Investment X offers to pay you $6,000 per year for 9 years, whereas Investment Y offers to pay you $8,200 per year for 5 years.
If the discount rate is 8 percent, what is the present value of these cash flows? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
If the discount rate is 23 percent, what is the present value of these cash flows? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
Explanation
The times lines are:
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0
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1
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2
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3
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4
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5
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6
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7
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8
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9
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PV
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$6,000
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$6,000
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$6,000
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$6,000
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$6,000
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$6,000
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$6,000
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$6,000
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$6,000
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0
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1
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2
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3
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4
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5
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PV
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$8,200
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$8,200
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$8,200
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$8,200
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$8,200
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To find the PVA, we use the equation:
PVA = C({1 – [1/(1 + r)t]}/r)
At an interest rate of 8 percent:
X@8%: PVA = $6,000{[1 – (1/1.08)9]/.08} = $37,481.33
Y@8%: PVA = $8,200{[1 – (1/1.08)5]/.08} = $32,740.22
And at an interest rate of 23 percent:
X@23%: PVA = $6,000{[1 – (1/1.23)9]/.23 } = $22,038.61
Y@23%: PVA = $8,200{[1 – (1/1.23)5]/.23 } = $22,988.48
Notice that the PV of Investment X has a greater PV than Investment Y at an interest rate of 8 percent, but a lower PV at an interest rate of 23 percent. 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 is more important since the cost of waiting (the interest rate) is so much greater.
Calculator Solution:
Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.
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Enter
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9
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8%
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±$6,000
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N
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I/Y
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PV
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PMT
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FV
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Solve for
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$37,481.33
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Enter
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5
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8%
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±$8,200
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N
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I/Y
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PV
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PMT
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FV
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Solve for
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$32,740.22
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Enter
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9
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23%
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±$6,000
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N
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I/Y
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PV
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PMT
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FV
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Solve for
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$22,038.61
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Enter
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5
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23%
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±$8,200
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N
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I/Y
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PV
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PMT
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FV
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Solve for
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$22,988.48
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Thank you!
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