Risk and Taxes

Skill: Analytical

10) What is the effective after-tax rate of each instrument, expressed as an EAR?

Answer: Credit Card

Interest is not deductible so,

*EAR* = (1 + .149/12)12 – 1 = 15.96%

Car Loan

Interest is not deductible so,

*EAR* = (1 + .059/12)12 – 1 = 6.06%

Home Equity Loan

Step #1 find the EAR

*EAR* = (1 + .0825/12)12 – 1 = 8.569%

Step #2 find the after tax cost

*aftertax* = *before tax* (1 – *T*) = .08569 (1 – .3) = .0599 or approximately 6.0%

Money Market Fund

This is already stated as an EAR, so *aftertax* =* before tax *(1 – *T*) = .051 (1 – .3) = .0357 or approximately 3.6%

Diff: 2

Section: 5.4 Risk and Taxes

Skill: Analytical

5.5 The Opportunity Cost of Capital

1) Which of the following statements is FALSE?

- A) The investor’s opportunity cost of capital is the best available expected return offered in the market on an investment of comparable risk and term of the cash flows being discounted.
- B) Interest rates we observe in the market will vary based on quoting conventions, the term of investment, and risk.
- C) The opportunity cost of capital is the return the investor forgoes when the investor takes on a new investment.
- D) For a risk-free project, the opportunity cost of capital will typically be greater than the interest rate of U.S. Treasury securities with a similar term.

Answer: D

Diff: 1

Section: 5.5 The Opportunity Cost of Capital

Skill: Conceptual

2) Which of the following statements is FALSE?

- A) The actual return kept by an investor will depend on how the interest is taxed.
- B) The equivalent after-tax interest rate is
*r*(1 –*τ*). - C) The highest interest rate, for a given horizon, is the rate paid on U.S. Treasury securities.
- D) It is important to use a discount rate that matches both the horizon and the risk of the cash flows.

Answer: C

Diff: 1

Section: 5.5 The Opportunity Cost of Capital

Skill: Conceptual

3) A tax free municipal bond pays an effective annual rate of 7.2%. If your tax rate is 30%, then the effective annual rate that a comparable corporate bond would have to offer you to earn an equivalent after tax return would be closest to:

- A) 5.0%
- B) 7.2%
- C) 9.4%
- D) 10.3%

Answer: D

Explanation: D) Before tax = after tax/(1 – T) = .072/(1 – .3) = .10285714

Diff: 2

Section: 5.5 The Opportunity Cost of Capital

Skill: Analytical

5.6 Appendix: Continuous Rates and Cash Flows

1) You are offered an investment that pays 8% APR compounded continuously. The effective annual rate for this investment is closest to:

- A) 7.70%
- B) 8.00%
- C) 8.33%
- D) 8.50%

Answer: C

Explanation: C) EAR = eAPR – 1 = e.08 – 1 = .083287

Diff: 1

Section: 5.A Appendix: Continuous Rates and Cash Flows

Skill: Analytical

2) You are offered an investment that offers and effective annual rate of 8%. If this investment offers continuous compounding, then the APR for this investment is closest to:

- A) 7.70%
- B) 8.00%
- C) 8.25%
- D) 8.33%

Answer: A

Explanation: A) APR = ln(1 + EAR) = ln(1.08) = 0.076961

Diff: 1

Section: 5.A Appendix: Continuous Rates and Cash Flows

Skill: Analytical

3) Wyatt Oil is considering drilling a new oil well that is initially expected to produce oil at a rate of 10 million barrels per year. Wyatt has a long-term contract that allows them to sell the oil at a profit of $2.50 per barrel. The cost of drilling the rig is $175,000,000. If the rate of oil production from the rig declines by 3% over the year and the discount rate is 9% per year (EAR), then using continuous compounding, the NPV of this new oil well is closest to:

- A) -$333,333,000
- B) $28,128,000
- C) $33,333,000
- D) $39,340,000

Answer: D

Explanation: D) rcc = ln(1 + .09) = .086178

gcc = ln(1 – .03) = -0.030459

NPV = -175,000,000 + = 39,339,837

Diff: 3

Section: 5.A Appendix: Continuous Rates and Cash Flows

Skill: Analytical

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