2. CAPITAL BUDGETING Consider a firm needs to choose between two kinds of machin
ID: 2667569 • Letter: 2
Question
2. CAPITAL BUDGETING
Consider a firm needs to choose between two kinds of machines called A and B
doing the same job. A could be used only for 3 years while B could be used for
one more year. Besides the initial costs of purchasing, there are expenditures for
maintenance every year. The costs of A and B are summarized in the following
table:
0 1 2 3 4
A 500 120 120 120
B 600 100 100 100 100
Note every entry represents a cost, i.e., a cash out-flow. The relevant discount rate
is 10%.
1
(a) What are the present values of costs in using these two machines? If we just
consider the present value, which machine should the firm use?
(b) Denote PVa and PVb the present value of costs you get in the above ques-
tion. Now, let’s consider the case in which the firm continues the business
even if the chosen machine is out of useful life. In other words, the firm will
replace the used machine by new one. In this way, the firm is concerned with
the average cost of using either type of machines, since this is the cost hap-
pened every period regardless of the specific useful life of one machine. It
turns out that the job is to find out the equivalent annual cost Ca and Cb of
those machines. In order to do this, for instance, we can imagine the present
value of costs of using A can be represented by an annuity of 3 years with
yearly payment Ca, that is
PVa = Ca x A^3 0.1
where A^3 0.1 indicates the present value of an annuity of 3 years with yearly payment being 1 dollar and a discount rate 10%. The solution of above equation gives you Ca. You can find Cb in a similar way, but note that B can be used for 4 years.
Naturally, the firm will the one with a lower equivalent annual cost. In this
problem, which one will be chosen?
Explanation / Answer
1. (a) Present value of costs for machine A is as follows. Year Costs 0 500 1 120 2 120 3 120 Cost of capital is 10%. By using excel spread sheet, inset PV is formula bar and set the values as above, rate as 10%, Nper is 3, Pmt is 120. By clicking we can get PV of cost for project A as =$298.42 Present value of cost = Initial cost + $289.42 =$500 + $298.42 =$798.42. For Machine B Year Costs 0 600 1 100 2 100 3 100 4 100 By using excel as above, we can calculate the present value of cost. Present value is = Initial cost + $319.99 =$600 + $316.99 =$916.99 If we just consider the present value of the cost Machine A is preferable. (b) PVa = Ca * A^3 0.1 $798.42 = Ca* Present value annuity factor(3,10%) =Ca*2.4869 Ca =$789.42/2.4869 =$317.43 PVb = Cb A^4 0.1 $916.99 = Cb*present Value annuity factor(4,10%) =Cb*3.7908 Cb = $916.99/3.7908 =$241.9 In this problem Machine B will be chosen. Because it is with lower annual cost. In this problem Machine B will be chosen. Because it is with lower annual cost.Related Questions
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