Investment X offers to pay you $6,500 per year for 9 years, whereas Investment Y

Question

Investment X offers to pay you $6,500 per year for 9 years, whereas Investment Y offers to pay you $8,900 per year for 5 years.

If the discount rate is 5 percent, what is the present value of these cash flows? (Enter rounded answers as directed, but do not use rounded numbers in intermediate calculations. 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? (Enter rounded answers as directed, but do not use rounded numbers in intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)

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Investment X offers to pay you $6,500 per year for 9 years, whereas Investment Y offers to pay you $8,900 per year for 5 years.

Explanation / Answer

Requirement 1:

Part A)

The present value is calculated by discounting annual cash flows with the use of a specific discount rate. The formula for calculating present value is:

Present Value = Cash Flow Year 0 + Cash Flow Year 1/(1+Discount Rate)^1 + Cash Flow Year 2/(1+Discount Rate)^2 + Cash Flow Year 3/(1+Discount Rate)^3 + Cash Flow Year 4/(1+Discount Rate)^4 + Cash Flow Year 5/(1+Discount Rate)^5 and so on.

____________

Using the values provided in the question, we get,

Present Value (Investment X) = 0 + 6,500/(1+5%)^1 + 6,500/(1+5%)^2 + 6,500/(1+5%)^3 + 6,500/(1+5%)^4 + 6,500/(1+5%)^5 + 6,500/(1+5%)^6 + 6,500/(1+5%)^7 + 6,500/(1+5%)^8 + 6,500/(1+5%)^9 = $46,200.84

Present Value (Investment Y) = 0 + 8,900/(1+5%)^1 + 8,900/(1+5%)^2 + 8,900/(1+5%)^3 + 8,900/(1+5%)^4 + 8,900/(1+5%)^5 = $38,532.34

___________

Part B)

Investment X has has the higher present value at 5 percent.

_________________________

Requirement 2:

Part A)

The present value is calculated by discounting annual cash flows with the use of a specific discount rate. The formula for calculating present value is:

Present Value = Cash Flow Year 0 + Cash Flow Year 1/(1+Discount Rate)^1 + Cash Flow Year 2/(1+Discount Rate)^2 + Cash Flow Year 3/(1+Discount Rate)^3 + Cash Flow Year 4/(1+Discount Rate)^4 + Cash Flow Year 5/(1+Discount Rate)^5 and so on.

____________

Using the values provided in the question, we get,

Present Value (Investment X) = 0 + 6,500/(1+23%)^1 + 6,500/(1+23%)^2 + 6,500/(1+23%)^3 + 6,500/(1+23%)^4 + 6,500/(1+23%)^5 + 6,500/(1+23%)^6 + 6,500/(1+23%)^7 + 6,500/(1+23%)^8 + 6,500/(1+23%)^9 = $23,875.16

Present Value (Investment Y) = 0 + 8,900/(1+23%)^1 + 8,900/(1+23%)^2 + 8,900/(1+23%)^3 + 8,900/(1+23%)^4 + 8,900/(1+23%)^5 = $24,950.91

___________

Part B)

Investment Y has has the higher present value at 23% percent.

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