Caine Bottling Corporation is considering the purchase of a new bottling machine
ID: 2487562 • Letter: C
Question
Caine Bottling Corporation is considering the purchase of a new bottling machine. The machine would cost $208,845 and has an estimated useful life of 8 years with zero salvage value. Management estimates that the new bottling machine will provide net annual cash flows of $39,400. Management also believes that the new bottling machine will save the company money because it is expected to be more reliable than other machines, and thus will reduce downtime. Assume a discount rate of 11%.
Calculate the net present value.
How much would the reduction in downtime have to be worth in order for the project to be acceptable?
Net present value?Explanation / Answer
Using the present value of an ordinary annuity formula, the present value of the cash flows would be:
PVOA = PMT [(1 - (1 / ((1 + i) ^n))) / i ]
Where:
PVOA = Present Value of an Ordinary Annuity
PMT = Amount of each payment (39,400)
i = Discount Rate per Period (0.11)
n = Number of Periods (8)
= $195,552.66
$202,757.24 - 208,845 = ($6,087.76) NPV
Net present value= -$6,087.76
The project is giving a negative net present value which means present value of cash inflows is less than the initial capital investment.
Now , we need to calculate the amount of annual savings (net cash inflows) which makes the project acceptable.
A project becomes acceptable when sum of present value of cash inflows is equal to cash outlay.
Or we can say where NPV is zero or greater than 0.
Present value of cash inflows-Present value of cash outflow=0
Present value of cash inflows-208845=0
Present value of cash inflows=208845
So now we know the sum of present value of annual cash inflows (annuity) should be equal to 208845 for the project to be acceptable.
Here we will use the concept of future value of an annuity wherein we know the required future value i.e.208845 , however we need to calculate the annuity amount.
K=11%=.11
N=8 years
Future value=208845
Putting these values in the formula we get the PMT as 17,610.03
To cross check the answer ,if we calculate the future value of this amount 71,610.03 for 8 years @11% ,we get the answer as 208845 which is correct.
Hence ,the machine should reduce the downtime having dollar worth 17610.03 each year for the project to be acceptable.
At this point ,NPV of the project will be zero.