SYDE 331
MANAGERIAL AND ENGINEERING ECONOMICS
Spring 2002
Assignment #5
Due:
Maximum marks: 22 marks
Question 1 (12 marks)
A manufacturing company needs to purchase a new CNC laser-welding centre. They are
considering three models:
Model
Capital cost
Net annual
savings
Salvage value
Service life
A
$40,000
$17,000
$8,000
5 years
B
$60,000
$22,000
$32,000
3 years
C
$30,000
$15,000
$7,000
5 years
The manufacturer has a tax rate of 46% and uses after-tax MARR of 11%. This new
machine will fall into CCA class 8. Using an after-tax PW analysis with repeated lives,
which should machine should the manufacturer purchase?
Question 2 (10 marks)
A lawn maintenance company owns a two-year old lawn mower. Maintenance costs on the
lawn mower will be $2400 in the next year and are expected to increase by $350 per year
thereafter. The depreciation rate is 15%. The lawn mower is currently worth $3500 and
will last four more years until it will be sold for its market value.
A new lawn mower costs $5000, and has a maximum life of six years. Maintenance costs
will be $1500 in the first year and will increase by 30% per year thereafter. The new mower
is expected to depreciate at 25% per year.
The company=s tax rate is 35%, the after-tax MARR is 10%, and the CCA rate for mowers
is 30%. Should the lawn maintenance company replace the old mower with a new mower
now? If not, when (in the next four years) should the old lawn mower be replaced by a new
one?
SYDE 331
MANAGERIAL AND ENGINEERING ECONOMICS
Spring 2002
Solutions to Assignment #5
Question 1
t = 46%
d = 20%
MARR = 11%
Repeated lives method: 15 years period
CCTFnew = 1 - (td*(1+ i/2))/((i + d)*(1 + i)) = 1 - (0.46*0.2)*(1 + 0.11/2)/((.11 + 0.2)*(1 +
0.11)) = 0.7179
CCTFold = 1 - td/(i + d) = 1 - (0.46*0.20)/(.11 + 0.20) = 0.7032
Model A:
First cost: $40,000 * (CCTFnew) = $28,717
Salvage value: $8,000 * (CCTFold) = $5,625
Net annual savings: $17,000 * (1 - t) = $9,180
PW for 15 years
= -28717 [1+ (P/F, 11%,5) + (P/F, 11%,10)] + 9180 (P/A, 11%, 15) + 5625 [(P/F, 11%, 5) +
(P/F, 11%, 10) + (P/F, 11%, 15)]
= -28717*(1 + 0.59345 + 0.35218) + 9180*(7.1909) + 5625*(0.59345 + 0.35218 + 0.20900)
= 16635
Model B
First cost: $60,000 * (CCTFnew) = $43,075
Salvage Value: $32,000 * (CCTFold) = $22,503
Net annual savings: $22,000 * (1 - t) = $11,880
PW for 15 years
= -43075 [1 + (P/F, 11%, 3) + (P/F, 11%, 6) + (P/F, 11%, 9) + (P/F, 11%, 12)] + 11880
(P/A, 11%, 15) + 22503 [(P/F, 11%, 3) + (P/F, 11%, 6) + (P/F, 11%, 9) + (P/F, 11%, 12) +
(P/F, 11%, 15)]
= -43075 [1 + (0.73119) + (0.53464) + (0.39092) + (0.28584)] + 11880 (7.1909) + 22503
[(0.73119) + (0.53464) + (0.39092) + (0.28584) + (0.20900)]
= 7091
Model C:
First cost: $30,000 * (CCTFnew) = $21,538
Salvage value: $7,000 * (CCTFold) = $4923
Net annual savings: $15,000 * (1 - t) = $8,100
PW for 15 years
= -21538 [1+ (P/F, 11%,5) + (P/F, 11%,10)] + 8100 (P/A, 11%, 15) + 4923 [(P/F, 11%, 5) +
(P/F, 11%, 10) + (P/F, 11%, 15)]
= -21538*(1 + 0.59345 + 0.35218) + 8100*(7.1909) + 4923*(0.59345 + 0.35218 + 0.20900)
= 22,025
Answer: Model C should be purchased.
Question 2
After-tax MARR = 10%
CCA rate = 30%
depreciation rate (for calculating salvage value): Challenger = 25%, Defender = 15%
tax rate = 35%
CCTFnew = 0.749431818
CCTFold = 0.7375
The EAC for the Challenger is found to be two years at a EAC of $2285.64, calculated as
follows:
EAC(Capital cost) in year i = annual payment that corresponds to the present value of an
annuity at 10% for i years of (Capital cost in year 0 * CCTFnew)
EAC(Maintenance cost) in year i = annual payment that corresponds to the present value
of an annuity of all maintenance costs to the end of year I, where each maintenance
cost is multiplied by (1-t) to get the after-tax cost
EAC(Salvage value) in year i = annual payment that corresponds to the present value of
an annuity at 10% for i years of (Present value of {alvage value in year i * CCTFold})
EAC(Total) in year i = EAC(Capital cost) +EAC(Maintenance year) - EAC(Salvage value)
The EAC of the Defender is minimized by keeping it one additional year. This gives an
EAC of $2478.75, calculated as follows:
EAC(Capital cost) in year i = not relevant
EAC(Maintenance cost) in year i = annual payment that corresponds to the present value
of an annuity of all maintenance costs to the end of year I, where each maintenance
cost is multiplied by (1-t) to get the after-tax cost
EAC(Salvage value) = EAC(Decline in net proceeds from sale):
For example, if sell now, receive revenue of $3500, but lose the present value of future tax
savings from CCA. This latter amount is $3500 x CCTFold, so the net cash impact is
$918.75.
If sell in two years, receive revenue of $2528.75, but lose the PV of future tax savings from
CCA of $2528.75 x CCTFold. This gives a net cash impact at the end of year 2 of
$663.80. This value must be discounted back to year 0 by finding their present value, so
the PV of this value is $548.59.
The difference between the cash impact from selling now vs. selling in two years is
calculated; that is:
decline in net proceeds from the sale = ($3500 received in Year 0 - 3500 *CCTFold)
- [PV of (salvage value in year i - salvage value in year i * CCTFold)]
EAC(Total) in year i = EAC(Decline in net proceeds from the sale) +EAC(Maintenance
year)
From the spreadsheets, we see that the EAC of the defender is less than the EAC of the
Challenger for the next four years, so the old mower should be kept for the next four years,
then replaced.