Question

1. A construction company operates a bulldozer that initially cost $28,000. The first year maintenance is $600, the second year is $900, and the third year is $1200. The salvage value at the end of the third year is $15,000. If the company decides to keep the bulldozer beyond the third year, the maintenance costs are $900 the fourth year, $1150 the fifth year, and $1300 the sixth year. There is a $7000 cost for overhaul if the bulldozer is kept at the end of the third year. The salvage value at the end of 6 years is $10,000. If the bulldozer is kept for two more years another overhaul at the end of six years is $14,000 Maintenance costs are expected to soar to $9900 for the seventh and eighth years Compare the annual costs if the bulldozer is kept for 3, 6, or 8 years assuming a rate of 10%. Which option would be the preferred based on annual costs? What if the rate is 8%?

Answer 1

First, we model all the cash flows in an Excel as follows

Discount rate	10%
Year	0	1	2	3	4	5	6	7	8
Initial investment	$ (28,000)
Maintenance		$ (600)	$ (900)	$ (1,200)	$ (900)	$ (1,150)	$   (1,300)	$ (9,900)	$ (9,900)
Savage value				$ 15,000			$   10,000
Overhaul				$ (7,000)			$ (14,000)

Next, we will find what are the cash flows in each year for all the 3 cases.
We discount cash flows in each year by the discount rate to get PV of cash flows in each year. We sum them up to arrive at the NPV for each option.

We use the concept of Equivalent Annual Costs to determine annual costs for each of the options.

We have the NPV for each option. We can look at this NPV as a present value of annuity over the life of each option. This annuity is nothing but the annual cost

Hence

$NPV = EAC \times Present value annuity factor$

$NPV = EAC \times \frac{1-(1 + r)^{-n}}{r}$

Hence

$EAC = \frac{NPV \times r}{1-(1 + r)^{-n}}$

We model this formula in Excel and get the following output

Discount rate	10%
Year	0	1	2	3	4	5	6	7	8
Initial investment	$ (28,000)
Maintenance		$ (600)	$ (900)	$ (1,200)	$ (900)	$ (1,150)	$   (1,300)	$ (9,900)	$ (9,900)
Savage value				$ 15,000			$   10,000
Overhaul				$ (7,000)			$ (14,000)
Net cash flow
Keep till 3	$ (28,000)	$ (600)	$ (900)	$ 13,800
PV of cash flows	$ (28,000)	$ (545)	$ (744)	$ 10,368
NPV	$(18,921)
EAC	$   (7,608)
Keep till 6	$ (28,000)	$ (600)	$ (900)	$ (8,200)	$ (900)	$ (1,150)	$      8,700
PV of cash flows	$ (28,000)	$ (545)	$ (744)	$ (6,161)	$ (615)	$     (714)	$      4,911
NPV	$(31,868)
EAC	$   (7,317)
Keep till 8	$ (28,000)	$ (600)	$ (900)	$ (1,200)	$ (900)	$ (1,150)	$ (15,300)	$ (9,900)	$ (9,900)
PV of cash flows	$ (28,000)	$ (545)	$ (744)	$     (902)	$ (615)	$     (714)	$   (8,636)	$ (5,080)	$ (4,618)
NPV	$(49,855)
EAC	$   (9,345)

EAC if the bulldozer is kept for 3 years is -$7,608
EAC if the bulldozer is kept for 6 years is -$7,317
EAC if the bulldozer is kept for 8 years is -$9,345

As the EAC is the lowest when the bulldozer is kept for 6 years, this option is preferred.

We now simply change the discount rate in the Excel model to 8% to see the following results

Discount rate	8%
Year	0	1	2	3	4	5	6	7	8
Initial investment	$ (28,000)
Maintenance		$ (600)	$ (900)	$ (1,200)	$ (900)	$ (1,150)	$   (1,300)	$ (9,900)	$ (9,900)
Savage value				$ 15,000			$   10,000
Overhaul				$ (7,000)			$ (14,000)
Net cash flow
Keep till 3	$ (28,000)	$ (600)	$ (900)	$ 13,800
PV of cash flows	$ (28,000)	$ (556)	$ (772)	$ 10,955
NPV	$(18,372)
EAC	$   (7,129)
Keep till 6	$ (28,000)	$ (600)	$ (900)	$ (8,200)	$ (900)	$ (1,150)	$      8,700
PV of cash flows	$ (28,000)	$ (556)	$ (772)	$ (6,509)	$ (662)	$     (783)	$      5,482
NPV	$(31,798)
EAC	$   (6,878)
Keep till 8	$ (28,000)	$ (600)	$ (900)	$ (1,200)	$ (900)	$ (1,150)	$ (15,300)	$ (9,900)	$ (9,900)
PV of cash flows	$ (28,000)	$ (556)	$ (772)	$     (953)	$ (662)	$     (783)	$   (9,642)	$ (5,777)	$ (5,349)
NPV	$(52,491)
EAC	$   (9,134)

EAC if the bulldozer is kept for 3 years is -$7,129
EAC if the bulldozer is kept for 6 years is -$6,878
EAC if the bulldozer is kept for 8 years is -$9,134

As the EAC is the lowest when the bulldozer is kept for 6 years, this option is preferred.