HW 2 Chapter 5 Solution(2)

HW 2 Chapter 5 Solution(2) - Chapter 5, Problem 2 To find...

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Unformatted text preview: Chapter 5, Problem 2 To find the PVA, we use the equation: PVA = C ( {1 [1/(1 + r)] t } / r ) At a 6 percent interest rate: X@6%: PVA = $4,300{[1 (1/1.06) 9 ] / .06 } = $29,247.28 Y@6%: PVA = $6,100{[1 (1/1.06) 5 ] / .06 } = $25,695.42 And at a 22 percent interest rate: X@22%: PVA = $4,300{[1 (1/1.22) 9 ] / .22 } = $16,281.03 Y@22%: PVA = $6,100{[1 (1/1.22) 5 ] / .22 } = $17,468.20 Notice that the PV of Investment X has a greater PV at a 6 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 annual payments. At a higher interest rate, getting these payments early are more important since the cost of waiting (the interest rate) is so much greater. Another way is to use the calculator: Calculator setup: CLR TVM X: $4,300 PMT , 9 N , 6% I/Y , CPT PV-> -$29,247.28, 22% I/Y , CPT PV-> -$16,281.03 Y: $6,100 PMT , 5 N , 6% I/Y , CPT PV-> -$25,695.42, 22% I/Y , CPT PV-> -$17,468.20 Discount Rate X: C = $4,300 Y: C = $6,100 6% $29,247.28 $25,695.42 22% $16,281.03 $17,468.20 Chapter 5, Problem 4 To find the PVA, we use the equation: PVA = C ( {1 [1/(1 + r)] t } / r ) PVA@15 yrs: PVA = $8,500{[1 (1/1.09) 15 ] / .09} = $68,515.85 PVA@40 yrs: PVA = $8,500{[1 (1/1.09) 40 ] / .09} = $91,437.56 PVA@75 yrs: PVA = $8,500{[1 (1/1.09) 75 ] / .09} = $94,297.15 To find the PV of a perpetuity, we use the equation:...
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HW 2 Chapter 5 Solution(2) - Chapter 5, Problem 2 To find...

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