Question

There are two mutually exclusive projects, where the basic information is provided below. Assume a DN alternative does not exist. MARR is 10% per year. Which project do you choose and why?

	Long term	Short Term (Lease)
Initial Cost	$45,000	$15,000
Major overhaul costs (every ten years)	$12,000	Not existent
Minor overhaul costs (every 5 years)	$6000	Not existent
Annual Operating cost	$2000	$1500
Useful Life	Infinity	10
Salvage value	$1,500	$2,500 (deposit return)

Answer 1

Answer:   * All amounts in $

Short Term (Lease) Project

MARR= 10% per Year,  Initial Cost = 15000,  Annual Opearting Cost = 1500

Salvage Value= 2500, Time = 10 yrs.

Year	0	1	2	3	4	5	6	7	8	9	10
Cashflow	15000	1500	1500	1500	1500	1500	1500	1500	1500	1500	-1000

PV of Short Term (Lease) Project is nothing but Present Value of all future Cash Flow including Initial Cost, Annual Cost and Salvage Value for 10 years.

So, PV = 15000 + 1500 [1/(1.1)^1 +1/(1.1)^2 + 1/ (1.1)^3 +.....................1/(1.1)^9] - [1000/(1.1)^10]

= 15000 + 8638.54- 385.5433

PV = 23253

Profitability Index (PI) = Total PV / Initial Investment = 23253/15000= 1.55

  Long Term Project

MARR= 10% per Year,  Initial Cost = 45000,  Annual Opearting Cost = 2000

Salvage Value= 1500, Time = 10 Infinity

Year	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	nth year
Cashflow	45000	2000	2000	2000	2000	8000	2000	2000	2000	2000	14000	2000	2000	2000	2000	8000	1500

PV= 45000 + [2000/(1.1)^1 + 2000/(1.1)^2+2000/(1.1)^3+2000/(1.1)4+(2000+6000)/(1.1)^5 + 2000/(1.1)^6 + .......+(2000+12000)/(1.1)^10+............] - 1500 at last

PV = 45000 + 2000[1/(1.1) + 1/(1.1)^2+............up to Infinite] + 6000 [1/(1.1)^5+1/(1.1)^15+1/(1.1)^25+....up to infinite] + 12000 [1/(1.1)^10+1/(1.1)^20+1/(1.1)^20+....up to infinite] -1500 at Infinite period

PV = 45000 + 20000 +6063+ 6083 + 0

PV = 77146

Profitability Index (PI) = Total PV / Initial Investment =77146/45000=1.71

Therefore, as per PI value, it is evident that Long Term Project will be more suitable as compare to Short Term (Lease) Project.