Disclaimer: This study guide contains problems that you may use to practice for the midterm exam #3. This is not an exhaustive list by any means. Additional problems will also be included in the exam, as well as modifications to the problems’ structure/content/question may be introduced. In addition, the midterm exam #3 will include many conceptual questions, that are not listed in this guide. To prepare for them, students need to read respective textbook chapters and review lecture slides and notes. In addition, I highly recommend students to review problems covered in class and in homework assignments. Cengage Adaptive Test Preparation is available for each Chapter in MindTap and is highly recommended for practice.

1.   Chapter #6

a.   Cost of money and factors that affect it

b.   Determinants of Interest Rates for corporate and treasury securities

c.    Term structure of interest rates and yield curve

d.   Pure expectation theory and its application

2.   Chapter #7

a.   Types of bonds, bond’s key features and cash flows

b.   Bond’s characteristics:

i.   Premium and discount bonds

ii.   YTM

c.   Valuation of a bond (with all kinds of payments) and all related computations:

i.   Coupon payments

ii.   Value of a bond

iii.   Yield To Maturity

iv.   Yield To Call

v.   Current Yield and Capital Gains Yield

d.   Bond’s relationships: coupon rate and YTM

e.   Bond’s risk: price risk and reinvestment risk

Practice problems

Chapter #6

Problem #1

Suppose 1-year T-bills currently yield 7.00% and the future inflation rate is expected to be constant at 4.70% per year. What is the real risk-free rate of return, r*? Disregard any cross-product terms, i.e., if  averaging is required, use the arithmetic average.

Answer: 2.3%

Solution:

rT一BillS = r* + IP ⇒ r* = rT一BillS − IP = 7% − 4.7% = 2.3%

Problem #2

Suppose the real risk-free rate is 2.50%, the average expected future inflation rate is 8.50%, and a maturity risk premium of 0.10% per year to maturity applies, i.e., MRP = 0.10%(t), where t is the number of years to maturity. What rate of return would you expect on a 1-year Treasury security, assuming the    pure expectations theory is NOT valid? Disregard cross-product terms, i.e., if averaging is required, use

the arithmetic average.

Answer: 11.1 %

Solution:

Pure expectation theory assumes that MRP does not exist (equal to zero). If pure expectation theory is incorrect then MRP does exist and we need to account for it according to the given formula MRP = 0.10%(t). Thus:

rT一SecuTity = r* + IP + MRP = 2.5% + 8.5% + 0.1% ∗ 1 = 11.1%

Problem #3

MLS Corporation's 5-year bonds yield 10.00%, and 5-year T-bonds yield 5.25%. The real risk-free rate is r* = 3.0%, the inflation premium for 5-year bonds is IP = 1.75%, the liquidity premium for MLS's bonds is LP =

0.75% versus zero for T-bonds, and the maturity risk premium for all bonds is found with the formula MRP = (t – 1) 0. 1%, where t = number ofyears to maturity. What is the default risk premium (DRP) on MLS's bonds?   Answer: 4%

Solution:

Since MLS is a corporation, then the formula for interest rate must include all premiums.

1) rMLS Bond = r* + IP + MRP + LP + DRP = 10%

2) rT一Bond = r* + IP + MRP = 5.25%

Corporate yield spread is the difference between interest rate on a corporate bond and a treasury bond of the same maturity. See below:

Subtract second equation from the first equation:

(r* + IP + MRP + LP + DRP) − (r* + IP + MRP) = 10% − 5.25%

LP + DRP = 4.75%

DRP = 4.75% − LP = 4.75% − 0.75% = 4%

Chapter #7

Problem #4

What is the value of a 20-year, 8% annual coupon bond with face value of $1,000, if rd =14%?

Answer: $602.61

Solution:

FV= 1000

I=14

PMT=80

Solve for PV = -602.61

Problem #5

What is the value of a 30-year, 12% semiannual coupon bond with face value of $1,000, if rd =11%?

Answer: $1,087.25

Solution:

FV= 1000

N=60

I=11/2=5.5

PMT=1000*12%/2=60

Solve for PV = -1,087.25

Problem #6

What is the YTM on the 10-year 9% annual coupon bond, selling for $887.

Answer: 10.91%

Solution:

FV= 1000

N=10

PMT=90

PV = -887

Solve for I =10.91

Problem #7

What is the nominal YTM on the 25-year 5% semiannual coupon bond , selling for $707.

Answer: nominal YTM =7.65%

Solution:

FV= 1000

N=25*2=50

PV= -707

PMT=1000*5%/2=25

Solve for I = 3.8227, Since the bond has semiannual coupons nominal YTM = 3.8227%*2=7.6454%

Problem #8

What is the effective YTM on the 25-year 5% semiannual coupon bond , selling for $707.

Answer: effective YTM 7. 79%

Solution:

FV= 1000

N=25*2=50

PV= -707

PMT=1000*5%/2=25

Solve for I = 3.8227, Since the bond has semiannual coupons effective YTM = (1+0.038227)2 -1=7.79%

Problem #9

What is the current YTM on the 15-year zero-coupon bond (no coupons are paid), selling for $554. What will the new value of the bond be in 10 years if the market required interest rate increases to 8%.

Answer: 4.02% and $680.58

Solution:

Step 1,find current YTM

FV= 1000

N=15

PMT=0

PV=-554

Solve for I = 4.02 – this is current YTM

Step 2,find bond’s value in 10 years, using new YTM=8%

FV= 1000

N=15-10=5 in ten years, there will be 5 years left until maturity ofthe bond

PMT=0

I=8, this is new YTM

Solve for PV = -680.58

Problem #10

Dalko Inc’s bonds currently sell for $980. They have a 10-year maturity, an annual coupon of $25, and a par value of $1,000. What is their current yield and capital gain yield?

Solution:

Step 1,find currentyield

CY=Annual coupon/Price = 25/980=0.0255 or 2.55%

Step 2, find capital gain yield

CGY = YTM-CY

Let’s find yield to maturity:

FV= 1000

N=10

PMT=25

PV=-980

Solve for I = 2.73% – this is current YTM

CGY = 2.73% - 2.55% = 0.18%

Answer: CY=2.55%, CGY=0.18%

Problem #11

Compusa Inc’s bonds currently sell for $1,155. They have a 15-year maturity, an annual coupon interest rate of   7.5%, and a par value of $1,000. This bonds may be called in 5 years for $1,075. Compute this bonds’ yield to call (YTC).

Solution: