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$15,000 / + $40,000 / = $352, Accountant: NPV = $13,000 + $31,000 / = $345, Bee an engineer. After your brother announces that the appropriate discount rate is 6%, you can recalculate the NPVs. Calculate them the same way as above except using the 6% discount rate. Engineer NPV = $292, Accountant NPV = $292, Your brother made a poor decision. At a 6% rate, he should study accounting. Since Goose receives his first payment on July 1 and all payments in one year intervals from July 1, the easiest approach to this problem is to discount the cash flows to July 1 then use the six month discount rate () to discount them the additional six months. PV = $875,000 / () + $650,000 / ()() + $800,000 / ()() + $1,000,000 / ()() + $1,000,000/()() + $300,000 / ()() + $240,000 / ()() + $125,000 / ()() = $5,051,150 Remember that the use of annuity factors to discount the deferred payments yields the value of the annuity stream one period prior to the first payment. Thus, the annuity factor applied to the first set of deferred payments gives the value of those payments on July 1 of 1989. Discounting by 9% for five years brings the value to July 1, 1984. The use of the six month discount rate (%) brings the value of the payments to January 1, 1984. Similarly, the annuity factor applied to the second set of deferred payments yields the value of those payments in 2006. Discounting for 22 years at 9% and for six months at % provides the value at January 1, 1984. The equivalent fiveyear, annual salary is the annuity that solves: $5,051,150 = C C = $5,051,150/ C = $1,298,596 The student must be aware of possible rounding errors in this problem. The difference between % semiannual and % and for six months at % provides the value at January 1, 1984. PV = $10,000 + ($35,000 + $3,500) [1 / ( )] [1 ( / ) 25 ] = $415, NPV = $40,000 + $10,000 [1 / ( )] [1 ( / )5 ] = $3, Revise the textbook. The amount of the loan is $400,000 () = $320,000The monthly payment is C = $320,000 / = $ 2,Thirty years of payments $ 2, (360) = $ 845,Eight years of payments $2, (96) = $225,The difference is the balloon payment of $619, The lease payment is an annuity in advance C + C = $4,000C (1 + ) = $4,000C = $ The effective annual interest rate is [ 1 + ( / 4) ] 4 – 1 = The present value of the tenyear annuity is PV = 900 = $5,Four remaining discount periods PV = $5, / () 4 = $4, The present value of Ernie’s retirement ine PV = $300,000 / () 30 = $417,The present value of the cabinPV = $350,000 / () 10 = $177,The present value of his savingsPV = $40,000 = $280,In present value terms he must save an additional $313,In future value termsFV = $313, () 10 = $616,He must saveC = $ / = $58,B57Answers to EndofChapter Problems