Question

A company wants to buy a lease for a mine that has four more years of productive life. It estimates that the returns will be $3469 at the end of the first year, $52978 at the end of both second and fourth year, and $61858 at the end of the third year. Using an interest rate of 8.6% p.a., the net present value if the lease costs $100000 is:

Answer 1

Given

Cash inflow at the end of year 1=$3469

Cash inflow at the end of year 2=$52978

Cash inflow at the end of year 3=$61858

Cash inflow at the end of year 4=$52978

Interest rate=i=8.6%

Present value of cash inflows=CF1*(P/F,8.6%,1)+CF2*(P/F,8.6%,2)+CF3*(P/F,8.6%,3)+CF4*(P/F,8.6%,4)

Present value of cash inflows=3469*(P/F,8.6%,1)+52978*(P/F,8.6%,2)+61858*(P/F,8.6%,3)+52978*(P/F,8.6%,4)

Let us calculate interest factors.

(P/F,i,n)=1/(1+i)^n

(P/F,8.6%,1)=1/(1+8.6%)^1=0.920810

(P/F,8.6%,2)=1/(1+8.6%)^2=0.847892

(P/F,8.6%,3)=1/(1+8.6%)^3=0.780747

(P/F,8.6%,4)=1/(1+8.6%)^4=0.718920

Present value of cash inflows=PVo= 3469*0.920810+52978*0.847892+61858*0.780747+52978*0.718920

Present value of cash inflows=PVo=134496.30

Present value of cash outflows=PVi=Initial Cost=$100000

NPV=-PVi+PVo=-100000+134496.30=$34496.30