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Ryerson University
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Finance
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FIN 300
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John Currie
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Chapter 6

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CHAPTER 6 DISCOUNTED CASH FLOW VALUATION Learning ObjectivesLO1How to determine the future and present value of investments with multiple cash flows LO2How loan payments are calculated and how to find the interest rate on a loan LO3How loans are amortized or paid off LO4How interest rates are quoted and misquotedAnswers to Concepts Review and Critical Thinking Questions1 LO1 The four pieces are the present value PV the periodic cash flow C the discount rate r and the number of payments or the life of the annuity t2 LO1 Assuming positive cash flows both the present and the future values will rise3 LO1 Assuming positive cash flows the present value will fall and the future value will rise4 LO1 Its deceptive but very common The basic concept of time value of money is that a dollar today is not worth the same as a dollar tomorrow The deception is particularly irritating given that such lotteries are usually government sponsored5 LO1 If the total money is fixed you want as much as possible as soon as possible The team or more accurately the team owner wants just the opposite6 LO1 The better deal is the one with equal installments 307 Solutions to Questions and ProblemsNOTE All end of chapter problems were solved using a spreadsheet Many problems require multiple steps Due to space and readability constraints when these intermediate steps are included in this solutions manual rounding may appear to have occurred However the final answer for each problem is found without rounding during any step in the problemBasic1 LO1 To solve this problem we must find the PV of each cash flow and add them To find the PV of a lump sum we usetPVFV1r 234 PV10950110104011011301101075110330637234 PV181950118104011811301181075118279422234 PV24950124104012411301241075124248988 2 LO1 To find the PVA we use the equationt PVAC111r rAt a 5 percent interest rate9 X5 PVA600011105 05 42646936 Y5PVA80001110505 4060554 And at a 22 percent interest rate9 X22PVA600011122 22 22717716 Y22 PVA800011122 22 2533524Notice that the PV of cash flow X has a greater PV at a 5 percent interest rate but a lower PV at a 22 percent interest rate The reason is that X has greater total cash flows At a lower interest rate the total cash flow is more important since the cost of waiting the interest rate is not as great At a higher interest rate Y is more valuable since it has larger cash flows at the beginning At the higher interest rate these bigger cash flows early are more important since the cost of waiting the interest rate is so much greater 3 LO1 To solve this problem we must find the FV of each cash flow and add them To find the FV of a lump sum we usetFVPV1r 32 FV8 940108109010813401081405530771 32 FV11 940111109011113401111405552096 32 FV24 940124109012413401241405653481Notice we are finding the value at Year 4 the cash flow at Year 4 is simply added to the FV of the other cash flows In other words we do not need to compound this cash flow308 4 LO1 To find the PVA we use the equationt PVAC111r r 15 PVA15 yrs PVA530011107 07482719440 PVA40 yrs PVA530011107 07706580675 PVA75 yrs PVA530011107 077524070 To find the PV of a perpetuity we use the equation PVCr PV5300077571429 Notice that as the length of the annuity payments increases the present value of the annuity approaches the present value of the perpetuity The present value of the 75 year annuity and the present value of the perpetuity imply that the value today of all perpetuity payments beyond 75 years is only 473585 LO1 Here we have the PVA the length of the annuity and the interest rate We want to calculate the annuity payment Using the PVA equationt PVAC111r r15 PVA34000C1110765 0765 We can now solve this equation for the annuity payment Doing so we get C3400087454816523887726 LO1 To find the PVA we use the equationt PVAC111r r8 PVA73000111085 085411660367 LO1 Here we need to find the FVA The equation to find the FVA ist FVAC1r1r20 FVA for 20 years4000111211122627811640 FVA for 40 years400011121112245907263 Notice that because of exponential growth doubling the number of periods does not merely double the FVA8 LO1 Here we have the FVA the length of the annuity and the interest rate We want to calculate the annuity payment Using the FVA equationt FVAC1r1r 10 90000C10681068 We can now solve this equation for the annuity payment Doing so we get C900001368661632657577309

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