ACF 103 Tutorial 2-3 Solns.doc

ACF 103 Fundamentals of FinanceTutorial 2-3 - SolutionsChapter 31.What is the total present value of the following series of cash flows, discounted at 10%? End of yearCash flow1$1,00021,0003-2,00043,000Answer:PV = $1,000(PVIFA10%,2) + (-$2,000)(PVIF10%,3)+$3,000(PVIF1%,4)= $1,000(1.736) - $2,000(0.751) + $3,000(0.683) = $1,736 - $1,502 + $2,049 = $2,283Actual, $2,281.952.How long would it take for your money to triple if you invested it at 9%, compounded annually?Answer:Let investment today equal X, then it will grow to 3X.Thus, (X)(FVIF9%,n) = 3X or (FVIF9%,n) = 3From Table I, FVIF9%,13 = 3.066, therefore n = a little less than 13 years.Actual, 12.75 years3.At your brothers 15th birthday party, he asks you how much he would have to deposit at the end of every month to finance a $4,250 motorcycle on his 18th birthday. He plans to put the money in a 12% savings account that compounds interest monthly.Answer:The future value interest factor of an ordinary annuity of $1 per month for 36 months (three years) at 1% per month (12% per year) is 42.077.The table at the back of the text lists the (FVIFA1%,35) = 41.660. This must be adjusted to 36 periods as follows: (41.660)(1.01) + 1 = 43.077.Then $4,250/43.077 = $98.66 must be deposited at the end of each month.4.Text book Ch 3 question # 9 (p.66)Answer:Year Amount PV Factor at 14% Present Value1 $1,200 0.877 $1,052.402 2,000 0.769 1,538.003 2,400 0.675 1,620.004 1,900 0.592 1,124.805 1,600 0.519 830.40Subtotal (a) . $6,165.60110 (annuity)*1,400 5.216 $7,302.4015 (annuity)*1,400 3.433 4,806.20Subtotal (b) . $2,496.20Total Present Value (a + b) . $8,661.80 Alternatively, to get sub-total (b): 5-10 (annuity)1,400(5.216 3.433)2,496.205.Text book Ch 3 question # 12 (p.67)Answer:a. Annuity of $10,000 per year for 15 years at 5%. The discount factor in the PVIFA table at the end of the book is 10.380.Purchase price = $10,000 10.380 = $103,800b. Discount factor for 10% for 15 years is 7.606Purchase price = $10,000 7.606 = $76,060As the insurance company is able to earn more on the amount put up, it requires a lower purchase price.c. Annual annuity payment for 5% = $30,000/10.380 = $2,890Annual annuity payment for 10% = $30,000/7.606 = $3,944The higher the interest rate embodied in the yield calculations, the higher the annual payments.6.Text book Ch 3 question # 13 (p.67)Answer:$190,000 = PMT (PVIFA17%, 20) = PMT(5.628)PMT = $190,000/5.628 = $33,7607.It is January 1 and you have made a New Years resolution to invest $2,000 in an Individual Retirement Account (IRA) at the end of every year for the next 30 years. If your money is compounded at an average annual rate of 9%, how much will you have accumulated at the end of 30 years?Answer:FVA30 = PMT(FVIFA9%,30),FVA30 = $2,000(136.308) = $272,616Actual, $272,615.088.Congratulations! You have just won first prize in a raffle and must choose between $20,000 in cash today or an annuity of $5,000 a year for five years. (The annuity payments would come to you at the end of each year.) Which of these two choices is worth more, assuming a 7% discount rate? Show your calculations.Answer:PVA5 = PMT(PVIFA7%,5),($5,000)(4.100) = $20,500The annuity is worth more than the $20,000 in cash today.Actual, $20,500.999.Your aunt is bragging about the great investment she made in a house that she bought 30 years ago for $20,000 and has just sold for $65,000.a. Calculate the rate of return on this investment.b. If the average annual rate of inflation has been 3.5% during this period, was this a great investment? Explain.Answer:a. $65,000 = $20,000(FVIFi%,30); So, 3.25 = (FVIFi%,30),From Table I, with n = 20, then i = a little over 4%b. This hardly qualifies as a great investment, since it has barely kept ahead of the inflation rate.Actual, 4.01%10.Ms. Early Saver has decided to invest $1,000 at the end of each year for the next 10 years, then she will just let the amount compound for 40 additional years. Her brother, Late Saver, has a different investment program: He will invest nothing for the next 10 years, but will invest $1,000 per year (at the end of each year) for the following 40 years. If we assume an 8% rate of return, compounded annually, which investment program will be worth more 50 years from now?Answer:Early Saver: FVA10 = $1,000(FVIFA8%,10) = $1,000(14.487) = $14,487FV40 = $14,487(FVIF8%,40) = $14,487(21.725) = $314,730.08Late Saver: FVA40 = $1,000(FVIFA8%,40) = $1,000(259.057) = $259,057The Early Saver investment program is worth more. (Theres a moral here: Start saving and investing as soon as you can.)Actual, $314,713.64 versus $259,056.5811.Text book Ch 3 question # 1 (p.65)Answer:12Text book Ch 3 question # 2 (p.66)Answer:13.Text