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 $50 (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 an 8% 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? Round your answer to the nearest cent.

Answer 1

900 Given Bond Price Cash Flow Year Amount 50 Nominal rate - Bank 2 50 3 50 4 1050 8% Solution Step 1: Calculate Rate compounded Quarterly 8% Yearly Nominal Rate Quarterly rate = Nominal / 4 2% Compounded rate ((1+Quarterly rate)^4)-1 8.24% Step 2: Calculate Present Value Year 1 2 Cashflow PVE PV 50 0.924 46.1923 5 0 0.853 42.6745 50 0.788 | 39.4247 1050 0.728 764.868 Present Value 893.16 3 4 (1/(1+r))^n where, PVF (Present Value Factor) = where r is discount rate, n is year PV (Present Value) = CFC X PVF Present Value of Bond is 893.16 $. Hence, to invest in securities is not good decision.