Midterm Exam Practice Problems

Examples of True or False statements

1. A 20-year 10% corporate bond was issued 10 years ago. You purchased this bond today, when it was

trading to yield 12%. Next day, the yield decreased to 7% and remained at this level indefinitely.

Disregarding the possibility of default, if you decide to sell the bond just before its maturity date, you

will have incurred a capital loss.

2. A 30-year 8% corporate bond was issued exactly 10 years ago. You purchased this bond today, when it

was trading to yield 6%. Tomorrow, the yield decreased down to 5%, only to increase to 8% after 10

years. At maturity, the bond's realized return must be equal to 7%.

3. You purchased a 10% corporate bond when it was trading to yield 8% and calculated its duration to be

16.5 years. Next day, your bond's YTM changed and remained at this new level indefinitely. When you

sold your bond after 17.8 years and calculated the realized return over the holding period, you

discovered the realized return was higher than the yield to maturity at which you purchased the bond.

Based on this information, we can conclude that the YTM had must have decreased after you had

acquired the bond.

4. When the YTM increases, the duration of a zero-coupon bond will decrease.

5. Second order approximation produces asymmetric volatility of a bond's price in response to

positive/negative changes in the YTM.

7. The invoice price as of the settlement day is equivalent to the dirty price as of the purchase date plus

2 days' worth of accrued interest.

8. For a bond with a positive coupon rate, which is to pay at least one coupon before its maturity date,

the value of duration must be smaller than the time to maturity.

PROBLEMS

PROBLEM 1:

Consider an ordinary annuity with growing cash flows. The annuity's first cash flow is given by C1>0, the

periodic rate of growth of the cash flows is fixed at g, and the periodic discount rate equals r, where

0

equation for the present value of a growing ordinary annuity with t payments, where t is an integer

greater than 2. Simplify your answer as much as possible (collect terms!). Show all substitutions and

manipulations to receive credit.

PROBLEM 2

State (do not derive) the expression for Macaulay Duration of a series of T cash flows. Identify the

'weights' in this expression and show that their values add up to 1.

PROBLEM 3

A $10,000 face value 12% coupon corporate bond matures on March 15, 2028. You purchase the bond

on July 16, 2015 (M1) at quoted price of 99.375. Please, compute the bond's YTM, its invoice price as of

the settlement date (M4), and its dirty price on the purchase date (M1). State the yield as a percentage

with 6 digits after the decimal point and the prices in dollars and cents. Show all calculator inputs. You

must use your calculator's bond function and disregard weekends/holidays.

PROBLEM 4

A 10% corporate bond with a face value of $10,000 and 30 years to maturity was issued in May of 2007.

You bought this bond in May of 2010 (on its coupon day after the coupon had already been paid) when

it was trading to yield 8%. Assume the market interest rate remained at 8% from then on and you sold

the bond in May of 2017 (on its coupon day after the coupon had already been paid). Please, find the

value of total interest, interest on interest, capital gain or loss, total income, and realized return for the

holding period between May 2010 and May 2017 (NOT since the time when it was first issued). Hint: Do

not assume you purchased this bond at par and do not use your calculator's bond function.

PROBLEM 5

Please, compute duration, modified duration, dollar duration, convexity, and modified convexity of an

8% corporate bond that matures in exactly two semesters (12 months) and trades to yield 14%. Then,

find the volatility using second order approximation assuming the yield has increased by 2%.

PROBLEM 6

Springfield mogul Montgomery Burns, age 80, wants to retire at age 100, so he can steal candy from

babies full time. Once Mr. Burns retires, he wants to withdraw $500 million at the beginning of each

year for 10 years from a special off-shore account that will pay 18% annually. In order to fund his

retirement, Mr. Burns will make 20 equal end-of-the-year deposits in this same special account that will

pay 18% annually. How large of an annual deposit must be made to fund Mr. Burns retirement plans?

PROBLEM 7

Your parents ask your advice on financing a new car purchase. BMW has been running a national sales

promotion that gives buyers of a new car (BMW 435ix) the choice of a $2,000 rebate or 0.6% APR

financing for 60 months. In addition, the local BMW dealer is offering 2.8% APR financing for 60 months

on all car purchases through a local bank, which could be used if your parents decide to take the rebate

and use it as an additional down payment on their BMW 435ix. Your parents found a well-equipped

BMW for a price of $52,000 and have $3,000 as a down payment. Should your parents take the $2,000

rebate with 2.8% APR financing or the 0.6% APR financing and no rebate? Show your work and justify

your decision.

PROBLEM 8

You are considering leasing space at a local mall for 4 years, so you can open a coffee shop. The initial outlay (CF0

- this is an expense) is $50,000. The shop is projected to generate the following cash flows: CF1=$10,000;

CF2=$15,000; CF3=$15,000; CF4=$20,000. If the cost of capital is r=2%, would you undertake this project? What

if the cost of capital were 10%? Calculate the NPV in each case and justify your decision. At what value of the cost

of capital would you just break even?

PROBLEM 9

Consider a bond with annual coupon payments. You purchased the bond when it was originally issued.

Immediately afterwards, the YTM changed and remained at this new level indefinitely. Today, at the end

of year 5 (immediately after the 5th coupon payment), your bond investment has the following

characteristics:

Total Interest (Coupons) = $7,671.45

Interest-on-Interest (I2) = $1,410.73

Total Income = $11,183.86

Realized Return (annual) = 11.524953%

State rates as a percentage with 6 digits after the decimal point. Please, calculate the following:

a. YTM at the end of Year 5 (ANSWER 8.450000%)

b. Realized yield (annual) at the end of Year 8 (ANSWER 11.003364%)

c. Realized return (annual) at maturity (ANSWER 9.111174%)

PROBLEM 10

You used second order approximation (with convexity correction) to establish the following:

YTM increases by 1% Bond A's price decreases 2.5%

YTM decreases by 3% Bond A's price increases 8.5%

Use 2nd order approximation to calculate Bond A's volatility for a 0.5% decrease in YTM. State your

answer as a percentage with six digits after the decimal point. (ANSWER 1.312500%)