Question

Calculate the equivalent annual costs of (a) overhauling and operating the Maracas for 12 more years (with and without the new engine and control system) and (b) buying and operating the proposed replacement vessel for 20 years. You should use the real discount rate for this analysis. Based on your answer, what should RNI do?

Mini Case #1: Capital Budgeting at Rio Negro, Inc.
Assignment Overview
Rio Negro, Inc. (RNI) is in the business of transporting cargo between ports in California and Washington. Its fleet
includes a small dry-cargo vessel, the Maracas. The Maracas is 25 years old and badly in need of an overhaul.
It is March 2016, and Michael John, the finance director, has just been presented with a proposal that would require
the one-time expenditures shown below in Table 1. If the proposal is accepted, these expenditures will be made in
the next few days. Mr. John believes that all these outlays could be depreciated for tax purposes in the seven-year
MACRS class (see Table 2 below for rates). Overhaul of the Maracas will begin as soon as the expenditures in
Table1 are made, but the vessel will be out of service for several months. The overhauled vessel would resume
commercial service in one year. RNI’s chief engineer’s estimates of the post-overhaul operating costs are in Table 3.
In addition to the overhaul described above, the chief engineer suggests installation of a brand- new engine and
control system. Installation of this new engine would cost an extra $600,000 (This additional outlay would also
qualify for tax depreciation in the seven-year MACRS class.). However, if the additional equipment is installed, it
would result in reduced fuel, labor, and maintenance costs as shown in Table 4.
The operating cost estimates in Tables 3 and 4 are current for March 2016. However, these costs will increase with
inflation, which is forecasted at 1.25% a year. Depreciation and operating costs attributable to the overhaul of
the Maracas will begin one year after the vessel is put back into commercial service. The revenues from operating
the vessel will be the same for both types of overhaul.

Even with the proposed overhaul, the Maracas cannot continue forever. After the overhaul, its remaining useful life
is estimated to be only 12 years. Its salvage value when finally taken out of service will be trivial. Thus, Mr. John
feels it is unwise to proceed without also considering the purchase of a new vessel. Racette & Sons (R&S), a
Colorado shipyard, has approached RNI with a design incorporating a Kort nozzle, extensively automated
navigation and power control systems, and much more comfortable accommodations for the crew. R&S is offering
the new vessel for a fixed price of $3,000,000, payable half immediately and half on delivery in one year. Estimated
annual operating costs of the new vessel are in Table 5. The operating cost estimates in the table are current for
March 2016, but will increase with inflation.

The crew would require additional training to handle the new vessel’s more complex and sophisticated equipment.
Training would result in a one-time cost of $50,000 payable one year following delivery of the new vessel. This cost
is tax deductible.
The estimated operating costs for the new vessel assume that it would be operated in the same way as the Maracas.
However, the new vessel will be able to handle a larger load on some routes, which is expected to generate
additional revenues of approximately $175,000 per year in the first year of operation. These revenues are expected
to grow at the rate of inflation. Revenues and operating costs from the new vessel will begin one year after it is
delivered. The new vessel is estimated to have a useful service life of 20 years, but it will be depreciated for tax
purposes according to the 7-year MACRS schedule. The new vessel is not expected to have any resale value at the
end of its 20-year useful life. All revenues and costs (including depreciation) associated with the new vessel will
begin one year after it is delivered.

The Maracas is carried on RNI’s books at a book value of only $100,000 and the book value of the spare parts is
$40,000. The Maracas could probably be sold now “as is,” together with its extensive inventory of spare parts, for
$200,000.

Mr. John stepped out on the foredeck of the Maracas as she chugged down the Cook Inlet. “A rusty old tub,” he
muttered, “but she’s never let us down. I’ll bet we could keep her going until next year while Racette & Sons are
building her replacement. We could use up the spare parts ($40,000) to keep her going and we should even be able
to sell or scrap her for book value when her replacement arrives.”

RNI evaluates capital investments of this type using a 8.5% cost of capital. (This is a nominal, not real, rate.) RCI’s
tax rate is 35%.
Table 1: Overhaul Expenditures
Overhaul engine and generators $340,000
Replace radar and other electronic equipment 75,000
Repairs to hull and superstructure 310,000
Painting and other repairs 95,000
$820,000

Table 2: Depreciation (in %) for the 7-year Modified Accelerated Cost Recovery System
Year 1 14.29
Year 2 24.49
Year 3 17.49
Year 4 12.49
Year 5 8.93
Year 6 8.93
Year 7 8.93
Year 8 4.45


Table 3: Post-overhaul Operating Costs (Basic Overhaul)
Fuel $450,000
Labor and benefits 480,000
Maintenance 141,000
Other 110,000
$1,181,000


Table 4: Post-overhaul Operating Costs (Overhaul plus new engine & control system)
Fuel $400,000
Labor and benefits 405,000
Maintenance 105,000
Other 110,000
$1,020,000

Answer 1

(a)

The net present value = Present value of all future cash inflows - Present value of all the cash outflows(initial investment)

The Equivalent annual cost = Net Present value by present value annuity factor of same period / the discount rate of respective project

Equivalent annual cost of Maracus for 12 more years

Formulas Associated in this spreadsheet

Overhead engine and generator	340000
Replace radar and other electronic equipment	75000
Repairs to hull and superstructure	310000
Painting and other repairs	95000
Total Expenditure	=SUM(B1:B4)
Fuel	450000
Labor and benefits	480000
Maintenance	141000
Other	110000
Total Operating cost	=SUM(B7:B10)
Increase operating cost as per inflation	0.025
Cost of capital(Nominal rate)	0.11
Annual Revenue	1400000
Year	0	1	2	3	4	5	6	7	8
Overhaul cost	=-B5
Annual Revenue		=B14	=C17*1.025	=D17*1.025	=E17*1.025	=F17*1.025	=G17*1.025	=H17*1.025	=I17*1.025
operating cost		=-B11	=C18*(1+$B$12)	=D18*(1+$B$12)	=E18*(1+$B$12)	=F18*(1+$B$12)	=G18*(1+$B$12)	=H18*(1+$B$12)	=I18*(1+$B$12)
7 year MACRS		0.1429	0.2449	0.1749	0.1249	0.0893	0.0893	0.0893	0.0445
Depriciation		=C19*-$B$5	=D19*-$B$5	=E19*-$B$5	=F19*-$B$5	=G19*-$B$5	=H19*-$B$5	=I19*-$B$5	=J19*-$B$5
EBIT		=C17+C18+C20	=D17+D18+D20	=E17+E18+E20	=F17+F18+F20	=G17+G18+G20	=H17+H18+H20	=I17+I18+I20	=J17+J18+J20
After tax(1-Tax rate 35%)		=C21*(1-35%)	=D21*(1-35%)	=E21*(1-35%)	=F21*(1-35%)	=G21*(1-35%)	=H21*(1-35%)	=I21*(1-35%)	=J21*(1-35%)
After tax salvage value
FCF		=C22-C20	=D22-D20	=E22-E20	=F22-F20	=G22-G20	=H22-H20	=I22-I20	=J22-J20
PVF@11%	=1/(1+11%)^B15	=1/(1+11%)^C15	=1/(1+11%)^D15	=1/(1+11%)^E15	=1/(1+11%)^F15	=1/(1+11%)^G15	=1/(1+11%)^H15	=1/(1+11%)^I15	=1/(1+11%)^J15
Present value of cash flows	=B25*B16	=C25*C24	=D25*D24	=E25*E24	=F25*F24	=G25*G24	=H25*H24	=I25*I24	=J25*J24
Year		9	10	11	12
Annual Revenue		=J17*1.025	=C30*1.025	=D30*1.025	=E30*1.025
operating cost		=J18*(1+$B$12)	=C31*(1+$B$12)	=D31*(1+$B$12)	=E31*(1+$B$12)
EBIT		=C31+C30	=D31+D30	=E31+E30	=F31+F30
After tax(1-Tax rate 35%)		=C32*(1-35%)	=D32*(1-35%)	=E32*(1-35%)	=F32*(1-35%)
After tax salvage value					=200000*(1-35%)
FCF		=C34+C33	=D34+D33	=E34+E33	=F34+F33
PVF@11%		=1/(1+11%)^C29	=1/(1+11%)^D29	=1/(1+11%)^E29	=1/(1+11%)^F29
Present value of cash flows		=C36*C35	=D36*D35	=E36*E35	=F36*F35
NPV	=SUM(B26:J26)+SUM(C37:F37)
Annuity Factor 12 years 11%	=-PV(11%,12,1,0)
Equivalent Annual Cost	=B38/B39

The following are the obtained results :

$340,000.00 Overhead engine and generator Replace radar and other electronic equipment Repairs to hull and superstructure Painting and other repairs Total Expenditure $75,000.00 $310,000.00 $95,000.00 $820,000.00 $450,000.00 $480,000.00 $141,000.00 $ 110,000.00 $1,181,000.00 2.50% 11.00% $1,400,000.00 $820,000.00 Fuel Labor and benefits Maintenance Other Total Operating cost Increase operating cost as per Cost of capital(Nominal rate) Annual Revenue Year Overhaul cost Annual Revenue operating cost 7 year MACRS Depriciation EBIT After tax(1-Tax rate 35%) After tax salvage value FCF PVF@11% Present value of cash flows $1,400,000.00 $1,181,000.00 14.29% $ 117,178.00 $ 101,822.00 $ 66,184.30 $1,435,000.00 $1,210,525.00 24.49% -$200,818.00 $23,657.00 $15,377.05 $1,470,875.00 $1,240,788.13 17.49% $143,418.00 $86,668.87 $56,334.77 $1,507,646.88 $1,545,338.05 $1,271,807.83 -$1,303,603.02 12.49% 8.93% $ 102,418.00 - $73,226.00 $133,421.05| $168,509.02 $86,723.68 $109,530.86 $1,583,971.50 $1,336,193.10 8.93% $73,226.00 $174,552.40 $113,459.06 $1,623,570.79 $1,369,597.93 8.93% $73,226.00 $180,746.86 $117,485.46 $1,664,160.06 $1,403,837.88 4.45% -$36,490.00 $223,832.18 $145,490.92 $183,362.30 0.900900901 $165,191.26 $216,195.05 0.811622433 $175,468.75 $199,752.77 0.731191381 $146,057.50 $189,141.68 0.658730974 $124,593.48 $182,756.86 0.593451328 $108,457.30 $186,685.06 0.534640836 $99,809.46 $190,711.46 0.481658411 $91,857.78 $181,980.92 0.433926496 $78,966.34 -$820,000.00 91 $1,705,764.06 $1,438,933.82 $266,830.23 $173,439.65 Year Annual Revenue operating cost EBIT After tax(1-Tax rate 35%) After tax salvage value FCF PVF@11% Present value of cash flows NPV Annuity Factor 12 years 11% Equivalent Annual Cost 1 01 111 121 $1,748,408.16 $1,792,118.36 $1,836,921.32 $1,474,907.171 -$1,511,779.85 $1,549,574.34 $273,500.99 $280,338.52 $287,346.98 $177,775.64 $182,220.03 $186,775.54 $130,000.00 $177,775.64 $182,220.03 $316,775.54 0.352184479 0.3172833140.285840824 $62,609.82 $57,815.38 $90,547.38 $449,176.32 6.492356149 $69,185.41 $173,439.65 0.390924771 $67,801.86

Therefore the equivalent annual cost of Maracus for 12 years is $69185.41