Question

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, net of additional operating costs, 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

Table 5: Operating Costs of New Vessel

Fuel $380,000

Labor and benefits 330,000

Maintenance 70,000

Other 105,000

$885,000

Calculate the present value of of the proposed overhaul of the Maracas, with and without the new engine and control system. Should RNI do the basic overhaul or the expanded overhaul with the new engine and control system?

*** Could you please show formulas? I

Answer 1

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

Formulas Associated

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	820000
Fuel	450000
Labor and benefits	480000
Maintenance	141000
Other	110000
Total Operating cost	1181000
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	-820000
Annual Revenue		1400000	1435000	1470875	1507646.875	1545338.047	1583971.498	1623570.785	1664160.055
operating cost		-1181000	-1210525	-1240788.13	-1271807.83	-1303603.02	-1336193.1	-1369597.93	-1403837.88
7 year MACRS		0.1429	0.2449	0.1749	0.1249	0.0893	0.0893	0.0893	0.0445
Depriciation		-117178	-200818	-143418	-102418	-73226	-73226	-73226	-36490
EBIT		101822	23657	86668.875	133421.0469	168509.023	174552.3986	180746.8586	223832.1801
After tax(1-Tax rate 35%)		66184.3	15377	56334.76875	86723.68047	109530.865	113459.0591	117485.4581	145490.917
After tax salvage value
FCF		183362	216195	199752.7688	189141.6805	182756.865	186685.0591	190711.4581	181980.917
PVF@11%	1	0.9009	0.81162	0.731191381	0.658730974	0.593451328	0.534640836	0.481658411	0.433926496
Present value of cash flows	-820000	165191	175469	146057.5029	124593.4834	108457.3042	99809.45609	91857.77784	78966.34172
Year		9	10	11	12
Annual Revenue		1705764	1748408	1792118.362	1836921.321
operating cost		-1438934	-1474907	-1511779.85	-1549574.34
EBIT		266830	273501	280338.5152	287346.9781
After tax(1-Tax rate 35%)		173440	177776	182220.0349	186775.5357
After tax salvage value					130000
FCF		173440	177776	182220.0349	316775.5357
PVF@11%		0.39092	0.35218	0.317283314	0.285840824
Present value of cash flows		67801.9	62609.8	57815.37658	90547.38004
NPV	449176.3156 (1269176.32277-820000)
Annuity Factor 12 years 11%	$6.49