Full-Time MBA student

Topics: Stock, Net present value, Bond Pages: 22 (1909 words) Published: April 15, 2014
﻿MGT 202: Solutions for Homework A (Spring 2014)

Chap 6

11.a.With a par value of \$1,000 and a coupon rate of 8%, the bondholder receives \$80 per year.

b.

c.If the yield to maturity is 6%, the bond will sell for:

18.a.The coupon rate must be 7% because the bonds were issued at face value with a yield to maturity of 7%. Now, the price is:

b.The investors pay \$641.01 for the bond. They expect to receive the promised coupons plus \$800 at maturity. We calculate the yield to maturity based on these expectations by solving the following equation for r:  r = 12.87%

Using a financial calculator, enter: n = 8; PV = ()641.01; FV = 800; PMT = 70, and then compute i = 12.87%

Chap 7

41.DIV1 = \$1
DIV2 = \$2
DIV3 = \$3
g = 0.06  P3 = (\$3  1.06)/(0.14 – 0.06) = \$39.75

Chap 8

19.a.NPV for each of the two projects, at various discount rates, is tabulated below.
NPVA = –\$20,000 + [\$8,000  annuity factor(r%, 3 years)]
= –\$20,000 +
NPVB =
Discount Rate
NPVA
NPVB
0%
\$4,000
\$5,000
2%
3,071
3,558
4%
2,201
2,225
6%
1,384
990
8%
617
-154
10%
-105
-1,217
12%
-785
-2,205
14%
-1,427
-3,126
16%
-2,033
-3,984
18%
-2,606
-4,784
20%
-3,148
-5,532
From the NPV profile, it can be seen that Project A is preferred over Project B if the discount rate is above 4%. At 4% and below, Project B has the higher NPV.

b.IRRA = Discount rate (r) which is the solution to the following equation:  r = IRRA = 9.70%
IRRB = Discount rate (r) which is the solution to the following equation:
= 0  IRRB = 7.72%
Using a financial calculator, find IRRA = 9.70% as follows: enter PV = (–)20; PMT = 8; FV = 0; n = 3; compute i
Find IRRB = 7.72% as follows: enter PV = (–)20; PMT = 0; FV = 25; n = 3; compute i

34.a.Present Value =
NPV = –\$80,000 + \$100,000 = \$20,000

b.Recall that the IRR is the discount rate that makes NPV equal to zero:
(– Investment) + (PV of cash flows discounted at IRR) = 0

Solving, we find that:
IRR = (\$5,000/\$80,000) + 0.05 = 0.1125 = 11.25%

Chap 11

9. a.
Year
Stock market return
T-bill return
Risk premium
Deviation from mean
Squared deviation
2003
31.64
1.02
30.62
19.146
366.57
2004
12.62
1.2
11.42
-0.054
0.00
2005
6.38
2.98
3.4
-8.074
65.19
2006
15.77
4.8
10.97
-0.504
0.25
2007
5.62
4.66
0.96
-10.514
110.54

Average

11.474

542.56

b.The average risk premium was: 11.474%

c. The variance (the average squared deviation from the mean) was 409.2538 (without correcting for the lost degree of freedom). Therefore: standard deviation =

16.Boom:
Normal:
Recession:

Variance =
Standard deviation = = 31.04%
Portfolio Rate of Return
Boom: (28 + 150)/2 = 61.00%
Normal: (8 + 27.5)/2 = 17.75%
Recession: (48 –100)/2 = –26.0%
Expected return = 17.58%
Standard deviation = 35.52%

Chap 12

6.a.The expected cash flows from the firm are in the form of a perpetuity. The discount rate is:
rf + (rm – rf ) = 4% + 0.4  (11% – 4%) = 6.8%
Therefore, the value of the firm would be:

b.If the true beta is actually 0.6, the discount rate should be:
rf + (rm – rf ) = 4% + [0.6  (11% – 4%)] = 8.2%
Therefore, the value of the firm is:

By underestimating beta, you would overvalue the firm by:
\$147,058.82 – \$121,951.22 = \$25,107.60

7.Required return = rf + (rm – rf ) = 6% + [1.25  (13% – 6%)] = 14.75%
Expected return = 16%
The security is underpriced. Its expected return is greater than the required return given its risk.

12.Figure shown below.
BetaCost of capital (from CAPM)
0.754% + (0.75  7%) = 9.25%
1.754% + (1.75  7%) = 16.25%

Beta
Cost of capital
IRR
NPV
1.0
11.0%
14%
+
0.0
4.0%
6%
+
2.0
18.0%
18%
0
0.4
6.8%
7%
+
1.6
15.2%
20%
+

13. The appropriate discount rate for the project is:
r = rf + (rm – rf ) = 4% + 1.4  (12% – 4%)...

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