ECON 255 Please direct any questions about grading or points to the TF who graded that question. Email Theresa if your points did not get added correctly or if there is some other logistics issue.

Problem Set 1

1. Describe why cash flow is important and the difference between net income and cash flow. (2) [Graded by Sid - Siddharth.Dixit@yale.edu]

To be profitable, a firm must create more cash flow than it uses A firm must take the cash it raises through debt and equity financing and invest in

assets that will generate at least enough cash to pay taxes, dividends (if any) and debt payments

Net income is revenues minus expenses. Expenses are matched to the revenues in that particular period, even if the cash has not yet been paid. Expenses also include noncash items, such as depreciation and deferred taxes. By contrast, the cash flow statement starts with net income and then adds back noncash expenses.

2. Working capital management includes decisions concerning which of the following?

Explain. (2) [Graded by Siddharth Dixit] I. accounts payable II. long-term debt III. accounts receivable IV. inventory

A. I and II only B. I and III only C. II and IV only D. I, II, and III only E. I, III, and IV only

1 point for the right answer and 2 points for the explanation. Working capital deals with current assets and current liabilities. I, III, and IV

are current assets.

3. James is the manager of GoodEats Co., a publicly traded food company. He owns 5% stock in the company. 2014 has been a great year for the company and the firm now has a surplus of cash. James will choose to do one (and ONLY one) of three things: 1) Pay himself a bigger salary; 2) distribute dividends to shareholders; or 3) invest more into the company. Choose one of these options and describe what kind of problems or conflicts could arise from your choice. (5) [Graded by Siddharth Dixit] Students can choose any option as long as they explain it well. Salary: Since he only owns 5% of the company, James may have an agency problem. Dividends: This solves the agency problem (and would be good for James since he

would get a share of the dividends). However, James is foregoing the opportunity cost of any investments he could make. It is possible he could have created more shareholder wealth (although not immediately tangible) by investing in assets that will provide a return.

Investment: If James has good investments, shareholders might not mind investment rather than dividends since it will create overall shareholder wealth. However, they may prefer dividends, especially if investment opportunities are not abundant.

4. For this question you will use the actual 2014 SEC 10k (annual financial reporting) of

Apple Inc. You can find Apples 10k at https://www.sec.gov/edgar/searchedgar/ companysearch.html by searching using Apples ticker name AAPL. Please scroll down and select the 2014-10-27 10k filing. If you have trouble navigating the SEC site you can also find the 10k at http://investor.apple.com/sec.cfm and sort filings by annual. If you have trouble finding the information you need to complete the problem an excel document with the statements will be included with your PSet on ClassesV2. A. In excel, create a common size income statement based on Apples 2014 income statement (called here consolidated statements of operations). (2 points) [Graded by Sid]

Actual Common Size Net sales $ 182,795 100% Cost of sales 112,258 61.4% Gross margin 70,537 38.6% Operating expenses:

Research and development 6,041 3.3% Selling, general and administrative 11,993 6.6% Total operating expenses 18,034 9.9% Operating income 52,503 28.7% Other income/(expense), net 980 0.5% Income before provision for income taxes 53,483 29.3% Provision for income taxes 13,973 7.6% Net income $ 39,510 21.6% Dividends and Dividend Equivalents Paid $ 11,126 6.1%

B. Now compute 2014 Liquidity Ratios (4 points) [Graded by Inigo inigo.sanchez-lozano@yale.edu]

i. Calculate the current ratio.

Total current assets =$68,531 and total current liabilities = $63,448

Current ratio = $68,531/$63,448=1.08

ii. Calculate the quick ratio

Inventory = $2,111

Quick ratio = ($68,531-2,111)/$63,448=1.05 [1.04684]

iii. How are these different and why is that important?

The quick ratio does not include inventory and this is important because it is considered the least liquid type of current assets.

C. A Financial Leverage Ratio: calculate the 2014 debt to equity ratio (2 points) [Graded by Inigo]

Total liabilities = $120,292 and Total Equity =$111,547

Debt to Equity ratio = $120,292/$111,547=1.0784

D. An Asset Utilization Ratio: calculate and interpret the 2014 inventory turnover ratio (2 points) [Graded by Inigo]

Cost of sales = $112,258 Inventory = $2,111

Inventory Turnover = 53.17 This means that Apple sold off or turned over its entire inventory (assuming it keeps that level on average) over 53 times during the year.

E. Profitability Ratios: Calculate the 2014 profit margin, return on assets, and return on equity ratios. (3 points) [Graded by Inigo]

Total assets = $231,839, Total Equity =$111,547, Net Sales=$ 182,795 and Net Income =$ 39,510

Profit margin = 21.6% ROA=17.04% ROE=35.42%

F. Growth Rate Analysis: Calculate Apples 2014 Internal Growth Rate and Sustainable Growth rate. Then interpret these growth rates. (Remember you need to calculate the dividend retention ratio first and you can find the exact amount of dividends paid on the Cash Flow Statement under financing activities.) (8 points) [Graded by Yehia yehia.ibrahim@yale.edu]

Retention ratio = (NI-DivPaid)/NI=(39,510-11,126)/39,510=71.84% Internal Growth Rate = (.1704*.7184)/(1-(.1704*.7184))=13.95% is the maximum growth rate Apple can achieve using no external financing of any kind. Sustainable Growth Rate = (.3542*.7184)/(1-(.3542*.7184))=34.13% is the maximum growth rate Apple can achieve with no external equity financing while maintaining a constant debt-equity ratio.

5. What will a deposit of $3,500 at 10% compounded quarterly be worth if left in the bank

for 7 years? (2) [Graded by Yehia] Students must show their work and formula to get full credit. No credit given for

just an answer. 1 point if they have the correct formula but incorrect answer. 2 points if they have the correct formula but did not compound quarterly.

FV= C * (1+r/n)T*n

3500(1+(.1/4))7*4 6,987

6. What is the future value of a $5,000 annuity for 10 years with an 8% discount rate? (2)

Students must show their work and formula to get full credit. No credit given for just an answer. 1 point if they have the correct formula but incorrect answer. [Graded by Yehia] FV= C[ (1+)^1

]

5,000[1.08^10)1.08 ] 72, 432.81

7. Warren Buffet calls you on the phone and wants to share two great investment ideas with

you, but you only have enough capital to choose one. (8) [Graded by Megan megan.browder@yale.edu]

Option A: You receive a fixed payment of $5,000 each year forever. Payments will start in 5 years, the discount rate is 8% and the payments will grow at 2% each year.

Option B: You receive $10,000 each year for five years with a return of 10%. Explain which option you should choose and why. Show any calculations or formulas used.

Option A is a growing perpetuity (3 points). o PV=

o 5000.08.02 o PV in 5 years= 83,333.33 o PV today= 56,715.27

Will also accept 61,252.49 (discounting 4 years) If you did not discount you lost 1 point.

Option B is an annuity (3 points).

o PV=C[ 1

1(1+)^

] o 37,907.87

Or you can compare the FV of B to the PV in 5 years of A (61,051 versus 83,333.33)

You should choose Option A (1 point) because the PV is higher (1 point).

8. Dawn will graduate this semester with $43,800 in student loans. She must begin paying her loan six months after graduation. The interest rate on all of her loans is 6.5% and they did not accumulate interest while she was in school. If Dawn would like to repay her loans within 10 years, how much will her monthly payment be? How much would she have paid in interest? How much would she need to pay monthly if she would like to repay her loans in 5 years? Show any calculations or formulas used. (11) [Graded by Megan]

a. I tried to give as much credit as I could for this problem. If you had the right equations (annuities) but did not have the right numbers the max credit you could have gotten was 5 points. Common mistakes on the answers:

i. Taking into account the 6 months of interest but then using 120/60 months for the time (minus 6 points)

ii. Not accounting for the 6 months of interest when figuring total interest (minus 2 points)

iii. Using years instead of months. This is a monthly payment so you need to convert the rate and t into months. Because of compounding, you get the wrong answer if you simply find the yearly payment and divide by 12.(minus 6 points)

iv. Simply using the TVM functions in excel. Because you need to convert into months, if you just use the TVM excel functions you will get the wrong answers. (if you did not show formulas, 0 points)

v. Rounding errors. If the error did not result in a big difference I only took off a couple of points. But if you rounded to the nearest dollar you were way off on the interest calculations. Even if you rounded your final answer, it is important to continue to use the exact figure in your subsequent calculations.

b. There are three ways to interpret the problem (any of which would get you full credit). First, This is an annuity. P=[

1(1+)]. YOU MUST CONVERT THE RATE INTO MONTHS AND USE MONTHS FOR t

i. She starts paying immediately 1. P=[ .065/1243800

1(1.065)120] a. Monthly payment, 10 years= 497.34 b. 59,680.82-43,800= 15,880.82 in interest for 10 years

2. P=[ .065/12438001(1+.065/12)60] a. P= monthly payment, 5 years= $857

ii. She starts paying at the end of the 6th month 1. In this case, you need to account for the interest over the six

months. 2. The 6m starting value is $45,242.92 (43,800*((1+.065/12)^6)) 3. The monthly payment for the remaining 114 months years is

$532.97. If you used 120 months that is incorrect because she needs to pay the loan off in 10 years and she has already used up 6 months.

4. Total payments after ten years= 60,758.85 (532.97*114) 5. Interest= 60,758.85-43,800= 16,958.85. Note you have to use

43,800, not 45,242.92 because the 45,242.92 includes the 6 months of interest.

6. Monthly payment for 5 years: 968.58 iii. She waits but starts paying at the end of the 5th month/beginning of the

6th month 1. The starting value is 44,999.17

2. Now your t will need to be 115 since you used 5 months to figure out the starting value.

3. The monthly payment is 526.77 for 10 years 4. Total payments are 60,578.19. Total interest paid is 16,778.19 5. The monthly payment for 5 years is 948.28.

9. Your grandfather is 80 years old and has accumulated $120,000 in savings. He would like

to spend all of his savings by his 90th birthday (in 10 years). He places his savings into an account earning 7% annually and will receive 10 equal annual withdrawal (the first one occurring 1 year from now). At the end of 10 years, his balance will be 0. How much will his annual withdrawal be? (8) [Graded by Oscar Oscar.Melo-Vega@yale.edu]

This is an annuity. P=[ 1(1+)]

17,085.30

10. After a great decade of investing, you have decided to retire early at the ripe old age of thirty. You have saved $1.2 million and would like to draw $150,000 per year. Because of your superior investing skills, your savings will earn 12% annually. How many years will your savings last? (8) [Graded by Oscar]

28.4 years

11. If a project has a net present value equal to zero, then (2 points) [Graded by Cheng - c.peng@yale.edu] I. The present value of the cash inflows exceeds the initial cost of the project. II. The project produces a rate of return that just equals the rate required to accept the

project. III. The project is expected to produce only the minimally required cash inflows. IV. Any delay in receiving the projected cash inflows will cause the project to have a

negative net present value. A. II and III only B. II and IV only C. I, II, and IV only D. II, III, and IV only E. I, II, and III only

12. An investment with an initial cost of $14,000 produces cash flows of $4,000 annually for 5 years. If the cash flow is evenly spread out over the year and the firm can borrow at 10%, the discounted payback period is _____ years. (8 points) [Graded by Cheng]

4 + {(14,000 - 3636.36 - 3305.79 - 3005.25 - 2732.05 - 2483.69)/2483.69} = 4.53

13. The Ziggy Trim and Cut Company can purchase equipment on sale for $4,300. The asset

has a three-year life, will produce a cash flow of $1,200 in the first and second year, and $3,000 in the third year. The interest rate is 12%. Calculate the project's NPV and IRR. Should the project be taken? Use excel formulas to compete these calculations and show your excel formulas as part of your work. (8 points) [Graded by Cheng]

Take some points off if they do not show the excel formulas used take off some points.

c0 c1 c2 c3 -4300 1200 1200 3000 =NPV(0.12,A3:D2)+A2 -136.60 =IRR(A2:D2,0.12) 0.1041

14. You are considering the following two mutually exclusive projects. Both projects will be depreciated using straight-line depreciation to a zero book value over the life of the project. Neither project has any salvage value. Using excel, calculate the NPV of each project and decide which project to pursue, if at all. Show your formula as part of your work. (11 points) [Graded by Zoe - Zoe.Wang@yale.edu]

Year Project A (Required rate of return is 10%)

Project B (Required rate of return is 13%)

0 -75,000 -70,000 1 19,000 10,000 2 48,000 16,000 3 12,000 72,000

2~4 points off for not showing formulas used/wrong NPV function 9-11 points off for wrong answer + incorrect formulas

Project Required rate of return 0 1 2 3 A 0.10 -75000 19000 48000 12000 B 0.13 -70000 10000 16000 72000 Project Formula Result A =NPV(B2,D2:F2)+C2 -9,042.07 B =NPV(B3,D3:F3)+C3 1,279.52 Choose B

15. Explain two differences and two similarities between net present value (NPV) and the profitability index (PI). (2 points) [Graded by Zoe] 0.5 point for each similarity/difference

Answers within reason are ok even if they do not exactly align with what is below.

Differences

PI may be useful in determining which projects to accept if funds are limited PI divides the future PV of cash flows by initial investment and NPV subtracts PV

of future cash flows by the initial investment

Similarities

The NPV and PI both account for the PV of cash flows both rules lead to the same accept/reject decision.