Answer: d. $1,534 positive net present value of the cash flows. Based on present value considerations, Dobson Construction should buy the machine.
Explanation:
To calculate the Net Present Value, we take the present values of all the future cashflows and subtract the initial cost from this amount.
Now, the cashflows are stable and this means that we can use the Present Value of an Annuity factor to find out the present value of the cashflows. We can then use a simple present value formula to find out the PV of the sale price.
I have attached a table that shows the PVIFA factors to make our calculations easier.
With interest rates at 12% and the year being 8 years, the PVIFA factors is 4.9676
Calculating therefore we have,
= 15,000 * 4.9676
= $74,514
This is the present value of 8 years of $15,000 cash flows.
In the same year, the machine can be sold for $5,000 so the present value of that is,
= 5000 / ( 1 + 12%)^8
= $2,020
Adding those together we get,
= 74,514 + 2,020
= 76,534
= $76,534
Subtracting the original cost we have,
= 76,534 - 75,000
= $1,534 in positive cashflow.
Net Present Value = $1,534
This means that Based on present value considerations, Dobson Construction should buy the machine due to a $1,534 positive net present value.
