【正文】 olve this problem, scan across the row labeled 10 years until you find . It is close to the factor for 9%, . Thus, the rate you will receive on this note is slightly more than 9%. You can find a more precise answer by interpolating between nine and ten percent. [ 10% 249。 [ 249。 a 233。 r b c 239。 d 235。 9% By interpolating, you are presuming that the ratio of a to b is equal to the ratio of c to d. (9 r ) / (9 10) = ( ) / ( ) r = % The exact value could be obtained by solving the annuity formula for the interest rate. Sophisticated calculators can pute the rate directly as %.[Note: A standard financial calculator’s TVM keys can solve for this rate. With annuity flows, the IRR key on “advanced” financial calculators is unnecessary.] a. The annuity amount can be puted by first calculating the PV of the $25,000 which you need in five years. That amount is $17, [= $25,000 / ]. Next pute the annuity which has the same present value. $17, = C $17, = C () C = $4, Thus, putting $4, into the 7% account each year will provide $25,000 five years from today. b. The lump sum payment must be the present value of the $25,000, ., $25,000 / = $17, The formula for future value of any annuity can be used to solve the problem (see footnote 11 of the text). Option one: This cash flow is an annuity due. To value it, you must use the aftertax amounts. The aftertax payment is $160,000 (1 ) = $115,200. Value all except the first payment using the standard annuity formula, then add back the first payment of $115,200 to obtain the value of this option. Value = $115,200 + $115,200 = $115,200 + $115,200 () = $1,201, Option two: This option is valued similarly. You are able to have $446,000 now。 this is already on an aftertax basis. You will receive an annuity of $101,055 for each of the next thirty years. Those payments are taxable when you receive them, so your aftertax payment is $72, [= $101,055 (1 )]. Value = $446,000 + $72, = $446,000 + $72, () = $1,131, Since option one has a higher PV, you should choose it. Let r be the rate of interest you must earn. $10,000(1 + r)12 = $80,000 (1 + r)12 = 8 r = = % First pute the present value of all the payments you must make for your children’s education. The value as of one year before matriculation of one child’s education is $21,000 = $21,000 () = $59,955. This is the value of the elder child’s education fourteen years from now. It is the value of the younger child’s education sixteen years from today. The present value of these is PV = $59,955 / + $59,955 / = $14, You want to make fifteen equal payments into an account that yields 15% so that the present value of the equal payments is $14,. Payment = $14, / = $14, / = $2, This problem applies the growing annuity formula. The first payment is $50,000()2() = $1,. PV = $1, [1 / ( ) {1 / ( )}{ / }40] = $21, This is the present value of the payments, so the value forty years from today is $21, () = $457, Use the discount factors to discount the individual cash flows. Then pute the NPV of the project. Notice that the four $1,000 cash flows form an annuity. You can still use the factor tables to pute their PV. Essentially, they form cash flows that are a six year annuity less a two year annuity. Thus, the appropriate annuity factor to use with them is (= ).YearCash FlowFactorPV1 $700$2 90031,000249。41,0002,51,00061,00071,25081,375Total$5, NPV = $5,000 + $5, = $ Purchase the machine.Chapter 5: How to Value Bonds and Stocks The amount of the semiannual interest payment is $40 (=$1,000 180。 / 2). There are a total of 40 periods。 ., two half years in each of the twenty years in the term to maturity. The annuity factor tables can be used to price these bonds. The appropriate discount rate to use is the semiannual rate. That rate is simply the annual rate divided by two. Thus, for part b the rate to be used is 5% and for part c is it 3%. PV=C+F/(1+r)40 a. $40 () + $1,000 / = $1,000 Notice that whenever the coupon rate and the market rate are the same, the bond is priced at par. b. $40 () + $1,000 / = $ Notice that whenever the coupon rate is below the market rate, the bond is priced below par. c. $40 () + $1,000 / = $1, Notice that whenever the coupon rate is above the market rate, the bond is priced above par. a. The semiannual interest rate is $60 / $1,000 = . Thus, the effective annual rate is 1 = = %. b. Price = $30 + $1,000 / = $ c. Price = $30 + $1,000 / = $ Note: In parts b and c we are implicitly assuming that the yield curve is flat. That is, the yield in year 5 applies for year 6 as well. Price = $2 () / + $4 () / + $50 / = $ The number of shares you own = $100,000 / $ = 2,754 shares Price = $ () / + $ () / + $ () / + {$ () () / ( )} / = $ [Insert before last sentence of question: Assume that dividends are a fixed proportion of earnings.] Dividend one year from now = $5 (1 ) = $ Price = $5 + $ / { ()} = $ Since the current $5 dividend has not yet been paid, it is still included in the stock price.Chapter 6: Some Alternative Investment Rules a. Payback period of Project A = 1 + ($7,500 $4,000) / $3,500 = 2 yearsPayback period of Project B = 2 + ($5,000 $2,500 $1,200) / $3,000 = years Project A should be chosen. b. NPVA = $7,500 + $4,000 / + $3,500 / + $1,500 / = $ NPVB = $5,000 + $2,500 / + $1,200 / + $3,000 / = $ Project B should be chosen. a. Average Investment: ($16,000 + $12,000