“Problem 1.
You have a project that is very similar to the types
of projects in PhelpCo (an all equity firm).
On average the project is expected to generate positive cash flows
starting next year (at t = 1) of $150,000, growing at 10 percent per year for
the foreseeable future.

Currently
the scale of PhelpCo is such that their earnings per share is $5.00. PhelpCo pays out all of its earnings as an
annual dividend. The current price of
PhelpCo is $40.00 per share.

a.
Given the above information about PhelpCo, what is the appropriate discount
rate that should be applied to the cash flows of your project?

b.
Given this opportunity cost (discount rate), what is the PV of your
project?

c.
An analyst that works for you estimated that the cost of the project (incurred
at t = 0) is $3,800,000. Should you
adopt the project? That is, is it the
case that the amount of money you have to spend to get the future cash flows is
less than these future cash flows are worth in present value terms?

Problem 2.

a.
What would an investor be
willing to pay for common stock in a firm that has no growth opportunities but
pays dividends of $6.00 per year, starting today? The next dividend will be paid in exactly 1
year. The required rate of return is a
stated annual rate of 12.5% compounded quarterly. If the investor buys now, they will receive
todays dividend.

b.
What would an investor be
willing to pay for common stock in a firm that is expected to pay an annual
dividend that will grow at 10 percent over the next 2 years, then grow at 5
percent for 3 years and then stop growing (i.e., will grow at zero percent)
from then on? The firm just paid its
dividend of $2.00. Thus, if an investor buys this stock, they will not receive
the dividend that was just paid. The
next dividend will be paid in one year.
The required rate of return is an effective annual rate of 10%.

Problem 3.

The ABC Company currently has $16,000,000
in physical assets that have always generated a steady stream of earnings for
the company. The management of the firm
has always paid all of its earnings to shareholders as a dividend. While there is risk in the return on assets,
the average return over many years has been steady at 10 percent. The firm has 1,000,000 shares
outstanding. The current ex-dividend
price of a share of equity is $15.00.

a. What is the required rate of return
for this firm implied by the current market price?

The management wants the company to
grow. Rather than pay out all of the
firms earnings as
a dividend this year (t = 0), the management wants to plow back 60 percent of
the earnings into the business.

b. Assuming that the management will be
able to maintain the return on assets it has achieved in the past as the firm
grows, what will be the ex-dividend stock price under the new growth
policy? Fill in the following table and
refer to appropriate entries when calculating the price.

t = 0 t = 1 t = 2

Investment Capital
Per Share:

Earnings
Per Share

New Investment
Per Share:

Dividend:
Per Share

Growth in dividend is

Price =

Price at t = 0: __________.

c. Should the management adopt this
policy? Why or why not?

Problem 4.

Which one of the
following corresponds to the highest effective annual rate?

a.
Stated rate of 18.3 percent compounded
monthly .

b.
Stated rate of 18.4 percent compounded
continuously .

c.
Stated rate of 18.4 percent compounded every six months
.

d.
Stated rate of 18.5 percent compounded
annually .

Problem 5.

Exactly one year ago
today (say 4/20/14), the prices on zero-coupon US treasury bonds were as
follows:

Maturity Price
In years
1 98
2 94
3 90
4.
82

The current (i.e.,
4/20/15) prices are as follows:

Maturity Price
In years
1 96
2 92
3 88
4 80

Questions:

a. What was the one-year
forward rate last year?

b. What was the one-year
forward rate for three years in the future last year?

c. Using the current
yield curve, what is the relationship between the forward rate and what
actually happened?

d. If the forward rate is
a prediction of the rates next year, what will a one-year zero sell for next
year? What will a two-year zero sell for
next year?

Price of a one-year zero
next year = ____________

Price of a two-year zero
next year = _____________

Problem 6.

Consider the following
data on various bonds trading at t = 0.

Bond Coupon Payment Face
Value Time to Maturity Price at t = 0

Rate Frequency
(per $1000 in
face value)

A 7% 4
times a year 1000 8 years ?
B 12%
once a year 1000 2 years 1100
C 0 2 times a year 1000 5 years 700

The prices are all
ex-coupon. That is, they are the price
you would pay immediately after the coupon has been paid. Thus, when you pay that price, you will
receive the next coupon one period later.

Answer the following
questions.

a.
What
is the yield to maturity on Bond B?

b. If the yield curve were flat at 5 percent
effective annual yield, what should the price of Bond A equal? (Note:
given all of the data above, it may not be flat.)

c.
If in
one year (i.e., at t = 1), the yield curve is flat at 6% (i.e., the yield to
maturity on zero-coupon bonds of all maturities is 6%), what will be the
holding period yield for Bond B if you bought Bond B at t = 0?

Problem 7.

You have taken out a
30-year fixed-rate mortgage for $500,000.00 that requires you to make a fixed
monthly payment every month for the next 360 months, with the first payment
being made exactly one month from now. The
stated interest rate is 4 percent, compounded monthly.

a.
What
are the monthly payments?

b.
For
the first payment, what is the amount of that payment that repays principle and
how much of that payment is an interest payment?

Principle repayment = ________________; Interest payment = ________________________.

c.
Right
after you make the first monthly payment (i.e., essentially one month from
now), using your answers to be above, what will be the remaining principle on
the loan?
(3
points)

d.
Right
after you make your first payment, what is the present value of the remaining
monthly payments using the stated interest rate of 4 percent, compounded
monthly? How does this compare to your
answer to c above? (3 points)

e.
Using
the result you can infer from comparing c and d above, answer the following
question. After your have made 180
monthly payments, (i) what is the remaining principle, (ii) how much of the 181st
payment is payment of interest, (iii) how much of the 181st payment
is to repay principle. (Do not go
through the lengthy process of building a 181 period spreadsheetuse the result from c and d above). (3 points)

Put answers here:

i. ____________, ii. __________________, ii._____________________

Show work below.

Problem 1. You have a project that is very similar to the types
of projects in PhelpCo (an all equity firm).
On average the project is expected to generate positive cash flows
starting next year (at t = 1) of $150,000, growing at 10 percent per year for
the foreseeable future. Currently
the scale of PhelpCo is such that their earnings per share is $5.00. PhelpCo pays out all of its earnings as an
annual dividend. The current price of
PhelpCo is $40.00 per share. a.
Given the above information about PhelpCo, what is the appropriate discount
rate that should be applied to the cash flows of your project? b.
Given this opportunity cost (discount rate), what is the PV of your
project? c.
An analyst that works for you estimated that the cost of the project (incurred
at t = 0) is $3,800,000. Should you
adopt the project? That is, is it the
case that the amount of money you have to spend to get the future cash flows is
less than these future cash flows are worth in present value terms? Problem 2.
a.
What would an investor be
willing to pay for common stock in a firm that has no growth opportunities but
pays dividends of $6.00 per year, starting today? The next dividend will be paid in exactly 1
year. The required rate of return is a
stated annual rate of 12.5% compounded quarterly. If the investor buys now, they will receive
todays dividend.b.
What would an investor be
willing to pay for common stock in a firm that is expected to pay an annual
dividend that will grow at 10 percent over the next 2 years, then grow at 5
percent for 3 years and then stop growing (i.e., will grow at zero percent)
from then on? The firm just paid its
dividend of $2.00. Thus, if an investor buys this stock, they will not receive
the dividend that was just paid. The
next dividend will be paid in one year.
The required rate of return is an effective annual rate of 10%.Problem 3. The ABC Company currently has $16,000,000
in physical assets that have always generated a steady stream of earnings for
the company. The management of the firm
has always paid all of its earnings to shareholders as a dividend. While there is risk in the return on assets,
the average return over many years has been steady at 10 percent. The firm has 1,000,000 shares
outstanding. The current ex-dividend
price of a share of equity is $15.00. a. What is the required rate of return
for this firm implied by the current market price? The management wants the company to
grow. Rather than pay out all of the
firms earnings as
a dividend this year (t = 0), the management wants to plow back 60 percent of
the earnings into the business. b. Assuming that the management will be
able to maintain the return on assets it has achieved in the past as the firm
grows, what will be the ex-dividend stock price under the new growth
policy? Fill in the following table and
refer to appropriate entries when calculating the price.t = 0 t = 1 t = 2Investment Capital Per Share: Earnings Per Share New Investment Per Share: Dividend: Per Share Growth in dividend is Price = Price at t = 0: __________.
c. Should the management adopt this
policy? Why or why not? Problem 4. Which one of the
following corresponds to the highest effective annual rate? a.
Stated rate of 18.3 percent compounded
monthly .b.
Stated rate of 18.4 percent compounded
continuously .c.
Stated rate of 18.4 percent compounded every six months
.d.
Stated rate of 18.5 percent compounded
annually . Problem 5. Exactly one year ago
today (say 4/20/14), the prices on zero-coupon US treasury bonds were as
follows: Maturity PriceIn years 1 98 2 94 3 904.
82The current (i.e.,
4/20/15) prices are as follows: Maturity PriceIn years 1 96 2 92 3 884 80Questions: a. What was the one-year
forward rate last year? b. What was the one-year
forward rate for three years in the future last year? c. Using the current
yield curve, what is the relationship between the forward rate and what
actually happened? d. If the forward rate is
a prediction of the rates next year, what will a one-year zero sell for next
year? What will a two-year zero sell for
next year? Price of a one-year zero
next year = ____________Price of a two-year zero
next year = _____________Problem 6. Consider the following
data on various bonds trading at t = 0.
Bond Coupon Payment Face
Value Time to Maturity Price at t = 0
Rate Frequency
(per $1000 in face value)A 7% 4
times a year 1000 8 years ?B 12%
once a year 1000 2 years 1100C 0 2 times a year 1000 5 years 700 The prices are all
ex-coupon. That is, they are the price
you would pay immediately after the coupon has been paid. Thus, when you pay that price, you will
receive the next coupon one period later.
Answer the following
questions. a.
What
is the yield to maturity on Bond B? b. If the yield curve were flat at 5 percent
effective annual yield, what should the price of Bond A equal? (Note:
given all of the data above, it may not be flat.) c.
If in
one year (i.e., at t = 1), the yield curve is flat at 6% (i.e., the yield to
maturity on zero-coupon bonds of all maturities is 6%), what will be the
holding period yield for Bond B if you bought Bond B at t = 0? Problem 7. You have taken out a
30-year fixed-rate mortgage for $500,000.00 that requires you to make a fixed
monthly payment every month for the next 360 months, with the first payment
being made exactly one month from now. The
stated interest rate is 4 percent, compounded monthly. a.
What
are the monthly payments? b.
For
the first payment, what is the amount of that payment that repays principle and
how much of that payment is an interest payment? Principle repayment = ________________; Interest payment = ________________________. c.
Right
after you make the first monthly payment (i.e., essentially one month from
now), using your answers to be above, what will be the remaining principle on
the loan? (3
points) d.
Right
after you make your first payment, what is the present value of the remaining
monthly payments using the stated interest rate of 4 percent, compounded
monthly? How does this compare to your
answer to c above? (3 points)e.
Using
the result you can infer from comparing c and d above, answer the following
question. After your have made 180
monthly payments, (i) what is the remaining principle, (ii) how much of the 181st
payment is payment of interest, (iii) how much of the 181st payment
is to repay principle. (Do not go
through the lengthy process of building a 181 period spreadsheetuse the result from c and d above). (3 points)Put answers here: i. ____________, ii. __________________, ii._____________________ Show work below. “