Larry Schrenk, Instructor
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.
b.
c.
d.
e.
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%)
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
Decision  Bad Project
b. Discounted Payback Period (3 year)
Discounted Payback 
500
200
200


 770.10  1,000
2
1.10 1.10  1.10 3
Decision  Bad Project
c. Net Present Value (NPV) Rule
NPV  1,000 
500
200
200
500



 $111.60
2
3
4
1.10 1.10 
1.10  1.10 
$110.60 > 0
Decision  Good Project
d. Internal Rate of Return (IRR)
1,000 
500
200
200
500



0
2
3
4
1  IRR 1  IRR 
1  IRR  1  IRR 
 IRR  15.17%  10%
Decision  Good Project
e. Modified Internal Rate of Return (MIRR)
1,000 
500(1.10)3  200(1.10)2  200(1.10)  500
1  MIRR 
4
0
 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
Decision  Bad Project
b. Discounted Payback Period (3 year)
Discounted Payback 
3,500 3,200
3,200


 8,230.65  10,000
2
1.10 1.10  1.10 3
Decision  Bad Project
c. Net Present Value (NPV) Rule
NPV  10,000 
3,500 3,200
3,200
2,500



 -$61.81
2
3
4
1.10 1.10 
1.10
1.10
   
-$61.81 < 0
Decision  Bad Project
d. Internal Rate of Return (IRR)
10,000 
3,500
3,200
3,200
2,500



0
2
3
4
1  IRR 1  IRR 
1  IRR  1  IRR 
 IRR  9.70%  10%
Decision  Bad Project
e. Modified Internal Rate of Return (MIRR)
10,000 
3,500(1.10)3  3,200(1.10)2  3,200(1.10)  2,500
1  MIRR 
4
0
 MIRR  9.83%  10%
Decision  Bad Project
7.
0
1
2
3
4
-300 250 150 -200 150
a. Payback Period (3 year)
Payback  250  150  200  200  300
Decision  Bad Project
b. Discounted Payback Period (3 year)
250
150
200
Discounted Payback 


 200.98  300
2
1.10 1.10  1.10 3
Decision  Bad Project
c. Net Present Value (NPV) Rule
NPV  300 
250
150
200
150



 $3.43
2
3
4
1.10 1.10 
1.10  1.10 
$3.43 > 0
Decision  Good Project
d. Internal Rate of Return (IRR)
300 
250
150
200
150



0
2
3
4
1  IRR 1  IRR 
1  IRR  1  IRR 
 IRR  10.88%  10%
Decision  Good Project
e. Modified Internal Rate of Return (MIRR)
300 
250(1.10)3  150(1.10)2  200(1.10)  150
1  MIRR 
4
0
 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
Decision  Bad Project
b. Discounted Payback Period (3 year)
Discounted Payback 
5,000 3,000
4,000


 10.030.05  15,000
2
1.10 1.10  1.10 3
Decision  Bad Project
c. Net Present Value (NPV) Rule
NPV  15,000 
5,000 3,000
4,000
5,000



 -$1,554.88
2
3
4
1.10 1.10 
1.10  1.10 
-$1,554.88 < 0
Decision  Bad Project
d. Internal Rate of Return (IRR)
5,000
3,000
4,000
5,000
15,000 



0
2
3
4
1  IRR 1  IRR 
1  IRR  1  IRR 
 IRR  5.15%  10%
Decision  Bad Project
e. Modified Internal Rate of Return (MIRR)
15,000 
5,000(1.10)3  3,000(1.10)2  4,000(1.10)  5,000
1  MIRR 
4
0
 MIRR  7.03%  10%
Decision  Bad Project
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
Decision  Bad Project
b. Discounted Payback Period (3 year)
Discounted Payback 
1,600 3,600
1,700


 5,706.99  10,000
2
1.10 1.10  1.10 3
Decision  Bad Project
c. Net Present Value (NPV) Rule
NPV  10,000 
1,600 3,600
1,700
4,500



 -$1,219.45
2
3
4
1.10 1.10 
1.10
1.10
   
-$1,219.45 < 0
Decision  Bad Project
d. Internal Rate of Return (IRR)
1,600
3,600
3,600
1,700
10,000 



0
2
3
4
1  IRR 1  IRR 
1

IRR
1

IRR

 

 IRR  4.85%  10%
Decision  Bad Project
e. Modified Internal Rate of Return (MIRR)
10,000 
1,600(1.10)3  3,600(1.10)2  3,600(1.10)  1,700
1  MIRR 
4
0
 MIRR  6.48%  10%
Decision  Bad Project
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
NPV  10,000 
3,600 3,100
2,500
4,700



 $923.16
2
3
4
1.10 1.10 
1.10
1.10
   
NPV  20,000 
8,300 4,900
5,200
7,200



 $418.58
2
3
4
1.10 1.10 
1.10  1.10 
$923.16 > $418.58
Decision  Do the First Project