Solutions to Capital Budgeting Assignment
These solutions were provided by Vicki Knight and edited slightly. Please realize that you don’t
have to discount each CF separately as was done in some of these problems as long as you record
the proper keystrokes on your calculator.
1. Long Branch Farms
Initial Investment
-$100,000
Purchase Price
- 15,000
Installation Cost
-$115,000
Operating Cash Flows
CF = (S-C) (1-t) + D(t) +/- ∆WC
= (20,000 – 5,000)(1-.40) + 23,000(.40)
= (15,000) (.60) + 9,200
= 9,000 + 9,200 = $18,200
Terminal Value
25,000 (1-.40) = 15,000
NPV = -115,000 + 18,200 + 18,200 + 18,200 + 18,200 +18,200 +15,000
1.16
(1.16)2 (1.16)3 (1.16)4
(1.16)5
(1.346) (1.561) (1.811)
(2.10)
= -115,000 + 15,689.66 +13,521.55 + 11,659.19 + 10,049.70 + 15,809.53
= -115,000 + 66,729.62
= -48,270.38
IRR =
Cash Flow:
-115,000
18,200
18,200
18,200
18,200
33,200
= -2.43%
No. the firm should not purchase the system. The NPV is a negative 48,270.38 and the IRR is
lower than the return rate of 16%.
2. Matrix Printers
Initial Investment
-1,500,000 Plant Purchase Price
- 250,000 Land Purchase Price
- 100,000 Working Capital
-1,850,000
Operating Cash Flows
= (300 – 175,000) (.66) + 100,000 (.34)
=
82,500
+ 34,000
=
116,500
Terminal Value
-700,000
Salvage Value
-153,000 Tax Effect (450,000 x .34) MV-700,000 BV-250,000
+100,000
Recoup WC
647,000
NPV =
-1,850,000 +
116,500 / (1.16)
116,500 / (1.16) 2
116,500 / (1.16) 3
116,500 / (1.16) 4
116,500 / (1.16) 5
116,500 / (1.16) 6
116,500 / (1.16) 7
116,500 / (1.16) 8
116,500 / (1.16) 9
116,500 / (1.16)10
116,500 / (1.16)11
116,500 / (1.16)12
116,500 / (1.16)13
116,500 / (1.16)14
116,500 + 647,000 / (1.16)15
-1,850,000 + 100,431.03 + 86,552.75 + 74,631.65 + 64,329.10 + 55,476.19 + 47,824.30 +
41,224.34 + 35,539.96 + 30,633.71 + 26,411.25 + 22,767.25 + 19,626.01 + 16,918.39 +
14,584.38 + 82,398.01
NPV = -1,130,651.68
IRR = Cash Flow = -1,850,000 +116,000 (14 times) + 763,500
IRR = -2.38
No, they should not make the investment. The NPV is negative and the IRR is below the
required rate of 16%.
3. International Soup Company
Initial Investment
-250,000
-12,500
+40,000
+ 8,000
-30,000
-244,500
OCF -
Purchase Price
Installation
Sale Price of Replaced Asset
∆ in tax (20,000 x .40)(60,000 CBV – 40,000 CMV)
WC
(40,000) (1-.40) + (40,500) (.40)
24,000 + 16,200
= 40,200
Depreciation ( 52,500 depr. New – 12,000 depr. Old)
Terminal Value
+25,000
Salvage Value
-10,000
Tax Effect (25,000 x .4)
WC
+30,000
45,000
NPV = -244,500 + 40,200 / 1.16 + 40,200 / (1.16)2 + 40,200 / (1.16)3 + 40,200 / (1.16)4 +
40,200+45,000 / (1.16)5
= -244,500 + 34,655.17 + 29,866.27 +25,752.72 + 22,197.68 + 40,571.43
= -244,500 + 153,043.27
NPV = -91,456.73
IRR = -244,500
= .18%
40,200 40,200
Payback = -244,500
40,200
40,200
40,200
40,200
85,200
Payback = 4.98 years
40,200 40,200 85,200
204,300
164,100
123,900
87,700
83,700 / 85,200 = .98
The firm should not replace the old machine. The NPV is negative. The required return is well
above the IRR, and the payback will take almost 5 years which is the time left with the old
machine.
4. Special-Purpose Truck
Initial Investment
-50,000 Purchase Price
-10,000 Modify
- 2,000 ∆ WC
-62,000
Operating Cash Flows
(0 – (-22,000))(1-.40) + (12,000)(.40)
= 18,000
BV at 3 years 24,000
MV at 3 years 20,000
Terminal Value
+20,000
Salvage Value
+ 1,600 (4,000 x .40)
+ 2,000
23,600
NPV
= -62,000 + 18,000 / 1.13 + 18,000 / (1.13)2 + 18,000 + 23,600 / (1.13)3
= -62,000 + 15,929.20 + 14,095.54 + 28,828.83
= - 3,146.43
IRR
-62,000
18,000
18,000
41,600
= 10.391 Do not purchase the truck. Has –NPV of -$3143.27 and IRR is lower than 13%
return required.
5. Blue Note Jazz Productions
Sales = 300,000 x $35 = $10,500,000
Cost = 3,000,000 + .25 (10,500,000) = $5,625,000
Initial Investment
-4,000,000 Purchase Price
- 300,000 WC
$-4,300,000
Operating Cash Flows:
CF = (S-C) (1-t) + D (t)
= (10,500,000 – 5,625,000) (1 - .40) + 800,000 (.40)
= (4,875,000) (.60)
+ 320,000
= 2,925,000 + 320,000
= $3,245,000
Terminal Value:
1,500,000
Salvage Value
+ 40,000
Tax Effect (Year 3 Book Value – 1,600,000, Year 3 Market Value –
1,500,000 = difference of 100,000 – loss)
(100,000 x .40)
+300,000
Recoup WC
$1,840,000
NPV = -4,300,000 + 3,245,000 / 1.12 + 3,245,000 / (1.12)2 + 3,245,000+1,840,000 /
(1.12)3
= -4,300,000 + 2,897,321.43 + 2,587,719.30 + 3,619,217.08
= -4,300,000 + 9,104,257.81
= $4,804,257.81
IRR = 64.80%
Cash flow: -4,300,000
3,245,000
3,245,000
5,085,000
MIRR = 43.81%
-4,300,000 Present Value
3,245,000 ----4,070,528 FV
3,245,000----- 3,634,400 FV
5,085,000 FV
Total FV = 12,789,928
N=3
Yes, the project should be accepted. It has a positive NPV and the IRR is well above the
required return of 12%.
6. Southwest Airlines
Initial Cost
-160,000 Purchase price
OCF
1st 5 years = (31,000) (.66) + 22,857.143 (.34)
= 20,460 + 7,771.429
= 28,231.43
Last 2 years = (28,000) (.66) + 22,857.143 (.34)
= 18,480 + 7,771.429
= 26,251.43
NPV
= -160,000 + 28,231.43 / 1.13 + 28,231.43 / (1.13)2 + 28,231.43 / (1.13)3 + 28,231.43 / (1.13)4 +
28,231.43 / (1.13)5 + 26,251.429 / (1.13)6 + 26,251.429 / (1.13)7
= -160,000 + 24,983.57 + 22,107.62 + 19,564.40 + 17,319.896 + 15,326.51 + 12,608.76 +
11,156.58
= -160,000 + 123,067.34 = -36,932.66 (NPV)
IRR
-160,000
28,231.43
28,231.43
28,231.43
28,231.43
28,231.43
26,251.429
26,251.429
= 5.083% No, they should not make the investment. It has a – NPV and the IRR is below the
13% return required.
7. Ball Corporation
Note: If you choose to use the replacement chain method then simply compare the NPV of
Project B to the NPV of the following cash flows for Project A, which is chained.
CF0
-5,000
CF1 CF2 CF3 CF4 CF5 CF6
3,000 3,000 3,000 3,000 3,000 3,000
-5,000
-2,000
NPV of A (chained) is $4,309.21
The NPV of B is $5,243.41
Take Project B.
To use the EAA method simply follow these three steps:
A
B
A. Find the NPV of each unchained project:
$2,460.55
$5,243.41
B. Clear your calculator and enter the NPV as PV, the life of the asset as N, and the required rate
of return.
C. Solve for PMT, which is your EAA.
$989.43
$1,203.93
(Choose B)
Remember: If your NPV is negative then the EAA will be negative and vice-versa.
8. Lucent vs. Sony
Lucent Technologies System
-54,000 Purchase Price
4,000 Annual operating expenses
9 years
Lucent (NPV) = -54,000 + -4,000 / (1.09) + -4,000 / (1.09)2 + -4,000 / (1.09)3 + -4,000 / (1.09)4
+ -4,000 / (1.09)5 + -4,000 / (1.09)6 + -4,000 / (1.09)7 + -4,000 / (1.09)8 + -4,000 / (1.09)9
= -54,000 – 3,669.725 – 3,367.003 – 3,088.803 – 2,832.861 – 2,599.09 – 2,385.212 – 2,188.184
– 2,007.025 – 1,841.021
NPV = -77,979.52
EAC = On calculator:
Annuity payment ?
9 years – N
9% - I/YR
NPV = -77,979.52
EAC = -13,006.89
Toshiba Systems
-48,000 Purchase price
4,000 Annual Operating Expenses
7 years
NPV = -48,000 + -3,669.725 + -3,367.003 + -3,088.803 + -2,832.861 + -2,599.09 + -2,385.212 +
-2,188.184
NPV = -68,130.88
EAC = Annuity payment ?
7 years – N
9% - I/YR
PV - -68,130.88
EAC = -13,536.96
Sony should purchase the Lucent Technologies System with a lower EAC.
9. Real Estate Office
PURCHASE MACHINE:
Initial Inventory
-4,200 Purchase price
OCF
(-1,200) (.66) + (700) (.34)
= -792 + 238
= -554
Pmts -554
N
6
I/YR
75
PV
-2,640.66
-4,200 – 2,640.66
NPV = -6,840.66
EAC = NPV 6,840.66
N
6
I/YR
7%
Pmt. (EAC) = -1,435.14
LEASE MACHINE:
After tax lease cost = -2,000 / yr. x .66 = -1,320
Leasing the machine would be cheaper. On a per-year basis, leasing the machine has a EAC of $1,320 which is less than the purchasing EAC of -$1,435.14.
10. Piper vs. Cessna
Piper
Purchase price 375,000
Annual op. costs 24,000
Salvage value 150,000
7 years
Piper – NPV
-375,000 – 24,000 / (1.15) – 24,000 / (1.15)2 – 24,000 / (1.15)3 – 24,000 / (1.15)4 – 24,000 /
(1.15)5 – 24,000 / (1.15)6 + -24,000 + 150,000 / (1.15)7
-375,000 – 20,869.57 – 18,140.59 – 15,779.093 – 13,722.127 – 11,934.361 – 10,376.135 +
47,368.421
NPV = -418,453.46
EAC = annual pmt. ?
7
N
15% I/YR
-418,453.46 PV
EAC = -100,579.63
Cessna
Purchase Price 325,000
Annual Operating Costs 29,500
Salvage Value 100,000
8 years
Cessna – NPV
= -325,000 – 29,500 / (1.15) – 29,500 / (1.15)2 – 29,500 / (1.15)3 – 29,500 / (1.15)4 – 29,500 /
(1.15)5 – 29,500 / (1.15)6 – 29,500 / (1.15)7 + -29,500 + 100,000 / (1.15)8
= -325,000 – 25,652.174 – 22,297.81 – 19,395.135 – 16,866.78 – 14,669.32 – 12,754 –
11,090,226 + 23,046.747
NPV = -424,678.70
EAC = annual payment ?
8
N
15% I/YR
-424,678.70 PV
EAC = -94,639.69
The Cessna would be the best investment with a lower EAC than the Piper.