Question

You are starting a vegan restaurant and need to buy a vehicle for delivery orders. You have two models in mind. Model A costs $10,000 and is expected to run for 6 years; Model B is more expensive, with a price of $15,000 and an expected life of 10 years. The annual maintenance costs are $800 for Model A and $700 for Model B. Assume that the opportunity cost of capital is 10.6 percent.

Which model would you choose based on the relevant analysis?

Answer 1

Here we will use the "Equivalent Annual Annuity (EAA) approach" of capital budgeting to compare mutually exclusive projects with unequal lives. The formula to calculate EAA is as follows :

Where,

EAA = equivalent annuity cash flow

NPV = net present value

r = interest rate per period

n = number of periods

The following are the two NPVs for Model A and Model B :-

Model A

Year	Cash Inflow/(Outflow)	PV Factor (10.6%) {1/(1+r)^n}	Present Value (Cash Flow * PV Factor)
0	(10,000.00)	1	(10,000.00)
1	(800.00)	0.904159	(723.33)
2	(800.00)	0.817504	(654.00)
3	(800.00)	0.739153	(591.32)
4	(800.00)	0.668312	(534.65)
5	(800.00)	0.604261	(483.41)
6	(800.00)	0.546348	(437.08)
Net Present Value	(13,424)
Model B
Year	Cash Inflow/(Outflow)	PV Factor (10.6%) {1/(1+r)^n}	Present Value (Cash Flow * PV Factor)
0	(15,000.00)	1	(15,000.00)
1	(700.00)	0.904159	(632.91)
2	(700.00)	0.817504	(572.25)
3	(700.00)	0.739153	(517.41)
4	(700.00)	0.668312	(467.82)
5	(700.00)	0.604261	(422.98)
6	(700.00)	0.546348	(382.44)
7	(700.00)	0.493985	(345.79)
8	(700.00)	0.446641	(312.65)
9	(700.00)	0.403835	(282.68)
10	(700.00)	0.365131	(255.59)
Net Present Value	(17,996)

EAA for Model A = 0.106*(-13,424) / 1 - (1.106)^-6

= - $3,136.59

EAA for Model B = 0.106*(-17,996) / 1 - (1.106)^-10

= - $3,004.65

As, EAA value of Model B is better than EAA for Model A, the better model is Model B.

On relevant analysis shown above, Model B is better because it has less negative value as compared to Model A.