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 some securities which call for four payments,$50 at the end of each of the next 3 years,plus a payment of $1,050 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 an 8 percent simple (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?
A) $1,000
B) $866
C) $1,050
D) $901
E) $893

Question

Quizplus · Accepted Answer

To determine the present value of the securities, we need to discount each payment back to the present using the effective annual rate (EAR) of the bank deposit. The bank offers an 8% simple interest rate with quarterly compounding, so first, we calculate the EAR:EAR = (1 + 0.08/4)^(4) - 1 = (1 + 0.02)^(4) - 1 = 1.08243216 - 1 = 0.08243216 or 8.24%Now, we discount each of the cash flows from the securities back to the present using this EAR:PV = 50 / (1 + 0.0824) + 50 / (1 + 0.0824)^2 + 50 / (1 + 0.0824)^3 + 1050 / (1 + 0.0824)^4PV ≈ 50 / 1.0824 + 50 / 1.1723 + 50 / 1.2700 + 1050 / 1.3759PV ≈ 46.20 + 42.67 + 39.37 + 763.39PV ≈ 891.63The present value of the securities, rounded to the nearest dollar, is approximately $892, but since the options are in whole dollars and $892 is not an option, the closest value provided is $893. Therefore, the securities are a good investment if their cost is $900, as their present value to you is slightly less than the cost.

Assume That You Inherited Some Money