Dr Azer Önel
Engineering Economy Review Problems-III
2010
Applications of Money-Time Relationships
(Note: There may be typographical errors. Check results for all problems!)
1) (Prob. 4-2 Sullivan, 12th ed.) You are faced with making a decision on a large capital
investment proposal. The capital investment amount is $640,000. Estimated annual revenue at
the end of each year in the eight year study period is $180,000. The estimated annual year-end
expenses are $42,000 starting in year one. These expenses begin decreasing by $4,000 per
year at the end of year four and continue decreasing through the end of year eight. Assuming
a $20,000 market value at the end of year eight and a MARR = 12% per year, answer the
following questions.
a) What is the PW of this proposal?
b) What is the IRR of this proposal?
c) What is your conclusion about the acceptability of this proposal?
d) What is the simple payback period for this proposal?
e) Solve using FW, AW and discounted payback period.
Solution:
a) PW(12%) = -$640,000+$180,000(P/A,12%,8)-$42,000(P/A,12%,8)
+$4,000(P/G,12i%,6)(P/F,12%,2) +20,000(P/F,12i%,8)
PW (12%) = -$640,000+$180,000(4.9676)-$42,000(4.9676)
+$4,000(8.930) (0.7972) +20,000(0.4039)
= $82,082.78 > 0.
b) PW(IRR)= -$640,000+$180,000(P/A,i%,8)-$42,000(P/A,i%,8)
+$4,000(P/G,i%,6)(P/F,i%,2) +20,000(P/F,i%,8) = 0
Linear interpolation will be needed to solve for i%. We need two trial interest rates, one
resulting in a positive PW and another producing a negative PW. The IRR will then be
bracketed between these two interest rates. Since PW is not linear, the two interest rates
should be 10% or less apart to minimize error of linear interpolation. For this problem, the
two trial interest rates chosen were 15% and 18%.
i%
15%
i%
18%
PW
$9,790.06
0.00
-$51,623.16
18%  15%
i%  15%

$9,790.06  ($51,623.16) $9,790.06  0
Thus IRR = 15.48% > 12%.
c) Based on PW and IRR, the proposal is acceptable.
d) Simple payback period method: Calculates the number of years required for cash inflows to
just equal cash outflows; ignores time value of money (i% = 0/year) and all cash flows that
occur after payback period n' (n' ≥ n).
End of Year
0
1
2
3
4
5
Net Cash Flows
-$640,000
$138,000
$138,000
$138,000
$142,000
$146,000
Cumulative PW
at i% = 0/year
-$640,000
-$502,000
-$364,000
-$226,000
-$84,000
$62,000
n' = 5 years because the cumulative
balance turns (+) at year 5
Simple Payback Period n' = 5 years
2) (Prob. 4-16 Sullivan, 12th ed.) A company is considering constructing a plant to
manufacture a proposed new product. The land costs $300,000, the building costs $600,000,
the equipment costs $250,000, and $100,000 additional working capital† is required. It is
expected that the product will result in sales of $750,000 per year for ten years, at which time
the land can be sold for $400,000, the building for $350,000, and the equipment for $50,000.
All of the working capital would be recovered at the end of year 10. The annual labor,
materials, property taxes, maintenance, supplies and so on are estimated to total $475,000. If
the company requires a MARR of 15% per year on projects of comparable risk, determine if it
should invest in the new product line. Use the PW method.
Solution:
Initial investment/capital investment/ first cost at time zero/at present:
-$300,000 - $600,000 – $250,000 – $100,000 = -$1,250,000
Annual revenue/receipts/income/inflows: $750,000
Annual expenses/disbursements/costs/payments/outflows: -$475,000
Market/salvage value: $400,000 + $350,000 + $50,000 + $100,000† = $900,000
PW (15%) = -$1,250,000 + ($750,000-$475,000) (P/A, 15%,10) + $900,000 (P/F, 15%,10)
= $3,526.5 > 0 → they should invest in the new product line.
†
Working capital refers to the funds required for current assets that are needed for the startup
and support of operational activities. Some or all of the working capital is usually recovered at
the end of a project’s life.
3) Your company is considering the introduction of a new product line. The initial investment
required for this project is $500,000 and annual maintenance costs are anticipated to be
$35,000. Annual operating costs will be directly in proportion to the level of production at
$7.50 per unit, and each unit of product can be sold for $50.00. If the MARR is 10% and the
project has a life of 5 years, what is the minimum annual production level for which this
project is economically viable?
Solution:
Let X be the minimum annual production level.
AW = -500,000 (A/P,10%,5) – 35,000 – 7.50 X + 50.00 X = 0
500,000 (A/P,10%,5) + 35,000 = (50.00 – 7.50) X
166,898.74 = 42.50 X
X = 3,927.03 units
4) (Prob. 4-24 Sullivan, 12th ed.) Suppose that you borrow $1,000 from the Easy Credit
Company with the agreement to repay it over a 5-year period. Their stated interest rate is 9%
per year. They show you the following items in determining the monthly payment:
Principal
$1,000
Total interest (9%*5 years*$1,000) $450
They ask you to pay 20% of the interest immediately, so you leave with $1,000–$90=$910 in
your pocket. Your monthly payment is calculated as follows:
$1000  $450
 $2417  month
60
a) Draw a cash-flow diagram of this transaction.
b) Determine the effective annual interest rate.
Solution:
a) Your Point of View:
$910
End of Month
0
1
2
3
4
5
58
59
60
A = $24.17 / month
b) $910 = $24.17 (P/A, i%/month, 60), so (P/A, i%, 60) = 37.65
From the tables; (P/A,1%,60) = 44.9550 and (P/A,2%,60) = 34.7609.
Therefore, 1% < i% < 2%
Linear interpolation yields: i% = 1.7% per month
i% /year = (1.017)12 - 1 = 0.224 or 22.4%/year
5) (Prob. 4-22 Sullivan, 12th ed.) A manufacturing firm which has excess capacity will make
a bid to produce a new product as a subcontractor at its factory. This requires an additional
investment of $75,000 in new equipment. The contract would be for 5 years at an annual
production quantity of 20,000 units. Direct labor cost is estimated at $1.00 per unit and new
materials at $1.05 per unit. The incremental overhead will not exceed 60% of its direct labor
cost. The maintenance expenses on the new equipment would be $2,000 per year, and annual
taxes and insurance would average 5% of the investment cost. The new equipment could be
sold for $3,000 at the end of 5 years. The project will require $15,000 in working capital at
the start of the project and it would be fully recovered at the end of year 5. The firm’s MARR
is 20% on this contract. The firm wants to sell the product at a price so that it can make a
profit of 20% of the selling price. What should be the selling price?
Annual cost of maintenance, taxes and insurance per unit:
$2000+$75,000*5% = $5,750/year
$5,750/20,000 units = $0.2875/unit
Variable cost/unit: DL+DM+OH = $1+$1.05+$1*60% = $2.65/unit
Total unit cost (excluding capital recovery): $0.2875+$2.65 = $2.94/unit
Capital recovery cost & working capital:
WC occurs at t=0 & t=5.
CRC+WC= (75,000+15,000)(A/P,20%,5)-(3,000+15,000)(A/F,20%,5)
= $27,676.8
CRC+WC/unit = $27,676.8/20,000 units = $1.38/unit
Total unit cost = $1.38+$2.94 = $4.32
Unit price for the bid should be greater than $4.32
Selling price= $4.32*1.2= $5.18/unit
6) (Prob. 4-43 Sullivan, 12th ed.) Consider the following cash flow:
EOY
Cash flow $
0
-100
1
-50
2
0
3
20
4
120
5
220
6
320
a) If the MARR is 15%/year, is this project profitable?
b) Calculate the simple payback period.
c) Calculate the discounted payback period.
a) PW= -$100-$50(P/F,15%,1)+[$20(P/A,15%,4)+$100(P/G,15%,4)](P/F,15%,2)
= -$100 - $50(0.8696) + [$20(2.8550) + $100 (3.786)](0.7561)
= $185.95 > 0
Yes, this project is financially profitable.
b)
EOY
0
1
2
3
4
5
Cash Flow
- $100
- 50
0
20
120
220
Cumulative PW
- $100
- 150
- 150
- 130
- 10
210
Balance becomes positive at the end of year 5. Thus, payback period n' = 5 years.
c) Since simple payback = 5 years, discounted payback  5 years
Note: Discounted payback period considers time value of money.
PW0-5(15%) =-$100-$50(P/F,15%,1)+[$20(P/A,15%,3)+$100(P/G,15%,3)](P/F,15%,2)
PW0-5(15%) = -$100 - $50(0.8696) + [$20(2.2832) + $100(2.071)](0.7561)
= $47.63 > 0, thus discounted payback period n' = 5 years