Question

Mike Westfield is analyzing ordinary annuity investment by calculating the sum of the present values of its expected cash flows. Assuming an interest rate greater than 0%, which of the following would decrease the present value of the investment? a. Using a lower interest rate. b. The riskiness of the investment's cash flows decreases. c. Reducing the size of the annual payments by half (e.g., reducing the annual payment from $100 to $50) while doubling the number of annual payments (e.g., doubling the number of annual payments from 10 to 20). d. Doubling the size of the annual payments (e.g., doubling the annual payment from $100 to $200) while reducing the number of annual payments by half (e.g., reducing the number of annual payments from 10 to 5). e. None of the above will decrease the present value of the investment.

Answer 1

Mike Westfield

The present of the investment would decrease if you are:

c. Reducing the size of the annual payments by half (e.g., reducing the annual payment from $100 to $50) while doubling the number of annual payments (e.g., doubling the number of annual payments from 10 to 20).

Step-by-step explanation:

a) Data and Illustrations:

The present value of $100 annuity for 10 years at 10% = $614.50 ($100 * 6.145)

The present value of $50 annuity for 20 years at 10% = $428.70 ($50 * 8.574)

Compared to:

The present value of $100 annuity for 10 years at 10% = $614.50 ($100 * 6.145)

The present value of $200 annuity for 5 years at 10% = $758.20 ($200 * 3.791)

Or when a lower rate is used, for example 5%:

The present value of $100 annuity for 10 years at 5% = $772.20 ($100 * 7.722)

The present value of $100 annuity for 10 years at 10% = $614.50 ($100 * 6.145)