## (Solved) ARE 171A Dr. Whitney Fall 2003 HOMEWORK ASSIGNMENT 2 DUE Tuesday,

ARE 171A    Dr. Whitney

Fall 2003

HOMEWORK ASSIGNMENT 2

DUE Tuesday, Feb. 9th, in class

(note: your midterm is Thursday the 11th, so you might want to make a copy of your answers to study from )

1. (11 pts) After 25 years of devoted service to your employer, you have decided to retire. Your employer offers a pension program with the following menu of retirement benefit schedules from which you may choose:

a.  \$240,000 in cash today

b.  \$18,700 per year for 20 years, to be paid at the beginning of each year.

c.  \$1,600 per month for 20 years, to be paid at the end of each month.

You are 60 years old and in excellent health; thus you expect to live long enough to receive all benefits from any of the three payment options.  Also, assume the above payments are on an after-tax basis, so you do not need to consider tax effects.

To determine the relative merits of these three payment schedules, you calculate the present value of each payment option (a, b, and c) and rank the options from best to worst.  However you are not certain of the rate of interest that will prevail over the next 20 years.  Therefore you compute present values and rank the retirement plans under three alternative nominal interest rate outcomes:

(i) 4%;

(ii) 7% and

(iii) 10%.  (Assume compounding is annual for b. and monthly for c.)

(iv) To make your final decision, you calculate the expected present value of each payment option.  It is your belief that future investment rates of return will be low (4% rate) with probability .3; will be moderate (7% rate) with probability .5; and will be high (10% rate) with probability .2.  Which option (a,b or c) do you choose to enroll in?

2. (14 pts) Lee?s Print and Frame Shop plans to purchase a small commercial building to use as retail space. The building?s price is \$1.25 million.  The firm will make a 20% down payment in cash, and finance the balance with a fixed rate loan.  Loan payments will be made at the end of each month.

The firm is considering 2 different loan programs, both offered by the same lender. One plan has a 30-year term, with an interest rate of 6.6%. The other has a 15-year term, with an interest rate of 6.24%. Each loan is fully amortized with a fixed interest rate.

i.  Why do you think the 15-year loan offers a lower interest rate than the 30-year loan?

ii.  What is the required monthly payment for each loan above? How might this affect the firm?s choice of loan plan?

iii.  To help in choosing the best loan for its circumstances, the firm develops an amortization schedule for each of the loan plans above. Using a spreadsheet (much faster way!) or paper and pencil, develop an amortization schedule for the first 6 payments for each loan. You should have 6 columns: Payment Number (1 through 6);  Initial Loan Balance;  Payment Amount (which you calculated in part i);  Interest Paid;  Principal Paid; and Balance Outstanding.

iv.  Suppose Lee completed the purchase on June 30th, 2015.  Thus, at the end of 2015, 6 payments will have been made.  What is the remaining principal balance for each loan at the end of this 6 month period?  How much interest was paid during the 2015 calendar year, for each loan? (The latter is deductible as a business expense on the firm's 2015 tax return)

3.(5 pts)  Stephanie wants to open a savings account.  She investigates three types of accounts:

Bank A offers a stated rate of 3.00%, compounded annually

Bank B offers a stated rate of 2.90%, compounded weekly

Bank C offers a stated rate of 2.85%, compounded daily

Bank D offers a stated rate of 2.80%, compounded continuously.

Calculate the effective annual percentage rate (also called APY) earned by each of these accounts.  Which bank should she choose?

4.(6 points)  (This problem is based on a situation a friend of mine asked for advice about. Details changed!)

Mr. Drew is elderly and in poor health, and has \$1,000,000 that he plans to pass on to his two daughters immediately (Febr. 2016).  However, he is very concerned about fairness.  One of his daughters, Jane, was always very self-reliant, and has not received any significant gifts from her father in the past.  The other daughter, Chelsea, attended a graduate school program for which her father paid significant tuition.  He paid Chelsea?s \$20,000 for tuition in Feb. 2003, Feb. 2004 and Feb. 2005.   He also purchased her an \$18,000 car in Feb. 2011.

How should the \$1,000,000 in current assets be divided today, so that the present value of both girls? total payments are equal?  Assume the discount rate is 7%.

5.  (8 pts) Clara plans to invest in corporate bonds to earn retirement income.  However, she is concerned about possible future changes in interest rates, and how they might affect the value of her portfolio.

a.  Suppose she purchases a newly issued AA-rated corporate bond with par =\$1000, 5 years to maturity, semiannual interest payments, and a coupon rate of 5%.  What will its present value be a year from now, if the required rate of return on the bond: (i).  declines to 3%;( ii).  remains at 5%, or (iii).  rises to 7%?

b.  Or instead, she might rather purchase another newly issued AA-rated corporate with par = \$1000, 20 years to maturity, and a coupon rate of 6%.   What will its present value be a year from now, if the required  rate of return on the bond:( i).  declines to 4%; (ii).  remains at 6%, or( iii).  rises to 8%?

c.  Compare your answers to a and b.  How do your findings help explain the different interest rates currently being offered by the two bonds Clara is considering?

6. (4 pts)  Find the yield to maturity of the following bonds, using an online bond calculator such as:

http://www.zenwealth.com/businessfinanceonline/BV/YTM.html , or a financial calculator.

a.  A corporate bond selling for a market value of \$930, with 20 years to maturity, a coupon rate of 6.0% and semiannual interest payments.

b.  The same bond above, if its current market value was \$ 1070.

ARE 171A

Fall 2003

Dr. Whitney

HOMEWORK ASSIGNMENT 2

DUE Tuesday, Feb. 9th, in class

(note: your midterm is Thursday the 11th, so you might want to make a copy of your answers to

study from )

1. (11 pts) After 25 years of devoted service to your employer, you have decided to retire. Your

employer offers a pension program with the following menu of retirement benefit schedules from which

you may choose:

a. \$240,000 in cash today

b. \$18,700 per year for 20 years, to be paid at the beginning of each year.

c. \$1,600 per month for 20 years, to be paid at the end of each month.

You are 60 years old and in excellent health; thus you expect to live long enough to receive all benefits

from any of the three payment options. Also, assume the above payments are on an after-tax basis, so

you do not need to consider tax effects.

To determine the relative merits of these three payment schedules, you calculate the present

value of each payment option (a, b, and c) and rank the options from best to worst. However you are

not certain of the rate of interest that will prevail over the next 20 years. Therefore you compute

present values and rank the retirement plans under three alternative nominal interest rate outcomes:

(i) 4%;

(ii) 7% and

(iii) 10%. (Assume compounding is annual for b. and monthly for c.)

(iv) To make your final decision, you calculate the expected present value of each payment option. It is

your belief that future investment rates of return will be low (4% rate) with probability .3; will be

moderate (7% rate) with probability .5; and will be high (10% rate) with probability .2. Which option

(a,b or c) do you choose to enroll in?

2. (14 pts) Lee?s Print and Frame Shop plans to purchase a small commercial building to use as retail

space. The building?s price is \$1.25 million. The firm will make a 20% down payment in cash, and

finance the balance with a fixed rate loan. Loan payments will be made at the end of each month.

The firm is considering 2 different loan programs, both offered by the same lender. One plan

has a 30-year term, with an interest rate of 6.6%. The other has a 15-year term, with an interest rate of

6.24%. Each loan is fully amortized with a fixed interest rate.

i. Why do you think the 15-year loan offers a lower interest rate than the 30-year loan?

ii. What is the required monthly payment for each loan above? How might this affect the firm?s choice

of loan plan?

iii. To help in choosing the best loan for its circumstances, the firm develops an amortization schedule

for each of the loan plans above. Using a spreadsheet (much faster way!) or paper and pencil, develop

an amortization schedule for the first 6 payments for each loan. You should have 6 columns: Payment

Number (1 through 6); Initial Loan Balance; Payment Amount (which you calculated in part i);

Interest Paid; Principal Paid; and Balance Outstanding.

iv. Suppose Lee completed the purchase on June 30 th, 2015. Thus, at the end of 2015, 6 payments will

have been made. What is the remaining principal balance for each loan at the end of this 6 month

period? How much interest was paid during the 2015 calendar year, for each loan? (The latter is

deductible as a business expense on the firm's 2015 tax return)

3.(5 pts) Stephanie wants to open a savings account. She investigates three types of accounts:

Bank A offers a stated rate of 3.00%, compounded annually

Bank B offers a stated rate of 2.90%, compounded weekly

Bank C offers a stated rate of 2.85%, compounded daily

Bank D offers a stated rate of 2.80%, compounded continuously.

Calculate the effective annual percentage rate (also called APY) earned by each of these accounts.

Which bank should she choose?

4.(6 points) (This problem is based on a situation a friend of mine asked for advice about. Details

changed!)

Mr. Drew is elderly and in poor health, and has \$1,000,000 that he plans to pass on to his two daughters

immediately (Febr. 2016). However, he is very concerned about fairness. One of his daughters, Jane,

was always very self-reliant, and has not received any significant gifts from her father in the past. The

other daughter, Chelsea, attended a graduate school program for which her father paid significant

tuition. He paid Chelsea?s \$20,000 for tuition in Feb. 2003, Feb. 2004 and Feb. 2005. He also

purchased her an \$18,000 car in Feb. 2011.

How should the \$1,000,000 in current assets be divided today, so that the present value of both

girls? total payments are equal? Assume the discount rate is 7%.

5. (8 pts) Clara plans to invest in corporate bonds to earn retirement income. However, she is

concerned about possible future changes in interest rates, and how they might affect the value of her

portfolio.

a. Suppose she purchases a newly issued AA-rated corporate bond with par =\$1000, 5 years to

maturity, semiannual interest payments, and a coupon rate of 5%. What will its present value be a year

from now, if the required rate of return on the bond: (i). declines to 3%;( ii). remains at 5%, or (iii).

rises to 7%?

b. Or instead, she might rather purchase another newly issued AA-rated corporate with par = \$1000,

20 years to maturity, and a coupon rate of 6%. What will its present value be a year from now, if the

required rate of return on the bond:( i). declines to 4%; (ii). remains at 6%, or( iii). rises to 8%?

c. Compare your answers to a and b. How do your findings help explain the different interest rates

currently being offered by the two bonds Clara is considering?

6. (4 pts) Find the yield to maturity of the following bonds, using an online bond calculator such as:

http://www.zenwealth.com/businessfinanceonline/BV/YTM.html , or a financial calculator.

a. A corporate bond selling for a market value of \$930, with 20 years to maturity, a coupon rate of

6.0% and semiannual interest payments.

b. The same bond above, if its current market value was \$ 1070.

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