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Mathematics & Economics
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Financial Problems (Coursework Sample)

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E5–1 Assume a firm makes a $2,500 deposit into its money market account. If this account is currently paying 0.7% (yes, that's right, less than 1%!), what will the account balance be after 1 year? E5–2 If Bob and Judy combine their savings of $1,260 and $975, respectively, and deposit this amount into an account that pays 2% annual interest, compounded monthly, what will the account balance be after 4 years? E5–3 Gabrielle just won $2.5 million in the state lottery. She is given the option of receiving a total of $1.3 million now, or she can elect to be paid $100,000 at the end of each of the next 25 years. If Gabrielle can earn 5% annually on her investments, from a strict economic point of view which option should she take? E5–4 Your firm has the option of making an investment in new software that will cost $130,000 today and is estimated to provide the savings shown in the following table over its 5-year life: Year Savings estimate 1 $35,000 2 50,000 3 45,000 4 25,000 5 15,000 Should the firm make this investment if it requires a minimum annual return of 9% on all investments? E5–5 Joseph is a friend of yours. He has plenty of money but little financial sense. He received a gift of $12,000 for his recent graduation and is looking for a bank in which to deposit the funds. Partners' Savings Bank offers an account with an annual interest rate of 3% compounded semiannually, while Selwyn's offers an account with a 2.75% annual interest rate compounded continuously. Calculate the value of the two accounts at the end of one year, and recommend to Joseph which account he should choose. E5–6 Jack and Jill have just had their first child. If college is expected to cost $150,000 per year in 18 years, how much should the couple begin depositing annually at the end of each year to accumulate enough funds to pay the first year's tuition at the beginning of the 19th year? Assume that they can earn a 6% annual rate of return on their investment. E6–1 The risk-free rate on T-bills recently was 1.23%. If the real rate of interest is estimated to be 0.80%, what was the expected level of inflation? E6–2 The yields for Treasuries with differing maturities on a recent day a. Use the information to plot a yield curve for this date. b. If the expectations hypothesis is true, approximately what rate of return do investors expect a 5-year Treasury note to pay 5 years from now? Maturity Yield 3 months 1.41% 6 months 1.71 2 years 2.68 3 years 3.01 5 years 3.70 10 years 4.51 30 years 5.25 c. If the expectations hypothesis is true, approximately (ignoring compounding) what rate of return do investors expect a 1-year Treasury security to pay starting 2 years from now? d. Is it possible that even though the yield curve slopes up in this problem, investors do not expect rising interest rates? Explain. E6–3 The yields for Treasuries with differing maturities, including an estimate of the real rate of interest, on a recent day were as shown in the following table: Maturity Yield Real Rate of Interest 3 months 1.41% 0.80% 6 months 1.71 0.80 2 years 2.68 0.80 3 years 3.01 0.80 5 years 3.70 0.80 10 years 4.51 0.80 30 years 5.25 0.80 Use the information in the preceding table to calculate the inflation expectation for each maturity. E6–4 Recently, the annual inflation rate measured by the Consumer Price Index (CPI) was forecast to be 3.3%. How could a T-bill have had a negative real rate of return over the same period? How could it have had a zero real rate of return? What minimum rate of return must the T-bill have earned to meet your requirement of a 2% real rate of return? E6–5 Calculate the risk premium for each of the following rating classes of long-term securities, assuming that the yield to maturity (YTM) for comparable Treasuries is 4.51%. Rating Class Nominal interest rate AAA 5.12% BBB 5.78 B 7.82 E6–6 You have two assets and must calculate their values today based on their different payment streams and appropriate required returns. Asset 1 has a required return of 15% and will produce a stream of $500 at the end of each year indefinitely. Asset 2 has a required return of 10% and will produce an end-of-year cash flow of $1,200 in the first year, $1,500 in the second year, and $850 in its third and final year. E6–7 A bond with 5 years to maturity and a coupon rate of 6% has a par, or face, value of $20,000. Interest is paid annually. If you required a return of 8% on this bond, what is the value of this bond to you? E6–8 Assume a 5-year Treasury bond has a coupon rate of 4.5%. a. Give examples of required rates of return that would make the bond sell at a discount, at a premium, and at par. b. If this bond's par value is $10,000, calculate the differing values for this bond given the required rates you chose in part a. Encore International In the world of trendsetting fashion, instinct and marketing savvy are prerequisites to success. Jordan Ellis had both. During 2012, his international casual-wear company, Encore, rocketed to $300 million in sales after 10 years in business. His fashion line covered the young woman from head to toe with hats, sweaters, dresses, blouses, skirts, pants, sweatshirts, socks, and shoes. In Manhattan, there was an Encore shop every five or six blocks, each featuring a different color. Some shops showed the entire line in mauve, and others featured it in canary yellow. Encore had made it. The company's historical growth was so spectacular that no one could have predicted it. However, securities analysts speculated that Encore could not keep up the pace. They warned that competition is fierce in the fashion industry and that the firm might encounter little or no growth in the future. They estimated that stockholders also should expect no growth in future dividends. Contrary to the conservative securities analysts, Jordan Ellis felt that the company could maintain a constant annual growth rate in dividends per share of 6% in the future, or possibly 8% for the next 2 years and 6% thereafter. Ellis based his estimates on an established long-term expansion plan into European and Latin American markets. Venturing into these markets was expected to cause the risk of the firm, as measured by the risk premium on its stock, to increase immediately from 8.8% to 10%. Currently, the risk-free rate is 6%. In preparing the long-term financial plan, Encore's chief financial officer has assigned a junior financial analyst, Marc Scott, to evaluate the firm's current stock price. He has asked Marc to consider the conservative predictions of the securities analysts and the aggressive predictions of the company founder, Jordan Ellis. Marc has compiled these 2012 financial data to aid his analysis: Data item 2012 value Earnings per share (EPS) $6.25 Price per share of common stock $40.00 Book value of common stock equity $60,000,000 Total common shares outstanding 2,500,000 Common stock dividend per share $4.00 TO DO a. What is the firm's current book value per share? b. What is the firm's current P/E ratio? c. (1) What is the current required return for Encore stock? (2) What will be the new required return for Encore stock assuming that they expand into European and Latin American markets as planned? d. If the securities analysts are correct and there is no growth in future dividends, what will be the value per share of the Encore stock? (Note: Use the new required return on the company's stock here.) e. (1) If Jordan Ellis's predictions are correct, what will be the value per share of Encore stock if the firm maintains a constant annual 6% growth rate in future dividends? (Note: Continue to use the new required return here.) (2) If Jordan Ellis's predictions are correct, what will be the value per share of Encore stock if the firm maintains a constant annual 8% growth rate in dividends per share over the next 2 years and 6% thereafter? f. Compare the current (2012) price of the stock and the stock values found in parts a, d, and e. Discuss why these values may differ. Which valuation method do you believe most clearly represents the true value of the Encore stock? source..
Content:

Financial Problems
It is a financial based assignment based on number of financial problems including time value of money, project evaluation and bond analysis.
E5–1Assume a firm makes a $2,500 deposit into its money market account. If this
account is currently paying 0.7% (yes, that’s right, less than 1%!), what will the
account balance be after 1 year?
FV = PV (1+r) = 2,500*(1+0.7%) = $2,517.5
E5–2If Bob and Judy combine their savings of $1,260 and $975, respectively, and deposit
this amount into an account that pays 2% annual interest, compounded monthly,
what will the account balance be after 4 years?
= Compounded Monthly Rate = 2.01%
Combine Principle
1260 + 975 = $2,235
=2235 (1+2.01%)^4 = $2420.985
E5–3Gabrielle just won $2.5 million in the state lottery. She is given the option of
receiving a total of $1.3 million now, or she can elect to be paid $100,000 at the end
of each of the next 25 years. If Gabrielle can earn 5% annually on her investments,
from a strict economic point of view which option should she take?
PV = PMT[1-(1/(1+i)^n))/i]
PMT = 100,000
N = 25
I = 5%
PVa = 1,409394 > 1.3 Million
Garbrielle will take the option to have 100,000 for 25 years
E5–4Your firm has the option of making an investment in new software that will cost
$130,000 today and is estimated to provide the savings shown in the following table
over its 5-year life:
YearSavings estimate
1 $35,000
2 50,000
3 45,000
4 25,000
5 15,000
Should the firm make this investment if it requires a minimum annual return of 9%
on all investments?
We will use Net Present Value computation in this assignment
NPV ScheduleYearsUndiscountedDiscounted @ 9%Cash FlowCash Flow13500032110.0925000042084.0034500034748.2642500017710.635150009748.97Total 136,402 Less Initial Outlay 130,000 NPV 6,402 Hence the NPV is in Positive than the company should invest in it.
E5–5Joseph is a friend of yours. He has plenty of money but little financial sense. He
received a gift of $12,000 for his recent graduation and is looking for a bank in which
to deposit the funds. Partners’ Savings Bank offers an account with an annual interest
rate of 3% compounded semiannually, while Selwyn’s offers an account with a 2.75%
annual interest rate compounded continuously. Calculate the value of the two accounts
at the end of one year, and recommend to Joseph which account he should choose.
Actual Yield Compounded Semiannually is = 3.022%
Actual Yield Compounded Continuously is = 2.788%
Semi-Annually Investment @ 3.022% = 12,362.7 $
Continuous Investment @ 2.788% = 12,334 $
Should go for the bank pays Semi Annually.
E5–6Jack and Jill have just had their first child. If college is expected to cost $150,000
per year in 18 years, how much should the couple begin depositing annually at the
end of each year to accumulate enough funds to pay the first year’s tuition at the
beginning of the 19th year? Assume that they can earn a 6% annual rate of return
on their investment.
PV of Annuity
PV = 150,000
PMT = ?
N =18
PV = PMT[1-(1/(1+i)^n))/i]
PMT = 13,853$
E6–1 The risk-free rate on T-bills recently was 1.23%. If the real rate of interest is estimated
to be 0.80%, what was the expected level of inflation?
= 1.23% * (0.80) = 0.98%
E6–2The yields for Treasuries with differing maturities on a recent day
a. Use the information to plot a yield curve for this date.
b. If the expectations hypothesis is true, approximately what rate of return do investors expect a 5-year Treasury note to pay 5 years from now?
MaturityYield
3 months 1.41%
6 months 1.71
2 years 2.68
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