Question

New equipment used to control the thickness of fibre cement sheet cladding is being developed. It is estimated to sell for $130,000 more than the current design Based on present product data, the typical installer has the following probabilities of achieving different performance results and cost savings (relative to the current unit) in the first year of operation (assume these annual cost savings would be escalated 5% per year thereafter; a five-year analysis period is appropriate for this situation; the before-tax market MARR is 18% per year; and the net MV at the end of five years is 0): Cost Savings Performance Probability Results in First Year $65,000 42,500 Optimistic Most likely Pessimistic 0.20 0.60 0.20 17,000 Calculate the E(PW) and determine whether the new equipment is economically preferable to the current equipment. $12,500, old preferable $12,500, new preferable $16,212, old preferable $16,212, new preferable $19,720, new preferable

Answer 1

We will create a table of annual cost savings with a 5% increase each year. Then we will calculate the PW by discounting it with MARR which is given as 18%.
The next step is calculating the expected value and then summing to get the total expected value.

Year		Cost Saving
	Optimistic	Most Likely	Pessimistic
1	65000.00	42500.00	17000.00
2	68250.00	44625.00	17850.00
3	71662.50	46856.25	18742.50
4	75245.63	49199.06	19679.63
5	79007.91	51659.02	20663.61
	PW @ 18%	PW @ 18%	PW @ 18%
1	55084.75	36016.95	14406.78
2	49016.09	32048.98	12819.59
3	43616.01	28518.16	11407.26
4	38810.86	25376.33	10150.53
5	34535.08	22580.63	9032.25
PW	221062.78	144541.05	57816.42
Probability	0.20	0.60	0.20
Expected Value	44212.56	86724.63	11563.28
Total E(PW)		142500.47
Initial Cost		130000.00
Net Value		12500.47

The expected PW of the new equipment is $142500.47
The cost of the new equipment is $130000
142500.47 - 130000 = 12500.47

The net benefit of the new equipment is $12500.

Option B is correct.