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College of Business & Finance

The MBA ProgramFinancial Management (FINC 501)Mid-Term Examination Winter 2013Instructor:Dr. Wajeeh Elali

Student Name:

Student ID:

***Suggested Solutions***

REMARKS:

The purpose of this Exam is to help you reflect on the lectures and to apply the tools we have learnt to real life examples

The problems are to be answered in the space provided for them in this booklet.

Clearly show ALL your working and encircle the final answer.

Neatness will be greatly appreciated

This Exam consists of two parts (24 questions) on a total of 11 pages, including cover page.

Part I

MULTIPLE CHOICE QUESTIONS (5 POINTS EACH)

Show ALL CALCULATIONS. Answers without supporting calculations will be deemed a guess and will not receive any credit.

1.You are considering opening a new plant. The plant will cost $100 million upfront and will take one year to build. After that, it is expected to produce net cash flows of $30 million at the end of every year of production. The cash flows are expected to last forever. Should you make the investment if your opportunity cost is 8%?

a.Yes, since NPV= $247.22 million

b.No, since NPV= -$117.37 million

c.Yes, since NPV= $165.98 million

d.cannot be determined

Answer:a

Solution:

2.A company is considering a new project. The companys CFO plans to calculate the projects NPV by discounting the relevant cash flows (which include the initial up-front costs, the operating cash flows, and the terminal cash flows) at the companys cost of capital (COC). Which of the following factors should the CFO include when estimating the relevant cash flows?

a.Any sunk costs associated with the project.

b.Any interest expenses associated with the project.

c.Any opportunity costs associated with the project.

d.Statements b and c are correct.

e.All of the statements above are correct.

Answer: c

Solution:

The correct answer is c. Sunk costs should be excluded from the analysis, and interest expense is incorporated in the WACC and not the cash flows.

3.Noora Corp. is faced with an investment project. The following information is associated with this project:

YearAnnual

Net Income ($)Annual Depreciation Rate

150,0000.33

260,0000.45

370,0000.15

460,0000.07

The project involves an initial investment of $100,000 in equipment that has an estimated salvage value of $15,000. In addition, the company expects an initial increase in net operating working capital (NWC) of $5,000 that will be recovered in Year 4. The cost of capital (COC) for the project is 12 percent. What is the projects net present value (NPV)? (Round your final answer to the nearest whole dollar.)

a.$153,840

b.$159,071

c.$162,409

d.$168,604

Answer:d

Solution:

Step 1: Calculate depreciation:

Dep 1 = 100,000(0.33) = 33,000.

Dep 2 = 100,000(0.45) = 45,000.

Dep 3 = 100,000(0.15) = 15,000.

Dep 4 = 100,000(0.07) = 7,000.

Step 2: Calculate cash flows:

CF 0 = Initial Investment + Initial Increase in NWC

= 100,000 + 5,000 = 105,000.

CF= Net Income + Depreciation

CF 1= 50,000 + 33,000 = 83,000.

CF 2= 60,000 + 45,000 = 105,000.

CF 3= 70,000 + 15,000 = 85,000.

CF 4 = Net Income + Depreciation + Recovered NWC + Salvage Value

= 60,000 + 7,000 + 5,000 + 15,000 = 87,000.

Step 3: Calculate NPV:

Use CF key on calculator. Enter cash flows shown above. Enter I/YR = 12%. Solve for NPV = $168,603.89.

4.Gulf Products is considering a new project that develops a new laundry detergent, WOW. The company has estimated that the projects NPV is $3 million, but this does not consider that the new laundry detergent will reduce the revenues received on its existing laundry detergent products. Specifically, the company estimates that if it develops WOW the company will lose $500,000 in after-tax cash flows during each of the next 10 years because of the cannibalization of its existing products. Gulfs cost of capital is 10 percent. What is the net present value (NPV) of undertaking WOW after considering externalities?

a. $2,927,716.00

b. $3,000,000.00

c.-$ 72,283.55

d. $2,807,228.00

e.-$3,072,283.55

Answer:c

Solution:

Step 1:Calculate the NPV of the negative externalities due to the

cannibalization of existing projects:

Enter the following input data in the calculator:

CF0 = 0; CF1-10 = -500,000; I = 10; and then solve for NPV = $3,072,283.55.

Step 2:Recalculate the new projects NPV after considering externalities:

Adjusted NPV= +$3,000,000 - $3,072,283.55 = -$72,283.55.

5.A tenant wants to lease a building for $48,000 per year. She signs a five-year rental agreement that states that she will pay $24,000 every six months for the next five years. Which of the following is the timeline for her rental payments, assuming she makes the first payment immediately?

a)

Date(years)

0

1

2

3

4

5

Cash Flows(thousands)

$48

$48

$48

$48

$48

$48

b)

Date(years)

0

1/2

1

1 1/2

2

2 1/2

3

3 1/2

4

4 1/2

5

Cash Flows(thousands)

-$24

-$24

-$24

-$24

-$24

-$24

-$24

-$24

-$24

-$24

0

c)

Date(years)

0

1

2

3

4

5

6

3 1/2

4

4 1/2

5

Cash Flows(thousands)

$24

$24

$24

$24

$24

$24

$24

$24

$24

$24

$24

d)

Date(years)

0

1

2

3

4

5

Cash Flows(thousands)

-$48

-$48

-$48

-$48

-$48

-$48

Answer:b6.A bank offers a home buyer a 25-year loan at 8% per year. If the home buyer borrows $120,000 from the bank, how much must be repaid every year?a.$9,845.89

b.$10,786.66

c.$7,896.45

d.$11,241.45

Answer:d

Solution:

7.Suppose you could borrow using either a credit card that charges 1.5 percent per month or a bank loan with a 18 percent quoted interest rate that is compounded daily. Which should you choose?

a.the bank loan

b.the credit card loan

c.neither a nor b would be chosen

d.can not tell from the information given

e.both a and b

Answer:bSolution:

8.The future value of a lump sum at the end of five years is $1,000. The nominal interest rate is 10 percent and interest is compounded semiannually. Which of the following statements is most correct?

a.The present value of the $1,000 is greater if interest is compounded

monthly rather than semiannually.

b.The effective annual rate is greater than 10 percent.

c.The periodic interest rate is 5 percent.

d.Statements b and c are correct.

e.All of the statements above are correct.

Answer:dStatements b and c are correct; therefore, statement d is the correct choice. The present value is smaller if interest is compounded monthly rather than semiannually.

9.You are offered an investment opportunity that costs you $28,000, has a net present value (NPV) of $2278, lasts for three years, has interest rate of 10%, and produces the following cash flows:

The missing cash flow from year 2 is closest to:

a.$13,000b.$12,500

c.$10,000

d.$12,000Answer:d

Solution:

10.The timeline shown below best describes the cash flow of which of the following people?

Date(years)01234

Cash Flows-$3500$1000$1000$1000$1000

a.Dina, who loans a friend $3500, which friend then pays back the loan in four annual installments of $1000b.Zina, who borrows $3500, and then pays back the loan in four annual payments of $1000c.Tara, who borrows $3500, and then receives an annual payment of $1000

d.Sara, who puts down $3500 to buy a car, and then makes annual payments of $1000

Answer:a11.Which of the following statements is most correct?

a.

The present value of an annuity due will exceed the present value of an ordinary annuity (assuming all else equal).

b.

The future value of an annuity due will exceed the future value of an ordinary annuity (assuming all else equal).

c.

The nominal interest rate will always be greater than or equal to the effective annual interest rate.

d.

Statements a and b are correct.

e.

All of the statements above are correct.

Answer:d

Statements a and b are correct; therefore, statement d is the correct choice. The nominal interest rate will be less than the effective rate when the number of periods per year is greater than one.

12.If you deposit $300 at the beginning of each year for three years in a savings account that pays 6 percent interest per year, how much will you have at the end of three years?

a.$900.00

b.$1,315.25

c.$1,012.38

d.$1,304.83Answer:cSolution:

13.Project A has an internal rate of return (IRR) of 15 percent. Project B has an IRR of 14 percent. Both projects have a cost of capital of 12 percent. Which of the following statements is most correct?

a.Both projects have a positive net present value (NPV).

b.Project A must have a higher NPV than Project B.

c.If the cost of capital were less than 12 percent, Project B would have a higher IRR than Project A.

d.Statements a and c are correct.

e.All of the statements above are correct

Answer: aSolution:

Statement (a) is true; projects with IRRs greater than the cost of capital will have a positive NPV. Statement (b) is false because you know nothing about the relative magnitudes of the projects. Statement (c) is false because the IRR is independent of the cost of capital. Therefore, the correct choice is statement (a).

14.Sara recently invested $2,566.70 in a project that is promising to return 12 percent per year. The cash flows are expected to be as follows:

End of YearCash Flow

1$325

2400

3550

4?

5750

6800

What is the cash flow at the end of the 4th year?

a.$1,187

b.$ 600

c.$1,157

d.$ 655

e.$1,267

Answer:c

Solution: Find the present value of each of the cash flows:

PV of CF1 = $325/1.12 = $290.18. PV of CF2 = $400/(1.12)2 = $318.88. PV of CF3 = $550/(1.12)3 = $391.48. PV of CF5 = $750/(1.12)5 = $425.57. PV of CF6 = $800/(1.12)6 = $405.30. Summing these values you obtain $1,831.41. The present value of CF4 must then be $2,566.70 - $1,831.41 = $735.29. The value of CF4 is ($735.29)(1.12)4 = $1,157.

15.A firm with a cost of capital (COC) of 15% is evaluating four capital projects. The internal rates of return (IRR) are as follows:

ProjectIRR

116%

213%

317%

414%

The firm should

a. Accept project 4 and 1, and reject 2 and 3.

b. Accept project 4, 1, and 3, and reject 2

c. Accept project 3, and reject 1, 2, and 3.

d. Accept project 3, and 1, and reject 2 and 4.

Answer:d

Solution:

If IRR > COC ( accept

If IRR < COC ( reject16.Zina recently purchased a new automobile for $32,000. She made a $7,000 down payment and financed the balance over 48 months using a loan with a 12 percent annual nominal rate of interest. What are her monthly payments?

a. $512.98b. $577.87c. $658.35d. $688.98Answer:c

Solution:

17.You are interested in investing your money in a bank account. Which of the following banks provides you with the highest effective rate of interest?

a.Bank NBB; 8.00% with monthly compounding.

b.Bank CNN; 8.25% with annual compounding.

c.Bank RBC; 8.00% with quarterly compounding.

d.Bank CIBS; 8.00% with daily (365-day) compounding.

Answer:d

Solution:Alternative (d) is correct; the other alternatives are incorrect. Looking at responses (a) through (d), you should realize the choice with the greatest frequency of compounding will give you the highest EAR. This is alternative (d). The EAR of each of the alternatives is shown below.

18.To save money for a new house, you want to begin contributing money to a brokerage account. Your plan is to make 10 contributions to the brokerage account. Each contribution will be for $1,500. The contributions will come at the beginning of each of the next 10 years. The first contribution will be made at t = 0 and the final contribution will be made at t = 9. Assume that the brokerage account pays a 9 percent return with quarterly compounding. How much money do you expect to have in the brokerage account nine years from now (t = 9)?

a.$23,127.49

b.$25,140.65

c.$25,280.27

d.$21,627.49

e.$19,785.76

Answer:

a

Solution:

First, convert the 9 percent return with quarterly compounding to an effective rate of 9.308332%. With a financial calculator, NOM% = 9; P/YR = 4; EFF% = 9.308332%. (Dont forget to change P/YR = 4 back to P/YR = 1.) Then calculate the FV of all but the final payment. BEGIN MODE (1 P/YR) N = 9; I/YR = 9.308332; PV = 0; PMT = 1500; and solve for FV = $21,627.49. You must then add the $1,500 at t = 9 to find the answer, $23,127.49.

19.You have just arranged a $15,000 loan from your bank at an annual rate of 10%. The loan calls for annual payments of $1,000 over the next 14 years, and a final payment at the end of year 15. How big will the final payment (balloon) be?

a. $28,986

b. $29,098

c. $31,886

d. $31,946

Answer:c

Solution

20.West Island Industries is considering a project which has the following cash flows:

YearCash Flow

0?

1$2,000

23,000

33,000

41,500

The project has a payback period of 2.5 years. The firms cost of capital is 12 percent. What is the projects net present value?

a. $577.68

b. $676.74

c. $823.81

d. $977.56

e. None of the above, the answer is $______________.

Answer:e

Solution:

Initial Investment=$2,000+3,000+(3,000/2)=$6,500

Part IIProblemsQ1.You are running a hot Internet company. Analysts predict that its earnings will grow at 30% per year for the next five years. After that, as competition increases, earnings growth is expected to slow to 2% per year and continue at that level forever. Your company has just announced earnings of $1,000,000. What is the present value of all future earnings if the interest rate is 8%? (Assume all cash flows occur at the end of the year.)Solution:Timeline:

01234567

1(1.3)(1.3)2(1.3)3(1.3)4(1.3)5(1.3)5(1.02)(1.3)5(1.02)2

This problem consists of two parts:

(1) A growing annuity for 5 years;

(2) A growing perpetuity after 5 years.

First we find the PV of (1):

Now we calculate the PV of (2). The value at date 5 of the growing perpetuity is

Adding the present value of (1) and (2) together gives the PV value of future earnings:

Q2.Suppose you invest $2000 today and receive $10,000 in five years.a.What is the IRR of this opportunity?

b.Suppose another investment opportunity also requires $2000 upfront, but pays an equal amount at the end of each year for the next five years. If this investment has the same IRR as the first one, what is the amount you will receive each year?

Solution:

Solution part aTimeline

01235

-200010,000

IRR solves 2000=10000/(1+r)5So =37.97%.

Solution part b

Timeline

01235

-2000XXXX

X solves

= $949.27

Q3.You are shopping for a car and read the following advertisement in the newspaper: Own a new Spitfire! No money down. Four annual payments of just $10,000. You have shopped around and know that you can buy a Spitfire for cash for $32,500. What is the interest rate the dealer is advertising (what is the IRR of the loan in the advertisement)? Assume that you must make the annual payments at the end of each year.Solution:

Timeline:

01234

32,50010,00010,00010,00010,000

The PV of the car payments is a 4-year annuity:

Setting the NPV of the cash flow stream equal to zero and solving for r gives the IRR:

To find r we either need to guess or use the annuity calculator. You can check and see that r = 8.85581% solves this equation. So the IRR is 8.86%.

Q4.You have just purchased a home and taken out a $500,000 mortgage. The mortgage has a 30-year term with monthly payments and an APR of 6%.

a.How much will you pay in interest, and how much will you pay in principal, during the first year?

b.How much will you pay in interest, and how much will you pay in principal, during the 20th year (i.e., between 19 and 20 years from now)?Solution:

a.APR of 6% = 0.5% per month. Payment = .

Total annual payments = 2997.75 12 = $35,973.

Loan balance at the end of 1 year =.

Therefore, 500,000 493,860 = $6140 in principal repaid in first year, and 35,973 6140 = $29833 in interest paid in first year.

b.Loan balance in 19 years (or 360 1912 = 132 remaining pmts) is

.

Loan balance in 20 years = .

Therefore, 289,162 270,018 = $19,144 in principal repaid, and $35,973 19,144 = $16,829 in interest repaid.

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