Question

A small strip-mining coal company is trying to decide whether it should purchase or lease a new clamshell. If purchased, the "shell" will cost $177,500 and is expected to have a $50,000 salvage value after 6 years. Alternatively, the company can lease a clamshell for only $17,000 per year, but the lease payment will have to be made at the beginning of each year. If the clamshell is purchased, it will be leased to other strip-mining companies whenever possible, an activity that is expected to yield revenues of $10,000 per year. If the company's MARR is 14% per year, should the clamshell be purchased or leased on the basis of a future worth analysis? Assume the annual M&O cost is the same for both options. The future worth when purchased is $D The future worth when leased is $D . The clamshell should be ( (Click to select)).

Answer 1

Let us consider purchase option first

FW of purchase option=-177500*(F/P,0.14,6)+10000*(F/A,0.14,6)+50000

(F/P,0.14,6)=(1+0.14)^6=2.194973

(1 + i)" - 1 (F/A, i,n)=

(F/A, 0.14, 6) = (1 + 0.14)6 - 1 - = 8.535519 0.14

FW of purchase option=-177500*2.194973+10000*8.535519+50000=-$254,252.52

Now let us consider the lease option

FW of lease option=-17000*(F/A,0.14,6)*(1+0.14)

FW of lease option=-17000*8.535519*(1+0.14)=-$165,418.36

We can see that lease option has lower future cost in absolute terms. So, Lease option should be selected.