1.5455 = +
1.5455 = 1.2 + 0.2X
0.3455 = 0.2X
X = 1.7275.
11-7 a. Project A:
CF0 = -6000; CF1-5 = 2000; I/YR = 14.
Solve for NPVA = $866.16. IRRA = 19.86%.
MIRR calculation:
0 1 2 3 4 5
14%
| | | | | |
-6,000 2,000 2,000 2,000 2,000 2,000
1.14
2,280.00
(1.14)2
2,599.20
(1.14)3
2,963.09
(1.14)4
3,377.92
13,220.21
Using a financial calculator, enter N = 5; PV = -6000; PMT = 0; FV = 13220.21; and solve for MIRRA = I/YR = 17.12%.
Payback calculation:
0 1 2 3 4 5
| | | | | |
-6,000 2,000 2,000 2,000 2,000 2,000
Cumulative CF: -6,000 -4,000 -2,000 0 2,000 4,000
Regular PaybackA = 3 years.
Discounted payback calculation:
0 1 2 3 4 5
14%
| | | | | |
-6,000 2,000 2,000 2,000 2,000 2,000
Discounted CF: -6,000 1,754.39 1,538.94 1,349.94 1,184.16 1,038.74
Cumulative CF: -6,000 -4,245.61 -2,706.67 -1,356.73 -172.57 866.17
Discounted PaybackA = 4 + $172.57/$1,038.74 = 4.17 years.
Project B:
CF0 = -18000; CF1-5 = 5600; I/YR = 14.
Solve for NPVB = $1,225.25. IRRB = 16.80%.
MIRR calculation:
0 1 2 3 4 5
14%
| | | | | |
-18,000 5,600 5,600 5,600 5,600 5,600
1.14
6,384.00
(1.14)2
7,277.76
(1.14)3
8,296.65
(1.14)4
9,458.18
37,016.59
Using a financial calculator, enter N = 5; PV = -18000; PMT = 0; FV = 37016.59; and solve for MIRRB = I/YR = 15.51%.
Payback calculation:
0 1 2 3 4 5
| | | | | |
-18,000 5,600 5,600 5,600 5,600 5,600
Cumulative CF: -18,000 -12,400 -6,800 -1,200 4,400 10,000
Regular PaybackB = 3 + $1,200/$5,600 = 3.21 years.
Discounted payback calculation:
0 1 2 3 4 5
14%
| | | | | |
-18,000 5,600 5,600 5,600 5,600 5,600
Discounted CF: -18,000 4,912.28 4,309.02 3,779.84 3,315.65 2,908.46
Cumulative CF: -18,000 -13,087.72 -8,778.70 -4,998.86 -1,683.21 1,225.25
Discounted PaybackB = 4 + $1,683.21/$2,908.46 = 4.58 years.
Summary of capital budgeting rules results:
Project A Project B
NPV $866.16 $1,225.25
IRR 19.86% 16.80%
MIRR 17.12% 15.51%
Payback 3.0 years 3.21 years
Discounted payback 4.17 years 4.58 years
b. If the projects are independent, both projects would be accepted since both of their NPVs are positive.
c. If the projects are mutually exclusive then only one project can be accepted, so the project with the highest positive NPV is chosen. Accept Project B.
d. The conflict between NPV and IRR occurs due to the difference in the size of the projects. Project B is 3 times larger than Project A.
11-11 Project S: Using a financial calculator, enter the following data: CF0 = -15000; CF1-5 = 4500; I/YR = 14. NPVS = $448.86.
Project L: Using a financial calculator, enter the following data: CF0 = -37500; CF1-5 = 11100; I/YR = 14. NPVL = $607.20.
The decision rule for mutually exclusive projects is to accept the project with the highest positive NPV. In this situation, the firm would accept Project L since NPVL = $607.20 is greater than NPVS = $448.86.
11-12 Input the appropriate cash flows into the cash flow register, and then calculate NPV at 10% and the IRR of each of the projects:
Project S: CF0 = -1000; CF1 = 900; CF2 = 250; CF3-4 = 10; I/YR = 10. Solve for NPVS = $39.14; IRRS = 13.49%.
Project L: CF0 = -1000; CF1 = 0; CF2 = 250; CF3 = 400; CF4 = 800; I/YR = 10. Solve for NPVL = $53.55; IRRL = 11.74%.
Since Project L has the higher NPV, it is the better project, even though its IRR is less than Project S’s IRR. The IRR of the better project is IRRL = 11.74%.
11-18 Facts: 5 years remaining on lease; rent = $2,000/month; 60 payments left, payment at end of month.
New lease terms: $0/month for 9 months; $2,600/month for 51 months.
WACC = 12% annual (1% per month).
a. 0 1 2 59 60
1%
| | | | |
-2,000 -2,000 -2,000 -2,000
PV cost of old lease: N = 60; I/YR = 1; PMT = -2000; FV = 0; PV = ? PV = -$89,910.08.
0 1 9 10 59 60
1%
| | | | | |
0 0 -2,600 -2,600 -2,600
PV cost of new lease: CF0 = 0, CF1-9 = 0; CF10-60 = -2600; I/YR = 1. NPV = -$94,611.45.
Sharon should not accept the new lease because the present value of its cost is $94,611.45 – $89,910.08 = $4,701.37 greater than the old lease.
b. At t = 9 the FV of the original lease’s cost = -$89,910.08(1.01)9 = -$98,333.33. Since lease payments for months 0-9 would be zero, we can calculate the lease payments during the remaining 51 months as follows: N = 51; I/YR = 1; PV = 98333.33; and FV = 0. Solve for PMT = -$2,470.80.
Check:
0 1 9 10 59 60
1%
| | | | | |
0 0 -2,470.80 -2,470.80 -2,470.80
PV cost of new lease: CF0 = 0; CF1-9 = 0; CF10-60 = -2470.80; I/YR = 1. NPV = -$89,909.99.
Except for rounding; the PV cost of this lease equals the PV cost of the old lease.
c. Period Old Lease New Lease Lease
0 0 0 0
1-9 -2,000 0 -2,000
10-60 -2,000 -2,600 600
CF0 = 0; CF1-9 = -2000; CF10-60 = 600; IRR = ? IRR = 1.9113%. This is the periodic rate. To obtain the nominal cost of capital, multiply by 12: 12(0.019113) = 22.94%.
Check: Old lease terms:
N = 60; I/YR = 1.9113; PMT = -2000; FV = 0; PV = ? PV = -$71,039.17.
New lease terms:
CF0 = 0; CF1-9 = 0; CF10-60 = -2600; I/YR = 1.9113; NPV = ? NPV = -$71,038.98.
Except for rounding differences; the costs are the same.
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Solution for HW 2
4
-
13
ROE
= Profit margin
´
TA turnover
´
Equity multiplier
= NI/Sales
´
Sales/TA
´
TA/Equity.
Now we need to determine the inputs for the DuPont equation from the data that were given.
On the left we set up an income statement, and we
put numbers in it on the right:
Sales (given)
$10,000,000
–
Cost
na
EBIT (given)
$ 1,000,000
–
INT (given)
300,000
EBT
$ 700,000
–
Taxes (34%)
238,000
NI
$ 462,000
Now we can use some ratios to get some more data:
Total assets
turnover = 2 = S/TA; TA = S/2 = $10,000,000/2 = $5,000,000.
D/A = 60%; so E/A = 40%; and, therefore,
Equity multiplier = TA/E = 1/(E/A) = 1/0.4 = 2.5.
Now we can complete the DuPont equation to determine ROE:
ROE = $462,000/$10,000,000
´
$10,000,000/$5,000
,000
´
2.5 = 0.231 = 23.1%.
6
-
13
r
C8
= r* + IP
8
+ MRP
8
+ DRP
8
+ LP
8
8.3%
= 2.5% + (2.8%
´
4 + 3.75%
´
4)/8 + 0.0% + DRP
8
+ 0.75%
8.3%
= 2.5% + 3.275% + 0.0% + DRP
8
+ 0.75%
8.3%
= 6.525% + DRP
8
DRP
8
= 1.775%.
6
-
15
r* = 2%; MRP = 0%; r
1
= 5%; r
2
= 7%; X = ?
X represents the one
-
year rate on a bond one year from now (Year 2).
(1.07)
2
= (1.05)(1 + X)
Solution for HW 2
4-13 ROE = Profit margin TA turnover Equity multiplier
= NI/Sales Sales/TA TA/Equity.
Now we need to determine the inputs for the DuPont equation from the data that were given.
On the left we set up an income statement, and we put numbers in it on the right:
Sales (given) $10,000,000
– Cost na
EBIT (given) $ 1,000,000
– INT (given) 300,000
EBT $ 700,000
– Taxes (34%) 238,000
NI $ 462,000
Now we can use some ratios to get some more data:
Total assets turnover = 2 = S/TA; TA = S/2 = $10,000,000/2 = $5,000,000.
D/A = 60%; so E/A = 40%; and, therefore,
Equity multiplier = TA/E = 1/(E/A) = 1/0.4 = 2.5.
Now we can complete the DuPont equation to determine ROE:
ROE = $462,000/$10,000,000 $10,000,000/$5,000,000 2.5 = 0.231 = 23.1%.
6-13 r
C8
= r* + IP
8
+ MRP
8
+ DRP
8
+ LP
8
8.3% = 2.5% + (2.8% 4 + 3.75% 4)/8 + 0.0% + DRP
8
+ 0.75%
8.3% = 2.5% + 3.275% + 0.0% + DRP
8
+ 0.75%
8.3% = 6.525% + DRP
8
DRP
8
= 1.775%.
6-15 r* = 2%; MRP = 0%; r
1
= 5%; r
2
= 7%; X = ?
X represents the one-year rate on a bond one year from now (Year 2).
(1.07)
2
= (1.05)(1 + X)
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3000_sp13_hw2_solution.docx
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