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```					  Problem Set: Cost of Capital and Decision
Criteria
(Solutions Below)

Cost of Capital
1. Calculate the cost of equity if stock in a firm has a beta of 1.15. The
market risk premium is 8 percent, and T-bills are currently yielding 4
percent.

2. A bank has an issue of preferred stock with a \$6 stated dividend
that just sold for \$92 per share. What is the bank's cost of preferred
stock?

3. A firm is trying to determine its cost of debt. The firm has a debt issue
outstanding with 12 years to maturity that is quoted at 105 percent
of its face value of \$1,000. The issue makes semiannual payments
and has an coupon rate of 8 percent annually. What is the pretax
cost of debt? If the tax rate is 35 percent, what is the after-tax cost
of debt?

4. A firm has a target capital structure of 50 percent common stock, 5
percent preferred stock, and 45 percent debt. Its cost of equity is 16
percent, the cost of preferred stock is 7.5 percent, and the cost of
debt is 9 percent. The relevant tax rate is 35 percent. What is its
WACC?

Decision Rules
If r = 10%, determine whether or not to do the following projects
(questions 5-9) using each of the five decision criteria:

   Payback Period (3 year)
   Discounted Payback Period (3 year)
   Net Present Value (NPV) Rule
    Internal Rate of Return (IRR)
    Modified Internal Rate of Return (MIRR) (rRI = 10%)

5.
0      1   2   3   4
-1,000 500 200 200 500

6.
0      1     2     3     4
-10,000 3,500 3,200 3,200 2,500

7.
0   1   2    3   4
-300 250 150 -200 150

8.
0      1     2     3     4
-15,000 5,000 3,000 4,000 5,000

9.

0      1     2     3     4
-10,000 1,600 3,600 1,700 4,500

10. Use the NPV rule to decide on the better project (r = 10%).

0       1     2     3     4
-10,000 3,600 3,100 2,500 4,700
-20,000 8,300 4,900 5,200 7,200
Solutions
NOTE: I include the formulae solutions but you only need to know how to
do this on a financial calculator.

Cost of Capital
1. Calculate the cost of equity if stock in a firm has a beta of 1.15. The
market risk premium is 8 percent, and T-bills are currently yielding 4
percent.

Using the CAPM, we find:

RE = .04 + 1.15(.08) = .1320 or 13.20%

2. A bank has an issue of preferred stock with a \$6 stated dividend
that just sold for \$92 per share. What is the bank's cost of preferred
stock?

The cost of preferred stock is the dividend payment divided by the
price, so:

RP = \$6/\$92 = .0652 or 6.52%

3. A firm is trying to determine its cost of debt. The firm has a debt issue
outstanding with 12 years to maturity that is quoted at 105 percent
of face value. The issue makes semiannual payments and has an
coupon rate of 8 percent annually. What is the pretax cost of debt?
If the tax rate is 35 percent, what is the after-tax cost of debt?

P/Y = 2; N = 24; I/Y = 7.37%;
PV = 1,050; PMT = -40; FV = -1,000
PMT = (1,000 x 0.08)/2 = 40
N = 12 x 2 = 24

And the after-tax cost of debt is:

rD = 0.0737(1 – 0.35) = 0.0479 or 4.79%

4. A firm has a target capital structure of 50 percent common stock, 5
percent preferred stock, and 45 percent debt. Its cost of equity is 16
percent, the cost of preferred stock is 7.5 percent, and the cost of
debt is 9 percent. The relevant tax rate is 35 percent. What is its
WACC?
Using the equation to calculate the WACC, we find:

WACC = 0.50(0.16) + 0.05(0.075) + 0.45(0.09)(1 – 0.35)
= 0.1101 or 11.01%

Decision Rules
If r = 10%, determine whether or not to do the following projects
(questions 5-9) using each of the five decision criteria:

a.   Payback Period (3 year)
b.   Discounted Payback Period (3 year)
c.   Net Present Value (NPV) Rule
d.   Internal Rate of Return (IRR)
e.   Modified Internal Rate of Return (MIRR) (rRI = 10%)

NOTE: Where applicable, You may also use the financial calculator
functions to sole these problems.

5.
0      1   2   3   4
-1,000 500 200 200 500

a. Payback Period (3 year)

Payback  500  200  200  900  1,000

b. Discounted Payback Period (3 year)

500    200         200
Discounted Payback                                770.10  1,000
1.10 1.10  2
1.10 
3

c. Net Present Value (NPV) Rule

500    200         200      500
NPV  1,000                                     \$111.60
1.10 1.10  2
1.10  1.10 
3        4

\$110.60 > 0
Decision  Good Project
d. Internal Rate of Return (IRR)

500       200            200        500
1,000                                                0
1  IRR 1  IRR  2
1  IRR  1  IRR 
3           4

 IRR  15.17%  10%
Decision  Good Project

e. Modified Internal Rate of Return (MIRR)

500(1.10)3  200(1.10)2  200(1.10)  500
1,000                                                0
1  MIRR 
4

 MIRR  12.95%  10%
Decision  Good Project

6.
0      1     2     3     4
-10,000 3,500 3,200 3,200 2,500

a. Payback Period (3 year)

Payback  3,500  3,200  3,200  9,900  10,000

b. Discounted Payback Period (3 year)

3,500 3,200       3,200
Discounted Payback                                 8,230.65  10,000
1.10 1.10  2
1.10 
3

c. Net Present Value (NPV) Rule

3,500 3,200       3,200     2,500
NPV  10,000                                       -\$61.81
1.10 1.10  2
1.10  1.10 
3        4

-\$61.81 < 0

d. Internal Rate of Return (IRR)
3,500    3,200          3,200       2,500
10,000                                                0
1  IRR 1  IRR  2
1  IRR  1  IRR 
3           4

 IRR  9.70%  10%

e. Modified Internal Rate of Return (MIRR)

3,500(1.10)3  3,200(1.10)2  3,200(1.10)  2,500
10,000                                                        0
1  MIRR 
4

 MIRR  9.83%  10%

7.
0   1   2    3   4
-300 250 150 -200 150

a. Payback Period (3 year)

Payback  250  150  200  200  300

b. Discounted Payback Period (3 year)
250    150        200
Discounted Payback                            200.98  300
1.10 1.10  2
1.10 
3

c. Net Present Value (NPV) Rule

250    150        200      150
NPV  300                                      \$3.43
1.10 1.10  2
1.10  1.10 
3        4

\$3.43 > 0
Decision  Good Project

d. Internal Rate of Return (IRR)

250       150           200        150
300                                                0
1  IRR 1  IRR  2
1  IRR  1  IRR 
3           4

 IRR  10.88%  10%
Decision  Good Project
e. Modified Internal Rate of Return (MIRR)

250(1.10)3  150(1.10)2  200(1.10)  150
300                                                0
1  MIRR 
4

 MIRR  10.21%  10%
Decision  Good Project

8.
0      1     2     3     4
-15,000 5,000 3,000 4,000 5,000

a. Payback Period (3 year)

Payback  5,000  3,000  4,000  12,000  15,000

b. Discounted Payback Period (3 year)

5,000 3,000       4,000
Discounted Payback                                10.030.05  15,000
1.10 1.10  2
1.10 
3

c. Net Present Value (NPV) Rule

5,000 3,000       4,000     5,000
NPV  15,000                                      -\$1,554.88
1.10 1.10  2
1.10  1.10 
3        4

-\$1,554.88 < 0

d. Internal Rate of Return (IRR)
5,000    3,000          4,000       5,000
15,000                                              0
1  IRR 1  IRR  2
1  IRR  1  IRR 
3           4

 IRR  5.15%  10%

e. Modified Internal Rate of Return (MIRR)
5,000(1.10)3  3,000(1.10)2  4,000(1.10)  5,000
15,000                                                        0
1  MIRR 
4

 MIRR  7.03%  10%

9.

0      1     2     3     4
-10,000 1,600 3,600 1,700 4,500

a. Payback Period (3 year)

Payback  1 ,600  3,600  1,700  6,900  10,000

b. Discounted Payback Period (3 year)

1,600 3,600        1,700
Discounted Payback                                 5,706.99  10,000
1.10 1.10  2
1.10 
3

c. Net Present Value (NPV) Rule

1,600 3,600         1,700      4,500
NPV  10,000                                          -\$1,219.45
1.10 1.10  2
1.10 
3
1.10 
4

-\$1,219.45 < 0

d. Internal Rate of Return (IRR)
1,600    3,600          3,600       1,700
10,000                                              0
1  IRR 1  IRR  2
1  IRR  1  IRR 
3           4

 IRR  4.85%  10%

e. Modified Internal Rate of Return (MIRR)
1,600(1.10)3  3,600(1.10)2  3,600(1.10)  1,700
10,000                                                        0
1  MIRR 
4

 MIRR  6.48%  10%

10. Use the NPV rule to decide on the better project (r = 10%).

0       1     2     3     4
-10,000 3,600 3,100 2,500 4,700
-20,000 8,300 4,900 5,200 7,200

3,600 3,100       2,500       4,700
NPV  10,000                                          \$923.16
1.10 1.10  2
1.10 
3
1.10 
4

8,300 4,900       5,200     7,200
NPV  20,000                                      \$418.58
1.10 1.10  2
1.10  1.10 
3        4

\$923.16 > \$418.58
Decision  Do the First Project

```
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