Chapter 4, Problem 1LO

To determine

To determine- The present value of the future value of the future cash flows and yield to maturity of the four types of credit instruments is to be discussed.

Concept Introduction

Credit Market Instruments- There are four essential credit market instruments; simple loan, fixed payment loan, coupon bond and discount bond.

Simple loan- It is the amount of fund lent by a creditor to the borrower which must be repaid in principal and interest after a specified period of time known as the time of maturity of the loan.

Fixed Payment Loan- It refers to the funds given by the lender to the borrower which must be repaid as a fixed amount in a specific period of time (like a month, quarter or year). The value repaid in each period is inclusive of the principal and interest.

Coupon Bond- A coupon bond is issued by a corporation or government with a given face value, coupon rate and date of maturity. The lender issues the bond to the borrower. The latter receives a fixed interest income in each period equal to the coupon value. At the time of maturity, the face value of the bond is repaid to the creditor.

Discount Bond- A discount bond or a zero coupon bond is bought by the borrower at a price below its face value. The borrower gets no interest income or coupon interest as in the case of coupon bonds. Instead, he gets the face value as the time of maturity which is known to be higher than the investment made in purchasing.

Present value- It implies the current value of the future income or stream of cash flows calculated with a given discount rate. This discount rate is inversely related to the present value of the income.

Yield to maturity- It is the annual percentage rate or APR commonly known as the discount rate at which the sum of the future stream of income equals the current price of the bond. It is the most accurate measure of the interest rate and is often called the Internal Rate of Return or IRR

Explanation of Solution

For the simple loan, the present value (PV) of the amount to be repaid (C₁) after n years given that the rate of discount is r is:

????=
??
1
(??+??)
??

Here r is the discount rate of the yield to maturity for the simple loan.

For a fixed loan, the present value (PV) of the steam of cash flows to be repaid towards the loan taken by the borrower (C_i) where i is the time period for n number of years at a discount rate of r percent per period is:

????=
??=1
??
????
(1+??)
??

Here r is the yield to maturity.

For a coupon bond, the present value (PV) of the interest (C_i) earned per period i, where i ranges from 1 to n is:

????=
??=1
??
????
(1+??)
??
+
????
(1+??)
??

Where FV is the face value of the coupon and r is the rate of discount or the yield to maturity.

For the discounted coupon the present value is calculated using the same formula as the simple loan:

????=
??
1
(??+??)
??

Where C₁ is the face value of the bond, r is the rate of discount and n is the time period when the bond shall repay.