Question

Assume that you inherited some money. A friend of yours is working as an unpaid intern at a local brokerage firm, and her boss is selling securities that call for 4 payments of $80 (1 payment at the end of each of the next 4 years) plus an extra payment of $1,000 at the end of Year 4. Your friend says she can get you some of these securities at a cost of $900 each. Your money is now invested in a bank that pays a 10% nominal (quoted) interest rate but with quarterly compounding. You regard the securities as being just as safe, and as liquid, as your bank deposit, so your required effective annual rate of return on the securities is the same as that on your bank deposit. You must calculate the value of the securities to decide whether they are a good investment. What is their present value to you?

Answer 1

Answer: The securities are a good investment as their Present Value of $925.17 is greater than their cost of $900.

Explanation:

First calculate the Effective annual rate of return;

= (( 1 + r/n)^n) - 1

= ((1 + 10%/4 ) ^ 4 ) - 1

= 10.38%

The present value of the security is;

=  (80 / 1.1038 ) + (80 / 1.1038 ^ 2) + (80 / 1.1038 ^ 3) + (80 / 1.1038 ^ 4 ) + (1000 / 1.1038 ^ 4 )

= $925.17