Question

Donald Googal owns a garage and is contemplating purchasing a tire retreading machine for $17,000. After estimating costs and revenues, Donald projects a net cash inflow from the retreading machine of $3,740 annually for 13 years. Donald hopes to earn a return of 15% on such investments. What is the present value of the retreading operation? Should Donald Googal purchase the retreading machine? (For calculation purposes, use 5 decimal places as displayed in the factor table provided.) (Round answer to 2 decimal places, e.g. 15.25.)

Click here to view the factor table.

(a) The present value of the retreading operation is  .

(b) Donald Googal                                                           shouldshould not purchase the retreading machine.

Answer 1

outflow in year 1 = (17000)

inflow for 13 years = 3740 per year

discount rate = 15 %

present value of 3740 for 13 years can be found by using the annuity table .

discount factor for annuity, 15% for 13 years is 5.583(this value can be found from annuity table or it can be found by seperately multiplying the each years amount by the corresponding discount factor and adding them up just as given below)

alternative method ;

year	amount	discount factor	present value
1	3740	0.87	3253.8
2	3740	0.756	2827.44
3	3740	0.658	2460.92
4	3740	0.572	2139.28
5	3740	0.497	1858.78
6	3740	0.432	1615.68
7	3740	0.376	1406.24
8	3740	0.327	1222.98
9	3740	0.284	1062.16
10	3740	0.247	923.78
11	3740	0.215	804.1
12	3740	0.187	699.38
13	3740	0.163	609.62
		total	20884.16

so , present value for the amount 3740 for 13 years will be 3740*5.583=20880.42(small rounding differences are accepted)

net present value of  retreading operation is ,present value of cash inflows- present value of cash outflows

(a) present value of outflow 17000 in year 1 is 17000*1 =17000

present value of inflows for 13 years is = 3740*5.583=20880.42

net present value of retreading operation = 20880.42 - 17000= 3880.42

(b) Donald Googal  should purchase the retreading machine.because the operation have a positive net present value and indicates that the benefit on the machine is more than its cost . purchasing the machine is profitable for Donald Googal .