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FNCE 370v10 Assignment 2 Athabasca University
complete material
Assignment 2 is worth 5% of your final mark. Complete and submit Assignment 2 after you complete Lesson 6. Questio n Marks available Marks Awarded Referenc e 1 20 Lesson 2 2 4 Lesson 2 3 10 Lesson 3 4 13 Lesson 4 5 7 Lesson 4 6 10 Lesson 4 7 7 Lesson 4 8 9 Lesson 5 9 9 Lesson 5 10 5 Lesson 6 11 6 Lesson 6 Total 100
Note on Decimal Places
When working through numerical problems, use as many decimal places as shown on your financial calculator. Do not round your calculated answers until you have reached the final answer. When you reach your final answer, round as follows, unless the question specifies otherwise (e.g., see the instructions for pro-forma statements in Question 1).
- Percentages: round to two decimal places
- Dollars: round to two decimal places
- Others: round to four decimal places
Questions
Use the following information for Delta Corporation to answer question 1: (20 marks total) Year 20X1 20X Net sales $1,500,000 $1,656, Cost of goods sold 675,000 745, Depreciation 270,000 298, Interest paid 43,600 44, Cash 127,500 140, Accounts receivable 450,000 496, Inventory 525,000 579, Net fixed assets 1,800,000 1,987,
Current Assets Current Liabilities Cash 168,973.20 Accounts Payable 496,980. Accounts Receivable 596,376.00 Notes Payable 50,000. Inventory 695,770.80 Total Current Liabilities 546,980. Total Current Assets 1,461,120.00 Long-Term Debt 500,000. Fixed Assets 2,385,501.60 Total Liabilities 1,046,980. Total Assets 3,846,621.60 Owners Equity Common Stock 1,000,000. Retained Earnings 1,556,013. Total Liabilities and Equity
EFN Needed: 243,627. b. Based on its 20X2 information, what is Delta’s capital intensity ratio? Round your answer to four decimal places. (1 mark) Capital Intensity Ratio = Total Assets/Sales = 1,217,600/1,656,598 = 0. c. What is Delta’s full capacity sales if it is currently operating at 80% capacity (20X2)? Round your answer to the nearest integer. (1 mark) Full Capacity Sales(% of capacity used) = Current Sales X(80%) = 1,656,598 x = 2,070, d. Recalculate the firm’s external financing needed (EFN) for 20X3 if Delta is only operating at 80% capacity. Assume that if the 20X3 net sales is lower than full
capacity sales, then the net fixed assets in 20X3 will be the same as the net fixed assets in 20X2 (i.e., assume that the firm will purchase just enough fixed assets to cover depreciation expense for 20X3). Interpret this EFN number. (5 marks) Sales 1,656, COGS 745, Depreciation 298, EBIT 612, Interest Paid 44, Taxable Income 568, Taxes 199,129. Net Income 369,446. Dividends 110,834. Addition to Retained Earnings 258,612. Current Assets Current Liabilities Cash 140,811 Accounts Payable 414, Accounts Receivable 496,980 Notes Payable 50,000. Inventory 579,809 Total Current Liabilities 464, Total Current Assets 1,217,600 Long-Term Debt 500,000. Fixed Assets 1,987,918 Total Liabilities 964, Total Assets 3,205,518 Owners Equity Common Stock 1,000,000. Retained Earnings 1,241, Total Liabilities and Equity
EFN Needed: 0
Current Assets Current Liabilities Cash 176,013.75 Accounts Payable 517,687. Accounts Receivable 621,225 Notes Payable 50,000. Inventory 724,761.25 Total Current Liabilities 567,687. Total Current Assets 1,522,000 Long-Term Debt 500,000. Fixed Assets 2,484897.50 Total Liabilities 1,067,687. Total Assets 4,006,897.50 Owners Equity Common Stock 1,000,000. Retained Earnings 1,556,013. Total Liabilities and Equity
EFN Needed: 383,196.
The company will need $383,196.05 of external financing in order to operate at 100%
capacity of its sales.
- A firm’s sustainable growth rate can be calculated using the formula Sustainable growth rate = (p(S/A)(1 + D/E) x R) / [1 – (p(S/A)(1 + D/E) x R)] Discuss the relationship between sustainable growth rate and each of the four variables in the above formula. (4 marks)
- Profit Margin (P): an increase in profit margin increases the firm’s ability to generate funds which also increases its sustainable growth.
- Dividend policy: a decrease in the amount of net income paid out as dividends increases the amount of income retained (R), which increases internal equity as well as sustainable growth.
- Financial policy: an increase in a firm’s D/E Ratio increases its financial leverage which makes additional financing available and increases sustainable growth.
- Total Asset Turnover (S/A): An increase in a firm’s S/A increases the sales generated which decreases the need for new assets and thereby increases the sustainable growth rate.
- Use the present value and future value formulas to solve the following problems. Confirm your answers with your financial calculator. Show both methods of calculation in your answers. When performing your calculations, keep as many decimal places as you
can for intermediate answers, but round your final answers to two decimal places. ( marks total) a. If you invest $1000 today at 3% annual interest rate, how much money would you have in i) one year’s time? (1 mark) FV = 1000(1.03) = 1030. Calculator: PV = -1000, I = 3, PMT = 0, N = 1, FV = 1030 ii) 10 years’ time? (1 mark) FV = 1000(1.03)^10 = 1,343. Calculator: PV = -1000, I = 3, PMT = 0, N = 10 FV = 1,343. iii) 30 years’ time? (1 mark) FV = 1000(1.03)^30 = 2,427. Calculator: PV = -1000, I = 3, PMT = 0, N = 30, FV = 2,427. b. You estimate that you will need $350,000 to buy a house some time in the future. If your bank account pays an annual interest rate of 3%, how much money must you deposit now to purchase the house in i) one year’s time? (1 mark) PV = 350 , 000 /( 1. 03 ^ 1 ) = 339 , 805. 83 Calculator: FV = 350,000, PMT = 0, I = 3, N = 1, PV = -339,805. ii) 10 years’ time? (1 mark) PV = 350 , 000 /( 1. 03 ^ 10 ) = 260 , 432. 87 Calculator: FV = 350,000, PMT = 0, I = 3, N = 10, PV = -260,432. iii) 30 years’ time? (1 mark) PV = 350 , 000 /( 1. 03 ^ 30 ) = 144 , 195. 37 Calculator: FV = 350,000, PMT = 0, I = 3, N = 30, PV = -144,195. c. You are saving up to buy a $10,000 used car. You currently have $5,000 in your savings
money into this savings account, how long will you have to wait before you can buy the used car? (2 marks) 10,000 = 5,000(1.03^N) 2 = 1.03^N Ln(2) = N(Ln(1.03)) N = 23. Calculator: FV = 10,000, PMT = 0, I = 3, PV = -5,000, N = 23. d. You are saving up to buy a $10,000 used car. You currently have $5,000 in your savings account. If you do not put any more money into this savings account, what interest rate (in percentage) must you earn to achieve your goal of buying the used car in two years’ time? ( marks) 10,000 = 5,000(1+r)^2 2 = (1+r)^2 1.414213562 = 1+r r = 41.42% Calculator: FV = 10,000, PMT = 0, N = 2, PV = -5,000, I = 41.42%
4. This question consists of four main parts. When performing the calculations, keep as many decimal places as you can for intermediate answers, but round your final answers to two decimal places. (13 marks total) a. If you save $200 per month for 10 years at 12% annual percentage rate with monthly compounding, i) what is the future value annuity factor? (1 mark) FVAF=[( 1. 01 ^ 120 )- 1 ]/. 01 = 230. 04 ii) what is the future value? (1 mark) FV=200(230.0386895) = 46,007. b. Suppose that you have a choice between receiving $10,000 now and receiving $1000 per month for the next 12 months. Assuming that you can invest at a 12% annual percentage rate (APR) with monthly compounding, what is i) the present value annuity factor? (1 mark) PVAF=[( 1 - ( 1. 01 ^- 12 ))/. 01 ] = 11. 26 ii) the present value? (1 mark) PV=1000(11.25507747) = 11,255. iii) your choice? (1 mark) I would choose the second option and receive $1000 per month for 12 months. iv) the break-even annual rate of return at which you are indifferent between receiving $10,000 now and receiving $1000 per month for 12 months? (2 marks)
PV= -10,000, PMT= 1,000 FV= 0, N= 12, I= 2.
2.9229(12) = 35.07% = Annual rate of Return v) the break-even number of monthly payments at which you are indifferent between receiving $10,000 now and receiving $1000 per month, given an APR of 12% with monthly compounding? (1 mark) PV= -10,000, PMT= 1,000, FV= 0, I= 1, N= 10. 10.59 months which rounds down to 11 months due to it being reached during the 10 th month. vi) the break-even dollar amount of monthly payments, given an APR of 12% with monthly compounding and 12 months of payments? (1 mark) (Hint: Use the financial calculator for parts (iv), (v), and (vi). Clearly show the inputs you use for each calculation.) PV= -10,000, FV= 0, I= 1, N= 12, PMT= 888. Monthly PMT = $ c. You are saving $200 per month at 6% annual percentage return (APR) with monthly compounding. How many years will it take for your savings to accumulate to $10,000? (Hint: Use the financial calculator for this calculation, and clearly show the inputs you use.) (2 marks) PV= 0, PMT= -200, I=0.5139818, FV= 10,000, N= 44. 44.61/12 = 3.72 years d. You are saving $200 per month. What annual percentage rate of return must be earned for your savings to accumulate to $30,000 in 10 years? (2 marks) PV= 0, PMT= -200, FV=30,000, N=120, I=0. 0.3625(12) = 4.35%
5. This question consists of three parts. When performing the calculations, keep as many decimal places as you can for intermediate answers, but round your final answers to two decimal places. ( marks total) a. You have taken out a loan that requires you to repay $200 per month for 10 years at 12% annual percentage rate with monthly compounding. The first payment occurs today. What is the current value of this loan? (2 marks) PV = 200 [( 1 - ( 1. 01 ^- 120 ))/. 01 ] = 13 , 940. 10
b. You have purchased a three-year inflation-indexed investment. This investment will pay you $X every six months, with each payment adjusted upward for inflation. Let’s say that the proposed first payment is $300 (before inflation adjustment), the average forecasted inflation rate will be 0.5% every six months for the next three years, and your required annual rate of return is 6% (compounded semi-annually). What is the present value of this inflation-indexed investment? (Hint: You cannot use a financial calculator to solve this problem.) (4 marks) PMT= 300, r= 0.03, g= 0.005, N= 6 PV= ( 300 /(. 03 -. 005 ))( 1 – ( 1. 005 / 1. 03 )^ 6 ) PV= 1 , 644. 90 c. You have purchased an investment that promises to pay you a constant $300 every six months, indefinitely. Your required annual rate of return is 6%, compounded semi-annually; assume that this rate will be the same indefinitely. What is the present value of this investment three years from now? (Hint: You cannot use a financial calculator to solve this problem.) (1 mark) PV= PMT/r PV= 300/0.03 PV= 10,
6. Ms. Cressida bought a car for $48,000 exactly three years ago. After making an up-front equity payment of $5,000, she borrowed the rest of the car value from her bank in the form of a five-year loan. She negotiated a loan rate of 2.5% APR with semi-annual compounding. She makes loan payments of an equal dollar amount every two weeks (i.e., biweekly), and her first loan payment was due two weeks after she signed the loan contract. (10 marks total) a. What is the effective annual rate on Cressida’s loan? (1 mark) EAR=( 1 +( 0. 025 / 2 )^ 2 )- 1 = 0. 02515625 = 2. 52 % b. What is the effective biweekly interest rate on Cressida’s loan? (1 mark) EPR= 26 [( 1. 02515625 ^( 1 / 26 ))- 1 ] = 0. 024856914 = 2. 49 %, or 0. 0956 % Bi-weekly c. What is Cressida’s biweekly loan payment? (2 marks) 43 , 000 =PMT[( 1 - ( 1. 0009560351718 ^- 130 ))/ 0. 0009560351718 ] PMT= 351. 91 *The question states “an equal dollar amount every two weeks”, I will assume that just means the payment amounts stay constant at $351.91 and I will use that amount for the next question…
d. What is Cressida’s current loan balance? (2 marks) FV= 0, PMT= 351.9075318, N= 78, I=0.0009560351718, PV= -27,438.42 43,000 – 27,438.42 = 15,561. Current Loan Balance = $15,561. e. What is the total amount of interest that Cressida would have paid to the bank after five years of loan payments? (2 marks) 351.9075318(130 payments) = 45,747. 45,747.98 – 43,000 = 2,747.98 = Total Interest f. Show the amortization schedule (table) for the first five payments and the last five payments in the amortization table provided below. Round your answers in the table to two decimal places. (2 marks) Payment # Beginning balance Biweekly payment Interest payment Principal repayment Ending balance 1 $ 43,000.00 -$351.91^ -$310.80^ -$41.11^ $42,689. 2 $ 42,689.20 -$351.91^ -$311.10^ -$40.81^ $42,378. 3 $ 42,378.11 -$351.91^ -$311.39^ -$40.51^ $42,066. 4 $ 42,066.71 -$351.91^ -$311.69^ -$40.22^ $41,755. 5 $ 41,755.02 -$351.91^ -$311.99^ -$39.92^ $41,443. 126 $ 1,754.50 -$351.91^ -$350.23^ -$1.68^ $^ 1,404. 127 $ 1,404.27 -$351.91^ -$350.57^ -$1.34^ $^ 1,053. 128 $ 1,053.71 -$351.91^ -$350.90^ -$1.01^ $^ 702. 129 $ 702.81 -$351.91^ -$351.24^ -$0.67^ $^ 351. 130 $ 351.57 -$351.91^ -$351.57^ -$0.34^ -$^ 0.
- You are making plans for your retirement. You have just turned 30 and want to retire on your 65th birthday. Once retired, you plan to move to a tax-free Caribbean state, where you believe you can live comfortably on your retirement savings. You plan to make your first withdrawal from your retirement savings when you retire at age 65 and your last withdrawal one month before your 85 th^ birthday. Based on family history, you expect to live until exactly age 85. Your plan is to have a total of $1 million when you retire. Your current salary is $36,000 per year, or $3,000 per month. Your personal tax rate is approximately 30%. You estimate that you can earn an average return of 12% APR compounded annually on any money you invest over the next 60 years. You want to start putting aside a fixed amount of money at the end of every month until your retirement at age 65. You will make your first deposit one month from now and your last deposit on your 65 th^ birthday.
- Accounts payable 375,000 414,
- Notes payable 45,000 50,
- Calculator: FV = 0, PMT = -200, N = 120, I=1, PV = 13,940.
- Face value of $
Coupon rate of 3.5%, with annual coupon payments Yield to maturity of 2.51% All yields to maturity are compounded semi-annually. (9 marks total) a. What is the price of the one-year treasury bill? (2 marks) 0.0174 = (1000/PV)(1/1) – 1 1.0174 = 1000/PV PV = 982. b. What is the yield to maturity on Coupon Bond A? (2 marks) N= 4, FV= -1,000, PMT= -15, PV= 1018.90, R= 1. 1.01544447(2) = 2. YTM = 2.03% c. What is the price of Coupon Bond B? (2 marks) N= 5, FV= -1,000, PMT= -35, R= 2.51 PV= 1,045. d. If the inflation rate is 1.5%, what are the real yields on the one-year treasury bill, Coupon Bond A, and Coupon Bond B? (2 marks) One year treasury bill: 1.0174 = (1+Real)(1.015) Real = 0.24% Coupon Bond A: (1.0203088894) = (1+Real)(1.015) Real = 0.52% Coupon Bond B: (1.0251) = (1+Real)(1.015) Real = 1.00% e. If your personal real hurdle rate (the minimum rate of return required on investments) is 1%, which of the three fixed income securities would you choose to invest in? (1 mark) I would choose to invest in Coupon Bond B
9. Answer the following questions on bond valuation and duration. (9 marks total) a. Calculate the duration of a zero-coupon bond with five years to maturity, face value of $1000, and effective annual yield of 12.1604%. Show your calculations. What does your answer
PMT Period CF PV @ 12.1604% Weight of CF Duration 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 0 0 0 0 5 1000 563.381 1 5 PV = 1000 /( 1. 121604 ^ 5 ) = 563. 381 563.381/563.581 = 1 1(5) = 5 This tells us that this bond price will increase/decrease by 5 % for every 1 % in fluctuating interest. Zero coupon bonds will have the same duration as they do maturity. b. Calculate the duration of a coupon bond with the following features. What general conclusion can we make about the duration of coupon bonds relative to their time to maturity? ( marks) Face value of $ Five years to maturity Coupon rate of 11%, paid semi-annually Current price of $ (Hint: The effective annual yield should be 12.1604%.) The duration of this bond is 3.95 years, this tells us that coupon bonds duration are less than the length to maturity. They are also less risky than zero coupon bonds due to having a smaller duration compared to their time to maturity.
c. Duration is a measure of interest rate risk. Specifically, it measures the approximate percentage change in bond price given a small percentage change in interest rate (% bond price change / % interest rate change). For example, for a bond with a duration of five years, a 0.1% change in interest rate would change the bond’s price by 5 * 0.1% = 0.5%, approximately. Suppose that the interest rates on all bonds increase uniformly by 0.1% (this is what is commonly called a “parallel upward shift in yields of 10 basis points”). What is the percentage change in the price on the coupon bond in part (b)? What is the approximate coupon bond price? Note that bond yield and bond price are inversely related to each other (i.e., an increase in yield should lead to a decrease in bond price). (2 marks) Percent change: 3.95(0.10%) = 0.395 = 0.40% Bond Price: 957.46(.00395) = 3.7823, 957.46 – 3.7823 = 953. d. Recalculate the price of the coupon bond with five years to maturity, face value of $1000, coupon rate of 11% paid semi-annually, and a new yield to maturity equaling the original yield in part (b) plus 0.1%. Does it concur with your approximate coupon bond price calculated in part (c)? (Hint: The two answers in parts (c) and (d) should be fairly similar.) *( marks)* PMT Period
CF
PV @
Weight of CF Duration
PMT
Period
CF PV @
Weight of CF Duration 1 55 51. 9
