Question

A company is considering buying one of two new bottle capping machines. One of the alternatives (an expected life of 20 years) is from the Caps-R-Us company. The other (unexpected life of 10 years) is from the one top fits all company. One of the two must be purchased and neither is expected to have a salvage value at the end of its respective life. Present worth analysis will be utilized in making the decision. Fortunately the alternative from the Caps-R-us company has already been calculated for you. It was found that the present worth of the cost was $575,000 (based on his 20 year life).

For the One Top Fits All alternative, the following characteristics are known: the initial cost of the machine is $320,000. Yearly operating and maintenance costs are expected to be $7000 per year for the first seven years and $10,000 per year for the last three years. The machine requires a major overhaul costing $55,000 at the end of the fifth year of service. Based on present worth analysis, decide between these alternatives. Assume that the benefits for each alternative are identical. MARR = 7% ($623,355)

please do not use an excel for this

Answer 1

We now calculate the Present worth of costs of Top Fits all for the first 10 years which is as shown in the table below:

The Expected return on A = Rf + factor sensitivity* factor premium = 4+1.0*10 = 14%

The Expected return on B = 4+1.2*10 = 16%

The Expected return on C = 4+0.6*10 = 10%

The Assets B and C are correctly priced since the expected return calculated is the same as the actual return in the table.

Asset A is not correctly priced since the expected return is higher than the actual return

Year	Total Costs	PV
0	320000	320000
1	7000	6542.056075
2	7000	6114.071098
3	7000	5714.085138
4	7000	5340.266484
5	62000	44205.14313
6	7000	4664.395567
7	7000	4359.248193
8	10000	5820.091046
9	10000	5439.337426
10	10000	5083.492921
Present Value		413282.1871

Net Present Value (NPV) for 20 years of operation = 413282.1871 + 413282.1871/1.07^10 = $623,373 (Small diffderence between given answer of 623,355 and this is becuase of decimals and can be ignored)

Annual Present worth based on this = NPV*r/(1-(1+r)^-n) = 623,373*0.07/(1-1.07^-20) = 58,842

present worthof costs of Caps RU = 75,000

present worth of costs of Top fits = 58,842

We select one with lower costs which is Top Fits