Global Financial Management - Essay Example

1) Drawing time line for a $100 lump sum cash flow at the end of the year.[2] an ordinary annuity of $100per year for 3years , [3]an even cash flow stream of -$50, $100, $75 and $50 at the end of years 0 through 3.AnswersTimeline- this is a graphical representations used to show the timing of cash flows, where the tick marks represent end of periods therefore time 0 is today, time 1 is the end of the first 1.Solution: $100 lump sum at the end of 2nd year. I%Time Period012Cash flow100Solution: Ordinary annuity for a $100 annually for three years.

I%Time period012FV at year end100100100 Solution: Uneven cash flow stream I%Time period0123FV at year end-501007550What is the future value of an initial $100 after 3 years if it is invested in an account paying 10% annual rate?AnswersInterest rate = 0.1Cash flow = 100After 1 year: FV1 = PV1 + I1 + PV (I) = $100(1.10) = $110.00After 2 years: FV2 = FV1 + I2 = FV1 + FV2 (I) = FV1 (1 + I) OR PV (1+I) (1+I) = $110(1.10) = $121.00After 3 years: FV3 = FV2 + I3 = FV2 + FV2 (I) = FV2 (1 + I) = $121(1.10) = $133.

10Therefore:Time period0123FV at year end100110.00121133.10What is the present value of $100 to be received in 3 years if the appropriate interest rates 10%?PV = FVN ÷ (1 + I) ^ N = $100 (1÷1.10) ^3 = $100(0.7513) = $75.132) We sometimes need to find how long it will take a sum of money (or something else, such as earnings, population or price) to grow tom some specified amount. For example, if a company’s sales at a rate of 20% per year, how long will it take sales to double?

AnswerWe can use any numbers say $1 and $2, with this equationFVN = $2 = $1 (1 + I) ^N =$1(1.20) ^N N =3.8Using a calculator, plug I/YR = 20, PV = -1, PMT = 0, and FV = 2 then press N Button to find the numbers of years it would take 1 to double when the growth occurs at a 20% rate.3) If you want an investment to be double in three years, what rate of interest will it earn?Answers 1[1 + i] * 1[1 + i] ^2 * 1[1 + i] ^3 FV = $1(1 + i) ^3 = $2. $1(1 + i) ^3 = $2. (1 + i)^3 = $2/$1 = 2.1 + I = (2)1/31 + I = 1.

2599I = 25.99%.U can use a financial calculator to solve: enter N = 3, PV = -1, PMT = 0, FV = 2, then press the I button to find I = 25.99%.4) The difference between ordinary annuity and an ordinary annuity due? What type of annuity is shown below/ how would you change the time line to show the other type of annuity? 0 1 2 3 100 100 100AnswerThe above is ordinary annuity: it has its payments at the end of each period.To convert it to an annuity due, shift each payments to the left so that you end up with a payment under the 0 but non under the 3In ordinary annuity, the end of period payments is there while annuity due has beginning of period payments.5) (1) What is the future value of a 3 year ordinary annuity of $100 if the appropriate interest rate is 10%?

AnswerOne of the approach to use is to treat each annuity flow as a lump sum.i.e.FVAN = $100[1] + $100[1.10] + $100[1.10 * 1.10]=$100(3.3100)=$331.00(2) The present value of annuity?AnswerBy using the lump sum approach or a calculator, (Input N=3, I/YR= 10, PMT = 100, FV = 0) then press PV button.The present value (PV) is $248.68. (3) How will the future and present values when the annuity were an annuity due?AnswerIf at all the annuity were an annuity due, each payments would be shifted to the left, so each payment is compounded over an additional period or discounted back over one less period.

The future value of annuity will be: FVA3Due = $331.00(1.10) ^ 1 = $364.10The present value of an annuity due is: $100 + $90.91 + $82.64 = $273.556) What is the present value of the following uneven cash flow stream? The appropriate interest rate is 10% compound annually0 1 2 3 4 0 100 300 300 -50AnswerThe best approach is to find the PVs of each cash flow and then sum them as follows; 10%Time period01234FV at end year0100300300-50PV of each cash flow90.91247.93225.39-34.15530.

08Note that $50 year 4 outflow remains an outflow even when discounted.7) (1) Define the stated (quoted) or nominal rate INom as well as the periodic rate IperAnswerThe nominal rate simply is the cited percentage rate of return while the periodic rate is the rate changed by a lender or paid by a borrower each period.(2) Will the future value be larger or smaller if we compounded an initial amount more often annually for example, every months, or semiannually holding the stated interest rate unceasing?

With reasons.AnswerThe effective annual rate for 10% semiannually compounding is EAR = Effective annual rate = [(1 + INom) ÷M] ^m – 1.0 = [1 + 0.10/2] ^ 2 – 1.0 = 0.1025 = 10.25%For Monthly compounding EAR = 10.52% (3) What is the future value of $ 100 after 5 years under 12% annual compounding Semiannual compounding? Quarterly compounding? Monthly compounding? Daily compounding?AnswerUnder annual compounding, the $100 is compounded over 5 annual period at 12% rate of period INom= 12%.

FVn= = $100 = $100(1.12)5 = $176.23.Under semiannual compounding, the $100 is compounded over 10 semiannual period at 6% periodic rate.INom= 12%.FVn= = $100 = $100(1.06)10 = $179.08.For quarterly: FVn = $100(1.03)20 = $180.61.For monthly: FVn = $100(1.01)60 = $181.67. (4) What is the effective annual rate (EAR or EFF %)? What is the EFF% for a nominal rate of 12%, compounding semiannually, Compounded quarterly, compounded monthly, compounding daily?AnswerFor 12 percent semiannually compounding, the ear is 12.

3%EAR = Effective Annual Rate = INom = 12% and interest is compounded semiannually, then:EAR = = (1.06)2 – 1.0 = 1.1236 – 1.0 = 0.1236 = 12.36%.For quarterly compounding, the effective annual rate is:(1.03)4 - 1.0 = 12.55%.For monthly compounding, the effective annual rate is:= (1.01)12 - 1.0 = 12.55%.8) Will the effective annual rate ever be equal to the nominal (quoted) rate?AnswerWhen the annual compounding is used, then the nominal rate will be equal to the effective annual rate. If more frequent compounding is used, the effective annual rate will be above the nominal rate.9) (1) Construct amortization schedule for a $1000, 10% annual rate loan in 3 equal installments.

AnswerNote the face amount of the loan, $1000, is the present value of 3years annuity at a 10% rate.Time period0123PV for end year-1000PMTPMTPVA3 = PMT [1÷ (1+I) ^1] + PMT [1÷ (1+I) ^2] + PMT [1÷ (1 +I) ^3] = $1000 = PMT (1+I) ^-1 + PMT (1+I) ^-2 + PMT (1+I) ^-3We have an equation with only one unknown, so we can solve it to find PMT.The easy way is with a financial calculator. Input N=3, I/YR = 10, PV = 1000, FV = 0, and then press the PMT button to get PMT = 402.1148036, = $402.11Total paymentTotal int.paidPrin.paid$1.

206$206$1000(2) During Year 2, what is the annual interest expense for the borrower, and what is the annual interest income for the lenderAnswerPeriodBeginning BalancePaymentInterestPayment of PrincipleEnding Balance1$1000.00$402.11$100.00$302.11$697.892697.89402.1169.79332.32365.573365.57402.1336.56365.570.0010) Suppose that on January 1 you deposit $100 in an account that pays a nominal (quoted) interest rate of 11.33463%, with interest added (compounded) daily. How much will you have in your account on October 1, or 9 months later?

AnswerTime period0.01.02345273Flow of cash100I = 0.00031054 N = 273 FV = $108.8511) (1) What is the value at the end of year 3 of the following cash flow stream if the quoted interest rate is 10%, compounded semiannually?0 1 2 3 years100 100 100Since there are different situations here, the payments occur annually, but compounding occurs each 6 months, thus we cannot use normal annuity valuation techniques.Time period0246FV at end year0100100100$100(1.05*1.05)$100(1.05)^4$100(1.05)^6 $100 + $110.25 + $121.55 = $331.80(2) What is the PV of the same stream?

AnswerTo use a financial calculator, input N=3 I/YR = 10.25, PMT = 100, FV = 0, and then press the PV key to find the PV = $247.59.(3) Is the stream an annuity?Yes.(4) An important rule is that you should never show a nominal rate on a time line or use it in calculations unless what condition holds? (Hint: Think on annual compounding, when INom = EFF% = I per.). What would be wrong with your answers to part (1) and (20) if you used the nominal rate of 10% rather than the periodic rate Nom/2 = 10% /2 = 5%?

AnswerINom can be used in the calculations only when annual compounding occurs. If the nominal rate of 10% were used to discount the payment stream, the present value would be overstated by $272.32- $247.59 = $24.73.12) Suppose someone offered to sell you a note calling for the payment of $1000 in 15 months. They offer to sell it to you for $850 .You have $850 in a bank time deposit that pays a 6.76649% nominal rate with daily compounding, which is a 7% effective annual interest rate, and you plan to leave the money in the bank unless you buy the note.

The note is not risky you are sure it will be paid on schedule. Should you buy the note? Check the decision in three ways (1) by comparing your future value if you buy the note verses leaving your money in the bank; (2) by comparing the PV of the note with your current bank account and (3) by comparing the EFF $ on the note with that of the bank account.AnswerGreatest future wealthTime period0.012345456Cash flow850I = 0.00018538 N= 456FV = $924.97Buy the note: $1000 > $924.97Greatest Present wealth Time period0.

012345456Cash Flow1000I = 0.00018538, N = 456PV = $918.95Buy the note: The PV of the note is greater than its costs.Rate of returnTime period012345456Flow of cash8501000 N = 456 I = 0.035646% FAR = 13.89%Buy note: 13.89% > 7%CitationsSpiceland, J. D. (2009). Intermediate accounting (5th ed.). Boston: McGraw-Hill/Irwin.Kieso, D. E., Weygandt, J. J., & Warfield, T. D. (2012). Intermediate accounting (14th ed.). Hoboken, NJ: Wiley.Kieso, D. E., Weygandt, J. J., & Warfield, T. D. (2012). Intermediate accounting (14th ed.). Hoboken, NJ: Wiley.