Assignment Solution

Assignment on Bond Valuations

QUESTION NO. 1 Real and nominal rates interest Zane Perelli currently has $100 that he can spend today on polo shirts costing $25 each. Instead, he could invest the $100 in a risk-free U.S. Treasury security that is expected to earn a 9% nominal rate of interest. The consensus forecast of leading economists is a 5% rate of inflation over the coming year. A. How many polo shirts can Zane purchase today? B. How much money will Zane have at the end of 1 year if he forgoes purchasing the polo shirts today? C. How much would you expect the polo shirts to cost at the end of 1 year in light of the expected inflation? D. Use your findings in parts b and c to determine how many polo shirts (fractions are OK) Zane can purchase at the end of 1 year. In percentage terms, how many more or fewer polo shirts can Zane buy at the end of 1 year? E. What is Zane’s real rate of return over the year? How is it related to the percentage change in Zane’s buying power found in part d? Explain.

SOLUTION A. 100�25 = 4 𝑆ℎ𝑖𝑟𝑡𝑠 B. 100 × (1.09) = 109 C. 25 × (1.05) = 26.25 D. E.

109 4.1523 = 4.1523 →→ 26.25 4 1.09 − 1 = 3.8% 1.05

= 1.038 = 3.8% more shirts

QUESTION NO. 2

Complex Systems has an outstanding issue of $1,000-par-value bonds with 12% coupon interest rate. The issue pays interest annually and has 16 years remaining to its maturity date. A. If bonds of similar risk are currently earning a 10% rate of return, how much should the Complex Systems bond sell for today? B. Describe the two possible reasons why similar-risk bonds are currently earning a return below the coupon interest rate on the Complex Systems bond. C. If the required return were at 12% instead of 10%, what would the current value of Complex Systems’ bond be? Contrast this finding with your findings in part “A” and discuss. Solution 1 𝑖

A. 𝑃𝑉 = �𝐶𝐹( −

1 𝐹𝑉 � + �(1+𝑖)𝑡 � 𝑖(1+𝑖)𝑡

1 1 1000 − � + �(1+10%)16 � 10% 10%(1+10%)16

→→→ 𝑃𝑉 = �120(

𝑃𝑉 = 938.84 + 217.629 = $1156.47

B. Demand and Supply and life of the security

Saif Ullah PhD Finance Scholar [email protected] , 03216633261

Assignment on Bond Valuations 1 1 1000 − � + �(1+12%)16 � 12% 12%(1+12%)16

C. 𝑃𝑉 = �120(

QUESTION NO. 3

𝑃𝑉 = 836.87 + 163.12 = $1000

The relationship between a bond’s yield to maturity and coupon interest rate can be used to predict its pricing level. For each of the bonds listed, state whether the price of the bond will be at a premium to par, at par, or at a discount to par. Bond

Coupon interest rate

Yield to maturity Price

A

6%

10%

B

8%

8%

C

9%

7%

D

7%

9%

SOLUTION A. B. C. D.

Bond A is selling at Discount Bond B is selling at par value Bond C is selling at premium Bond D is selling to discount

QUESTION NO. 4 The Salem Company bond currently sells for $955 has a 12% coupon interest rate and a $1,000 par value, pays interest annually, and has 15 years to maturity. A. Calculate the yield to maturity (YTM) on this bond. B. Explain the relationship that exists between the coupon interest rate and yield to maturity and the par value and market value of a bond.

SOLUTION A. Find two discount rates and by using IRR find the correct number. I have calculated in MS Excel and it is 12.69% approximately. B. With the increase in YTM, Present Value decreases Coupon Rate and Present Value has direct relationship

QUESTION NO. 5 Find the value of a bond maturing in 6 years, with a $1,000 par value and a coupon interest rate of 10% (5% paid semiannually) if the required return on similar-risk bonds is 14% annual interest (7% semiannually) Saif Ullah PhD Finance Scholar [email protected] , 03216633261

Assignment on Bond Valuations

SOLUTION 1 1 1000 − � + �(1+7%)12 � 7% 12%(1+7%)12

A. 𝑃𝑉 = �120(

Saif Ullah PhD Finance Scholar [email protected] , 03216633261

𝑃𝑉 = 397.12 + 444.01 = $841.14