649 Words3 Pages

CHAPTER 4
INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
Solutions to Questions and Problems
3. To find the PV of a lump sum, we use:
PV = FV / (1 + r)t PV = $17,328 / (1.04)12 = $ 10,823.02 PV = $41,517 / (1.09)4 = $ 29.411.69 PV = $790,382 / (1.12)16 = $128,928.43 PV = $647,816 / (1.11)21 = $ 72,388.42
9. To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is:
FV = PV(1 + r)t
Solving for t, we get:
t = ln(FV / PV) / ln(1 + r)
FV = $160,000 = $25,000(1.032)t t = ln($160,000 / $25,000) / ln 1.032 t = 58.93 years
14. To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is:
FV = PV(1 + r)t
Solving for r, we get:
r = (FV / PV)1 / t – 1 r = ($10,500 / $5)1/113 – 1 r = .0704 or 7.04%
17. To find the PV of a lump sum, we use:
PV = FV / (1 + r)t PV = $160,000 / (1.1025)10 PV = $60,302.32
______________________________________________________________________________
CHAPTER 5
DISCOUNTED CASH FLOW VALUATION
Solutions to Questions and Problems
8. Here we have the FVA, the length of the annuity, and the interest rate. We want to calculate the annuity payment. Using the FVA equation:
FVA = C{[(1 + r)t – 1] / r} $25,000 = $C[(1.04758 – 1) / .0475]
We can now solve this equation for the annuity payment. Doing so, we get:
C = $25,000 / 9.46414 C = $2,641.55
14. For discrete compounding, to find the EAR, we use the equation:
EAR = [1 + (APR / m)]m – 1
So, for each bank, the EAR is:
First National: EAR = [1 + (.101 / 12)]12 – 1 = .1058 or 10.58%
First United: EAR = [1 + (.103 / 2)]2 – 1 = .1057 or

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