Question

John and Joseph are vice presidents of Copperbelt Money Management (CMM) and co-directors of the company's pension fund management division. A major new client, the Nkana League of Cities, has requested that CMM present an investment seminar to the mayors of the represented cities. John and Joseph, who will make the presentation, have asked you to help them by answering the following questions. a) What are a bond's key features? (4 Marks) b) How is the values of any asset whose value is based on expected future cash flows determined? (1 mark) c) What is the value of a 10-year, $1,000 par value bond with a 10% annual coupon, paid semi-annually, if its required return is 10%? (2 Marks) d) 1. What is the value of a 13% coupon bond that is otherwise identical to the bond described in part 'c' above? Would we now have a discount or a premium bond? (2 Marks) II. What is the value of a 7% coupon bond with these characteristics? Would we now have a discount or premium bond? (2 Marks) III. What would happen to the values of the 7%, 10% and 13% coupon bonds over time if the required return increased to 13%? (3 Marks) e) I. what is the yield to maturity on a 10-year, 4% semi-annual coupon, $ 1,000 par value bond that sells for $ 887.00 and another that sells for $ 1,134.20? What does the fact that it sells at a discount or at a premium tell you about the relationship between ra and the coupon rate? (3 Marks) II. what are the total return, the current yield and the capital gains yield for the premium bond in parts 'e(1)? Assume that it is held to maturity and the company does not default on it. (3 Marks) [TOTAL: 20 MARKS]

Answer 1

a) Key Features of a Bond are Face Value: It is the principal value that the amount the bond holder will receive on the date of maturity from the bond issuer. A bond price can be different from its face value and can be more or less. Coupon: Coupons are termed as periodic interest payments received by Bondholder from Bond issuers. A coupon amount is always paid on Face Value of a Loan. For eg if the FV of a Bond is $1000 and coupon rate is 7% annually, the bond holder will receive $70 as coupon yearly Time To Maturity Time to maturity is the time the bond becomes wwwwww due for redemption. For eg a 10 years bond will become due after 10 years of its issuance. b) Value of an asset say bond is calculated by dividing the Future Cash Flow by the required rate of return so as to calculate the Present Values and adding them up

c) FV $1000 Time to Maturity 10 Years Coupon Rate 10% (paid semi annually) Required Rate = 10% Since both coupon rate and required rate are same the Bond value will be equal to the Face Value of the Loan as the Present Value of all the cash inflows including Interest and Face Value will be $1000 d) 1)FV $1000 Time to Maturity 10 Years Time to Maturity (In periods) 200 Periods (semiannually) Coupon Rate 13%p.a (paid semi annually) 65 paid semi annually Required Rate 10% p.a i.e 5% semi annually wwww wwww Bond price 65* (PVAF(5%,20)+ 1000* PVIF(5%,20) =(65*12.46)+(1000*.3769) 809.9 376.9 -1186.8 Since the bond is issued at a higher price than face value it is a premium bond

2)FV $1000 Time to Maturity 10 Years Time to Maturity (In periods) 20 Periods (semiannually) Coupon Rate 7%p.a (paid semi annually) 35 paid semi annually Required Rate = 10% p.a i.e 5% semi annually wwwww wwwww Bond price 35*(PVAF(5%,20)+ 1000* PVIF(5 %,20) గగ (35*12.46)+(1000*.3769) - 436.1 +376.9 813 Since the bond is issued at a lower price than face value it is a discount bond. 3) Over time if the required return is increased to 13% the bond price will start to fall as the PV will start to fall because of discounting by an increasing interest rate. Bond prices and interest rate has inverse relationship.