An investment offers $9,200 per year for 17 years, with the first payment occurring 1 year from now. Assume the required return is 12 percent. Requirement 1: What is the value of the investment today? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Present value $ Requirement 2: What would the value be if the payments occurred for 42 years? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Present value $ Requirement 3: What would the value be if the payments occurred for 77 years? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Present value $ Requirement 4: What would the value be if the payments occurred forever? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Present value $

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Answer:

1.

Present value = $65500.60053 rounded off to $65500.60

2.

Present value = $76009.84174 rounded off to $76009.84

3.

Present value = $76654.22671 rounded off to $76654.23

4.

PV of perpetuity = $76666.66667 rounded off to $76666.67

Explanation:

The payments from the investment can be classified as being an ordinary annuity as the payments made by the investment offer are of constant amount and occur at the end of the period, occur after equal intervals of time and are for a defined and finite time period except for the payments made in case of requirement 4. The formula to calculate the present value of annuity that will be used in requirement 1, 2 and 3 is attached.

1.

Present value = 9200 * [(1 - (1 + 0.12)^-17)  /  0.12]

Present value = $65500.60053 rounded off to $65500.60

2.

Present value = 9200 * [(1 - (1 + 0.12)^-42)  /  0.12]

Present value = $76009.84174 rounded off to $76009.84

3.

Present value = 9200 * [(1 - (1 + 0.12)^-77)  /  0.12]

Present value = $76654.22671 rounded off to $76654.23

4.

If the payments occur for an infinite period of time, they can be classified as a perpetuity.

The formula to calculate the present value of perpetuity is as follows,

PV of perpetuity = Cash Flow / r

Where,

r is the required rate of return or discount rate

PV of perpetuity = 9200 / 0.12

PV of perpetuity = $76666.66667 rounded off to $76666.67

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