Question

In: Finance

You are starting a vegan restaurant and need to buy a vehicle for delivery orders. You...

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?

Solutions

Expert Solution

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.


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