Problem Set 5
Financial Management
Spring 2005
Net Advantage of Leasing
1.
Your company needs a piece of high-technology equipment which could be purchased outright for
$600,000. If purchased, it would be depreciated over a five-year life to a $200,000 estimated salvage
value. Alternatively, the equipment could be leased from the manufacturer on a five-year lease, with
annual payments of $100,000 (due in advance). Your company is in the 34% marginal income tax
bracket. For reference, the T-bill rate at the time is 10%, and the expected return on the market
portfolio is 15%. Develop a profile of the NAL to determine how sensitive the decision is to changes
in the discount rate used. What effect does uncertainty about the salvage value have on the decision?
2.
Wyandot Community Hospital needed to acquire a piece of equipment that cost $600,000. If
purchased, it would be depreciated over a five-year life to a $200,000 estimated salvage value.
Alternatively, the equipment could be leased from the manufacturer on a five-year lease, with annual
payments of $100,000 (due in advance). For reference, the T-bill rate at the time is 10%, and the
expected return on the market portfolio is 15%. Develop a profile of the NAL to determine how
sensitive the decision is to changes in the discount rate used.
3.
Allied Aviation had a choice of buying or leasing their next ten-passenger turboprop twin. The cash
price was $3 million, but a 5-year lease could be obtained with annual payments of $500,000. If the
plane were purchased, it would be depreciated straight-line over a 25-year life to a zero salvage value.
In order to compare the purchase alternative to the lease alternative, it was estimated that the plane
would still be worth $2,400,000 at the end of five years. Allied is in the 34% marginal income tax
bracket. Compute the Net Advantage of Leasing at a discount rate of 12%. Develop a profile of the
NAL to determine how sensitive the decision is to changes in the discount rate used.
4.
A company needs a new fleet of shipping containers. The expected after-tax cash flows to own are an
outflow of $450,000 in year 0 with inflows of $50,000 at the end of years 1 through 4 and $100,000 at
the end of year 5. Cash outflows to lease would be $50,000 at the end of years 0 through 4. Calculate
the NAL, using a discount rate of 14% compounded annually. Develop a profile of the NAL to
determine how sensitive the decision is to changes in the discount rate used.
5.
Grove Aviation had to decide whether to lease an airplane or buy it on credit. Cash flows for the two
alternatives, after tax, are given in the table below. Compute the NAL at a discount rate of 9%. Then
develop a profile of the NAL to determine how sensitive the decision is to changes in the discount
rate used.
Year
0
1
2
3
4
5
6.
Buy
(250,000)
(600,000)
(600,000)
(600,000)
(600,000)
50,000
Lease
(500,000)
(500,000)
(500,000)
(500,000)
(500,000)
0
Georgetown Railroad had to decide whether to lease some rolling stock or buy it on credit. Cash
flows for the two alternatives, after tax, are given in the table below. Compute the NAL at a discount
rate of 12%. Then develop a profile of the NAL to determine how sensitive the decision is to changes
in the discount rate used.
Year
0
1
2
3
4
5
Prof. Kensinger
Buy
(200,000)
(281,000)
(288,500)
(296,000)
(303,000)
(41,000)
Lease
(270,000)
(270,000)
(270,000)
(270,000)
(270,000)
0
page 1
Problem Set 5
Financial Management
7.
Duquesne Steel Company decided to install a computerized process control system, but wasn't sure
whether to purchase the equipment or lease it. The after-tax cash flows for the two alternatives are
given in the table below. Develop a profile of the NAL to determine how sensitive this lease/buy
decision is to changes in the discount rate used for the calculation.
Year
0
1
2
3
4
5
8.
Spring 2005
Lease
(45,600)
(45,600)
(45,600)
(45,600)
(45,600)
0
Buy
(10,500)
(51,304)
(54,868)
(58,554)
(62,372)
20,533
Suppose your friend Marty is trying to decide whether to buy or lease a car. Marty could buy the car
with a $650 down payment followed by monthly payments of $600 for four years. Lease payments
would be just $400 per month for a four-year lease (48 monthly payments, each due in advance). An
initial fee of $650 plus the first month’s lease payment of $400 would be due upon lease signing (total
of $1,050 due at signing). The car is expected to have resale value of $16,600 at the end of four
years’ use (of course, Marty would have that value if the car were purchased, but the dealer would
keep it under the lease alternative). Both alternatives include a maintenance contract, so maintenance
costs would be the same whether buying or leasing. Marty’s opportunity cost of capital is 12% APR
with monthly compounding (periodic rate is 1% per month). Calculate the net advantage of leasing.
Prof. Kensinger
page 2
Financial Management
Solutions: Problem Set 5
Spring 2005
Net Advantage of Leasing
1.
Cash flows for the two alternatives, after tax, are as follows.
Year
0
1
2
3
4
5
Buy
(600,000)
27,200
27,200
27,200
27,200
227,200
Lease
(66,000)
(66,000)
(66,000)
(66,000)
(66,000)
0
Advantage
534,000
(93,200)
(93,200)
(93,200)
(93,200)
(227,200)
Discount
Rate
0%
6%
8%
10%
15%
20%
30%
NAL
(66,000)
41,275.10
70,681.28
97,495.22
154,957.46
201,423.35
270,914.80
IRR=3.48%
NAL Profile
$250,000.00
$200,000.00
$150,000.00
NPV
$100,000.00
$50,000.00
$0.00
0%
5%
10%
15%
20%
25%
($50,000.00)
($100,000.00)
($150,000.00)
($200,000.00)
Rate
Initial Estimates
Salvage Value Doubled
If salvage value estimate were doubled, ceteris paribus, the profile would shift to an indifference
point of 9.08%.
2.
Cash flows for the two alternatives, after tax, are as follows.
Year
0
1
2
3
4
5
Prof. Kensinger
Buy
(600,000)
0
0
0
0
200,000
Lease
(100,000)
(100,000)
(100,000)
(100,000)
(100,000)
0
Advantage
500,000
(100,000)
(100,000)
(100,000)
(100,000)
(200,000)
Discount
Rate
0%
6%
8%
10%
15%
20%
30%
NAL
(100,000)
4,037.80
32,670.68
58,829.19
115,066.82
160,751.03
229,510.12
IRR=5.73%
page 1
Solutions: Problem Set 5
Financial Management
Spring 2005
NAL Profile (Prob 2)
$200,000.00
$150,000.00
$100,000.00
$50,000.00
$0.00
NPV
0%
5%
10%
15%
20%
25%
($50,000.00)
($100,000.00)
($150,000.00)
($200,000.00)
($250,000.00)
($300,000.00)
Initial Estimates
Rate
Salvage Value Doubled
If salvage value estimate were doubled, ceteris paribus, the profile would shift to an indifference
point of 13.94%.
3.
Cash flows for the two alternatives, after tax, are as follows.
Year
0
1
2
3
4
5
Buy
(3,000,000)
40,800
40,800
40,800
40,800
2,440,800
Lease
(330,000)
(330,000)
(330,000)
(330,000)
(330,000)
0
Advantage
2,670,000
(370,800)
(370,800)
(370,800)
(370,800)
(2,440,800)
Discount
Rate
0%
6%
8%
10%
15%
20%
30%
NAL
(1,254,000)
(438,768.91)
(219,304.10)
(20,930.87)
397,865.05
729,194.44
1,209,379.55
IRR=10.22%
NAL Profile
$1,000,000.00
$500,000.00
$0.00
NPV
0%
5%
10%
15%
20%
25%
($500,000.00)
($1,000,000.00)
($1,500,000.00)
($2,000,000.00)
Rate
Initial Estimates
Salvage Value Increased
The NAL at 12% would be $158,775.39. If salvage value estimate were increased by $500,000,
ceteris paribus, the profile would shift to an indifference point of 12.31%. The NAL at 12% would
then be (28,455.47).
Prof. Kensinger
page 2
Solutions: Problem Set 5
Financial Management
4.
Spring 2005
Cash flows for the two alternatives, after tax, are as follows.
Year
0
1
2
3
4
5
Buy
(450,000)
50,000
50,000
50,000
50,000
100,000
Lease
(50,000)
(50,000)
(50,000)
(50,000)
(50,000)
0
Advantage
400,000
(100,000)
(100,000)
(100,000)
(100,000)
(100,000)
Discount
Rate
0%
6%
8%
10%
15%
20%
30%
NAL
(100,000)
(21,236.38)
729.00
20,921.32
64,784.49
100,938.79
156,443.02
IRR=7.93%
NAL Profile
$150,000.00
$100,000.00
NPV
$50,000.00
$0.00
($50,000.00)
($100,000.00)
0%
5%
10%
15%
20%
25%
Rate
The NAL at 14% would be $56,691.90.
5.
Cash flows for the two alternatives, after tax, are as follows.
Year
0
1
2
3
4
5
Buy
(250,000)
(600,000)
(600,000)
(600,000)
(600,000)
50,000
Lease
(500,000)
(500,000)
(500,000)
(500,000)
(500,000)
0
Advantage
(250,000)
100,000
100,000
100,000
100,000
(50,000)
Discount
Rate
0%
6%
8%
10%
15%
20%
30%
NAL
100,000
59,147.65
47,183.52
35,940.48
10,639.00
(11,220.42)
(46,842.39)
IRR=17.34%
The NAL at 9% would be $41,475.42.
Prof. Kensinger
page 3
Financial Management
Solutions: Problem Set 5
Spring 2005
NAL Profile (Prob 5)
$100,000.00
$80,000.00
$60,000.00
NPV
$40,000.00
$20,000.00
$0.00
($20,000.00)
($40,000.00)
0%
5%
10%
15%
20%
25%
Rate
6.
Cash flows for the two alternatives, after tax, are as follows.
Year
0
1
2
3
4
5
Buy
(200,000)
(281,000)
(288,500)
(296,000)
(303,000)
(41,000)
Lease
(270,000)
(270,000)
(270,000)
(270,000)
(270,000)
0
Advantage
(70,000)
11,000
18,500
26,000
33,000
41,000
Discount
Rate
0%
6%
8%
10%
15%
20%
25%
NAL
59,500
35,449.07
28,845.49
22,820.66
9,901.40
(548.48)
(9,096.32)
IRR=19.71%
NAL Profile
$60,000.00
$50,000.00
$40,000.00
NPV
$30,000.00
$20,000.00
$10,000.00
$0.00
($10,000.00)
0%
5%
10%
15%
20%
25%
Rate
Prof. Kensinger
page 4
Solutions: Problem Set 5
Financial Management
7.
Spring 2005
Cash flows for the two alternatives, after tax, are as follows.
Year
0
1
2
3
4
5
Buy
(10,500)
(51,304)
(54,868)
(58,554)
(62,372)
20,533
Discount
Rate
NAL
0%
(10,935)
6%
(12,652.41)
8%
(13,235.89)
10%
(13,816.39)
15%
(15,233.68)
20%
(16,577.43)
25%
(17,831.27)
The NAL is negative at all discount rates.
Lease
(45,600)
(45,600)
(45,600)
(45,600)
(45,600)
0
Advantage
(35,100)
5,704
9,268
12,954
16,772
(20,533)
NAL Profile
$0.00
($5,000.00)
($10,000.00)
NPV
($15,000.00)
($20,000.00)
($25,000.00)
($30,000.00)
480%
500%
460%
420%
440%
380%
400%
340%
360%
320%
280%
300%
260%
240%
200%
220%
180%
140%
160%
120%
80%
100%
40%
60%
0%
20%
($35,000.00)
Rate
8.
Use cash flow mode. Cash flows for the NAL calculation are as follows: C(0) is –400, C(1) is 200
with frequency 47, C(2) is –16,000 with frequency 1, interest is 1%. Calculate NPV. NPV is
negative. Answer is –2,853.43
Prof. Kensinger
page 5